diff --git a/Makefile b/Makefile deleted file mode 100644 index 72664bb..0000000 --- a/Makefile +++ /dev/null @@ -1,49 +0,0 @@ -thinkapjava: thinkapjava.tex - pdflatex thinkapjava - makeindex thinkapjava.idx - pdflatex thinkapjava - -code: - cd code; make - -hevea: - sed 's/\(figs\/[^.]*\).pdf/\1.eps/' thinkapjava.tex > thinkjava.tex - rm -rf html - mkdir html - hevea -O -e latexonly htmlonly thinkjava - hevea -O -e latexonly htmlonly thinkjava - imagen -png thinkjava - hacha thinkjava.html - cp up.png next.png back.png html - mv index.html thinkjava.css thinkjava*.html thinkjava*.png *motif.gif html - -plastex: - rm -rf /home/downey/thinkapjava/trunk/xml/.svn - cp thinkapjava.tex xml.tex - plastex --renderer=DocBook --theme=book --image-resolution=300 --filename=thinkapjava.xml xml.tex - rm -rf /home/downey/thinkapjava/trunk/xml/.svn - -xxe: - ~/Downloads/xxe-perso-4_8_0/bin/xxe xml/thinkapjava.xml - -epub: - cd html; ebook-convert thinkapjava.html thinkpython.epub - -DISTFILES = thinkapjava.pdf thinkapjava.tex.zip -DIR = /home/downey/public_html/greent/thinkapjava - -distrib: - rm -rf thinkapjava - mkdir thinkapjava thinkapjava/figs - cp thinkapjava.tex latexonly htmlonly thinkapjava - cp Makefile thinkapjava/Makefile - cp *.png *.html thinkapjava - cp figs/* thinkapjava/figs - zip -r thinkapjava.tex.zip thinkapjava - chmod 644 $(DISTFILES) - cp $(DISTFILES) $(DIR) - rsync -a html $(DIR) - echo 'pushd $(DIR)/..; sh back; popd' - -clean: - rm -f *~ *.aux *.dvi *.idx *.ilg *.ind *.log *.out *.toc thinkjava.* diff --git a/ProjectHome.md b/ProjectHome.md new file mode 100644 index 0000000..c67f1e3 --- /dev/null +++ b/ProjectHome.md @@ -0,0 +1 @@ +Think Java: How to Think Like a Computer Scientist is an introductory textbook to help students prepare for the Computer Science AP exam. \ No newline at end of file diff --git a/back.png b/back.png deleted file mode 100644 index 9c88472..0000000 Binary files a/back.png and /dev/null differ diff --git a/code/Cards/Card1.java b/code/Cards/Card1.java deleted file mode 100644 index 2ffdb78..0000000 --- a/code/Cards/Card1.java +++ /dev/null @@ -1,150 +0,0 @@ -/* - * Example code for Think Java (http://thinkapjava.com) - * - * Copyright(c) 2011 Allen B. Downey - * GNU General Public License v3.0 (http://www.gnu.org/copyleft/gpl.html) - * - * @author Allen B. Downey - */ - - -public class Card1 { - /* - * Test code. - */ - public static void main(String[] args) { - Card[] cards = Card.makeDeck(); - - // check that findBisect finds each card - int index; - for (int i=0; i<52; i++) { - index = Card.findBisect(cards, cards[i], 0, cards.length-1); - if (index != i) { - Card.printCard(cards[i]); - System.out.println("Wrong!"); - } - } - } -} - -/* - * In this version of the Card class, a deck is an array - * of Cards, and everything is written as a class method. - */ -class Card { - int suit, rank; - - /* - * No-argument constructor. - */ - public Card() { - this.suit = 0; this.rank = 0; - } - - /* - * Constructor with arguments. - */ - public Card(int suit, int rank) { - this.suit = suit; this.rank = rank; - } - - /* - * Prints a card in human-readable form. - */ - public static void printCard(Card c) { - String[] suits = { "Clubs", "Diamonds", "Hearts", "Spades" }; - String[] ranks = { "narf", "Ace", "2", "3", "4", "5", "6", - "7", "8", "9", "10", "Jack", "Queen", "King" }; - - System.out.println(ranks[c.rank] + " of " + suits[c.suit]); - } - - /* - * Return true if the cards are equivalent. - */ - public static boolean sameCard(Card c1, Card c2) { - return (c1.suit == c2.suit && c1.rank == c2.rank); - } - - /* - * Compares two cards: returns 1 if the first card is greater - * -1 if the seconds card is greater, and 0 if they are the equivalent. - */ - public static int compareCards(Card c1, Card c2) { - - // first compare the suits - if (c1.suit > c2.suit) return 1; - if (c1.suit < c2.suit) return -1; - - // compare the ranks - if (c1.rank > c2.rank) return 1; - if (c1.rank < c2.rank) return -1; - return 0; - } - - /* - * Makes an array of 52 cards. - */ - public static Card[] makeDeck() { - Card[] cards = new Card [52]; - - int index = 0; - for (int suit = 0; suit <= 3; suit++) { - for (int rank = 1; rank <= 13; rank++) { - cards[index] = new Card(suit, rank); - index++; - } - } - return cards; - } - - /* - * Prints an array of cards. - */ - public static void printDeck(Card[] cards) { - for (int i=0; i c2.suit) return 1; - if (c1.suit < c2.suit) return -1; - - // if the suits are the same, - // use modulus arithmetic to rotate the ranks - // so that the Ace is greater than the King. - // WARNING: This only works with valid ranks! - int rank1 = (c1.rank + 11) % 13; - int rank2 = (c2.rank + 11) % 13; - - // compare the rotated ranks - - if (rank1 > rank2) return 1; - if (rank1 < rank2) return -1; - return 0; - } -} - - -/* - * A Deck contains an array of cards. - */ -class Deck { - Card[] cards; - - /* - * Makes a Deck with room for n Cards (but no Cards yet). - */ - public Deck(int n) { - this.cards = new Card[n]; - } - - /* - * Makes an array of 52 cards. - */ - public Deck() { - this.cards = new Card [52]; - - int index = 0; - for (int suit = 0; suit <= 3; suit++) { - for (int rank = 1; rank <= 13; rank++) { - this.cards[index] = new Card(suit, rank); - index++; - } - } - } - - /* - * Prints a deck of cards. - */ - public static void printDeck(Deck deck) { - for (int i=0; i c2.suit) return 1; - if (suit < c2.suit) return -1; - - // if the suits are the same, - // use modulus arithmetic to rotate the ranks - // so that the Ace is greater than the King. - // WARNING: This only works with valid ranks! - int rank1 = (rank + 11) % 13; - int rank2 = (c2.rank + 11) % 13; - - // compare the rotated ranks - - if (rank1 > rank2) return 1; - if (rank1 < rank2) return -1; - return 0; - } -} - - -/* - * A Deck contains an array of cards. - */ -class Deck { - Card[] cards; - - /* - * Makes a Deck with room for n Cards (but no Cards yet). - */ - public Deck(int n) { - this.cards = new Card[n]; - } - - /* - * Makes an array of 52 cards. - */ - public Deck() { - this.cards = new Card [52]; - - int index = 0; - for (int suit = 0; suit <= 3; suit++) { - for (int rank = 1; rank <= 13; rank++) { - this.cards[index] = new Card(suit, rank); - index++; - } - } - } - - /* - * Prints a deck of cards. - */ - public void print() { - for (int i=0; i c2.suit) return 1; - if (c1.suit < c2.suit) return -1; - - // if the suits are the same, - // use modulus arithmetic to rotate the ranks - // so that the Ace is greater than the King. - // WARNING: This only works with valid ranks! - int rank1 = (c1.rank + 11) % 13; - int rank2 = (c2.rank + 11) % 13; - - // compare the rotated ranks - - if (rank1 > rank2) return 1; - if (rank1 < rank2) return -1; - return 0; - } -} - - -/* - * A Deck contains an array of cards. - */ -class Deck { - Card[] cards; - - /* - * Makes a Deck with room for n Cards (but no Cards yet). - */ - public Deck(int n) { - this.cards = new Card[n]; - } - - /* - * Makes an array of 52 cards. - */ - public Deck() { - this.cards = new Card [52]; - - int index = 0; - for (int suit = 0; suit <= 3; suit++) { - for (int rank = 1; rank <= 13; rank++) { - this.cards[index] = new Card(suit, rank); - index++; - } - } - } - - /* - * Prints a deck of cards. - */ - public static void printDeck(Deck deck) { - for (int i=0; i 0) - choice = 2; - - // make the new deck refer to the winner card - if (choice == 1) { - result.cards[k] = d1.cards[i]; i++; - } else { - result.cards[k] = d2.cards[j]; j++; - } - } - return result; - } - - /* - * Sort the Deck using merge sort. - */ - public static Deck mergeSort(Deck deck) { - if (deck.cards.length < 2) { - return deck; - } - int mid = (deck.cards.length-1) / 2; - - // divide the deck roughly in half - Deck d1 = subdeck(deck, 0, mid); - Deck d2 = subdeck(deck, mid+1, deck.cards.length-1); - - // sort the halves - d1 = mergeSort(d1); - d2 = mergeSort(d2); - - // merge the two halves and return the result - // (d1 and d2 get garbage collected) - return merge(d1, d2); - } -} diff --git a/code/Cards/CardSoln3.java b/code/Cards/CardSoln3.java deleted file mode 100644 index d00e3e5..0000000 --- a/code/Cards/CardSoln3.java +++ /dev/null @@ -1,341 +0,0 @@ -/* - * Example code for Think Java (http://thinkapjava.com) - * - * Copyright(c) 2011 Allen B. Downey - * GNU General Public License v3.0 (http://www.gnu.org/copyleft/gpl.html) - * - * @author Allen B. Downey - */ - -import java.math.BigInteger; - -public class CardSoln3 { - /* - * Test code. - */ - public static void main(String[] args) { - Card card = new Card(1, 1); - card.print(); - String s = card.toString(); - System.out.println(s); - System.out.println(card); - - Card card2 = new Card(1, 1); - System.out.println(card.equals(card2)); - - Deck deck = new Deck(); - - // check sortDeck - deck.shuffle(); - deck.sort(); - checkSorted(deck); - - // check that findBisect finds each card - int index; - for (int i=0; i<52; i++) { - index = deck.findBisect(deck.cards[i], 0, - deck.cards.length-1); - if (index != i) { - System.out.println("Not found!"); - } - } - - // make a subdeck - Deck hand = deck.subdeck(8, 12); - hand.print(); - - // check that findBisect doesn't find a card that's not there - Card badCard = new Card(1, 1); - index = hand.findBisect(badCard, 0, hand.cards.length-1); - if (index != -1) { - System.out.println("Found?"); - } - - // check mergeSort - deck.shuffle(); - deck = deck.mergeSort(); - checkSorted(deck); - } - - /* - * Checks that the deck is sorted. - */ - public static void checkSorted(Deck deck) { - for (int i=0; i<51; i++) { - int flag = deck.cards[i].compareTo(deck.cards[i+1]); - if (flag != -1) { - System.out.println("Not sorted!"); - } - } - } -} - -/* - * A Card represents a playing card with rank and suit. - */ -class Card { - int suit, rank; - - static String[] suits = { "Clubs", "Diamonds", "Hearts", "Spades" }; - static String[] ranks = { "narf", "Ace", "2", "3", "4", "5", "6", - "7", "8", "9", "10", "Jack", "Queen", "King" }; - - /* - * No-argument constructor. - */ - public Card() { - this.suit = 0; this.rank = 0; - } - - /* - * Constructor with arguments. - */ - public Card(int suit, int rank) { - this.suit = suit; this.rank = rank; - } - - /* - * Prints a card in human-readable form. - */ - public void print() { - System.out.println(ranks[rank] + " of " + suits[suit]); - } - - /* - * Prints a card in human-readable form. - */ - public String toString() { - return ranks[rank] + " of " + suits[suit]; - } - - /* - * Return true if the cards are equivalent. - */ - public boolean equals(Card that) { - return (this.suit == that.suit && this.rank == that.rank); - } - - /* - * Compares two cards: returns 1 if the first card is greater - * -1 if the seconds card is greater, and 0 if they are the equivalent. - */ - public int compareTo(Card that) { - - // first compare the suits - if (this.suit > that.suit) return 1; - if (this.suit < that.suit) return -1; - - // if the suits are the same, - // use modulus arithmetic to rotate the ranks - // so that the Ace is greater than the King. - // WARNING: This only works with valid ranks! - int rank1 = (this.rank + 11) % 13; - int rank2 = (that.rank + 11) % 13; - - // compare the rotated ranks - - if (rank1 > rank2) return 1; - if (rank1 < rank2) return -1; - return 0; - } -} - - -/* - * A Deck contains an array of cards. - */ -class Deck { - Card[] cards; - - /* - * Makes a Deck with room for n Cards (but no Cards yet). - */ - public Deck(int n) { - this.cards = new Card[n]; - } - - /* - * Makes an array of 52 cards. - */ - public Deck() { - this.cards = new Card [52]; - - int index = 0; - for (int suit = 0; suit <= 3; suit++) { - for (int rank = 1; rank <= 13; rank++) { - this.cards[index] = new Card(suit, rank); - index++; - } - } - } - - /* - * Prints a deck of cards. - */ - public void print() { - for (int i=0; i 0) - choice = 2; - - // make the new deck refer to the winner card - if (choice == 1) { - result.cards[k] = d1.cards[i]; i++; - } else { - result.cards[k] = d2.cards[j]; j++; - } - } - return result; - } - - /* - * Sort the Deck using merge sort. - */ - public Deck mergeSort() { - if (cards.length < 2) { - return this; - } - int mid = (cards.length-1) / 2; - - // divide the deck roughly in half - Deck d1 = subdeck(0, mid); - Deck d2 = subdeck(mid+1, cards.length-1); - - // sort the halves - d1 = d1.mergeSort(); - d2 = d2.mergeSort(); - - // merge the two halves and return the result - // (d1 and d2 get garbage collected) - return merge(d1, d2); - } -} diff --git a/code/FileIO/Words.java b/code/FileIO/Words.java deleted file mode 100644 index 680e1a4..0000000 --- a/code/FileIO/Words.java +++ /dev/null @@ -1,36 +0,0 @@ -/* - * Example code for Think Java (http://thinkapjava.com) - * - * Copyright(c) 2011 Allen B. Downey - * GNU General Public License v3.0 (http://www.gnu.org/copyleft/gpl.html) - * - * @author Allen B. Downey - */ - -import java.io.*; - -public class Words { - - public static void main(String[] args) { - - try { - processFile("words.txt"); - } catch(Exception ex) { - System.out.println("That didn't work. Here's why:"); - ex.printStackTrace(); - } - } - - public static void processFile(String filename) - throws FileNotFoundException, IOException { - - FileReader fileReader = new FileReader(filename); - BufferedReader in = new BufferedReader(fileReader); - - while (true) { - String s = in.readLine(); - if (s == null) break; - System.out.println(s); - } - } -} \ No newline at end of file diff --git a/code/FileIO/words.txt b/code/FileIO/words.txt deleted file mode 100644 index c9ff69c..0000000 --- a/code/FileIO/words.txt +++ /dev/null @@ -1,98569 +0,0 @@ - -A -A's -AOL -AOL's -Aachen -Aachen's -Aaliyah -Aaliyah's -Aaron -Aaron's -Abbas -Abbasid -Abbasid's -Abbott -Abbott's -Abby -Abby's -Abdul -Abdul's -Abe -Abe's -Abel -Abel's -Abelard -Abelard's -Abelson -Abelson's -Aberdeen -Aberdeen's -Abernathy -Abernathy's -Abidjan -Abidjan's -Abigail -Abigail's -Abilene -Abilene's -Abner -Abner's -Abraham -Abraham's -Abram -Abram's -Abrams -Absalom -Absalom's -Abuja -Abyssinia -Abyssinia's 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-Nickelodeon's -Nicklaus -Nicklaus's -Nickolas -Nicobar -Nicobar's -Nicodemus -Nicodemus's -Nicola -Nicola's -Nicolas -Nicole -Nicole's -Nicosia -Nicosia's -Niebuhr -Niebuhr's -Nielsen -Nielsen's -Nietzsche -Nietzsche's -Nieves -Nieves's -Nigel -Nigel's -Niger -Niger's -Nigeria -Nigeria's -Nigerian -Nigerians -Nightingale -Nightingale's -Nijinsky -Nijinsky's -Nike -Nike's -Nikita -Nikita's -Nikkei -Nikki -Nikki's -Nikolai -Nikolai's -Nikolayev -Nikolayev's -Nikon -Nikon's -Nile -Nile's -Nimitz -Nimitz's -Nimrod -Nimrod's -Nina -Nina's -Nineveh -Nineveh's -Nintendo -Niobe -Niobe's -Nippon -Nippon's -Nirenberg -Nirenberg's -Nirvana -Nisan -Nisan's -Nisei -Nisei's -Nissan -Nissan's -Nita -Nita's -Nixon -Nixon's -Nkrumah -Nkrumah's -NoDoz -NoDoz's -Noah -Noah's -Nobel -Nobel's -Nobelist -Nobelist's -Nobelists -Noble -Noble's -Noe -Noe's -Noel -Noel's -Noelle -Noelle's -Noels -Noemi -Noemi's -Noh -Noh's -Nola -Nola's -Nolan -Nolan's -Nome -Nome's -Nona -Nona's -Nora -Nora's -Norbert 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-Nuremberg -Nuremberg's -Nureyev -Nureyev's -NutraSweet -NutraSweet's -NyQuil -NyQuil's -Nyasa -Nyasa's -Nyerere -Nyerere's -O -O'Brien -O'Casey -O'Connell -O'Connor -O'Donnell -O'Hara -O'Higgins -O'Keeffe -O'Neil -O'Neill -O'Rourke -O'Toole -OHSA -OHSA's -OK -OKs -Oahu -Oahu's -Oakland -Oakland's -Oakley -Oakley's -Oates -Oates's -Oaxaca -Oaxaca's -Ob -Ob's -Obadiah -Obadiah's -Oberlin -Oberlin's -Oberon -Oberon's -Occam -Occam's -Occident -Occident's -Occidental -Occidentals -Occidents -Oceania -Oceania's -Oceanus -Oceanus's -Ochoa -Ochoa's -Oct -Oct's -Octavia -Octavia's -Octavio -Octavio's -October -October's -Octobers -Odell -Odell's -Oder -Oder's -Odessa -Odessa's -Odets -Odets's -Odin -Odin's -Odis -Odis's -Odom -Odom's -Odysseus -Odysseus's -Odyssey -Odyssey's -Oedipal -Oedipus -Oedipus's -Oersted -Oersted's -Ofelia -Ofelia's -Offenbach -Offenbach's -OfficeMax -OfficeMax's -Ogbomosho -Ogbomosho's -Ogden -Ogden's -Ogilvy -Ogilvy's -Oglethorpe -Oglethorpe's -Ohio -Ohio's -Ohioan 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-zincking -zincs -zing -zing's -zinged -zinger -zingers -zinging -zings -zinnia -zinnia's -zinnias -zip -zip's -zipped -zipper -zipper's -zippered -zippering -zippers -zippier -zippiest -zipping -zippy -zips -zircon -zircon's -zirconium -zirconium's -zircons -zit -zither -zither's -zithers -zits -zodiac -zodiac's -zodiacal -zodiacs -zombie -zombie's -zombies -zonal -zone -zone's -zoned -zones -zoning -zonked -zoo -zoo's -zoological -zoologist -zoologist's -zoologists -zoology -zoology's -zoom -zoomed -zooming -zooms -zoos -zucchini -zucchini's -zucchinis -zwieback -zwieback's -zygote -zygote's -zygotes -Ångström -éclair -éclair's -éclairs -éclat -éclat's -élan -élan's -émigré -émigrés -épée -épées -étude -étude's -études diff --git a/code/Graphics/CardTable.java b/code/Graphics/CardTable.java deleted file mode 100644 index b42d903..0000000 --- a/code/Graphics/CardTable.java +++ /dev/null @@ -1,97 +0,0 @@ -/* - * Example code for Think Java (http://thinkapjava.com) - * - * Copyright(c) 2011 Allen B. Downey - * GNU General Public License v3.0 (http://www.gnu.org/copyleft/gpl.html) - * - * @author Allen B. Downey - */ - -import java.awt.Canvas; -import java.awt.Color; -import java.awt.Graphics; -import java.awt.Image; - -import javax.swing.ImageIcon; -import javax.swing.JFrame; - -public class CardTable extends Canvas { - private Image[][] images; - private int cardWidth, cardHeight; - - /* - * Creates a CardTable. - * cardset is the String name of the folder that contains the card images. - */ - public CardTable(String cardset) { - setBackground(new Color(0x088A4B)); - - // create an array of card images - String suits = "cdhs"; - images = new Image[4][14]; - for (int suit = 0; suit <= 3; suit++) { - for (int rank = 1; rank <= 13; rank++) { - char c = suits.charAt(suit); - String s = String.format("%s/%02d%c.gif", cardset, rank, c); - images[suit][rank] = new ImageIcon(s).getImage(); - } - } - - // get the width and height of the cards and set the size of - // the frame accordingly - cardWidth = images[1][1].getWidth(null); - cardHeight = images[1][1].getHeight(null); - - // set the size temporarily to get the insets - setTableSize(14, 4); - } - - /* - * Sets the table size. - * x and y are in units of card width/height. - */ - public void setTableSize(double x, double y) { - setSize((int)(x * cardWidth), - (int)(y *cardHeight)); - } - - /* - * Draws a card at the given coordinates. - * x and y are in units of card width/height. - */ - public void drawCard(Graphics g, int suit, int rank, double x, double y) { - Image image = images[suit][rank]; - g.drawImage(image, - (int)(x * cardWidth), - (int)(y * cardHeight), - null); - } - - /* - * Special method invoked when the Frame needs to be drawn. - */ - public void paint(Graphics g) { - for (int suit = 0; suit <= 3; suit++) { - for (int rank = 1; rank <= 13; rank++) { - double x = rank-1 + suit/5.0; - double y = suit / 2.0; - drawCard(g, suit, rank, x, y); - } - } - } - - public static void main(String[] args) { - // make the frame - JFrame frame = new JFrame(); - frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); - - // add the CardTable - String cardset = "cardset-oxymoron"; - Canvas canvas = new CardTable(cardset); - frame.getContentPane().add(canvas); - - // show the frame - frame.pack(); - frame.setVisible(true); - } -} diff --git a/code/Graphics/GraphicsDemo.java b/code/Graphics/GraphicsDemo.java deleted file mode 100644 index 6976832..0000000 --- a/code/Graphics/GraphicsDemo.java +++ /dev/null @@ -1,27 +0,0 @@ -/* - * Example code for Think Java (http://thinkapjava.com) - * - * Copyright(c) 2011 Allen B. Downey - * GNU General Public License v3.0 (http://www.gnu.org/copyleft/gpl.html) - * - * @author Allen B. Downey - */ - -import java.awt.Frame; -import java.awt.Graphics; - -public class GraphicsDemo extends Frame { - - public static void main(String[] args) { - GraphicsDemo gd = new GraphicsDemo(); - gd.setSize(400, 400); - gd.setVisible(true); - } - - /* - * Special method invoked when the Frame needs to be drawn. - */ - public void paint(Graphics g) { - g.fillOval(100, 100, 200, 200); // draw a circle - } -} diff --git a/code/Graphics/Mickey.java b/code/Graphics/Mickey.java deleted file mode 100644 index 610ee92..0000000 --- a/code/Graphics/Mickey.java +++ /dev/null @@ -1,58 +0,0 @@ -/* - * Example code for Think Java (http://thinkapjava.com) - * - * Copyright(c) 2011 Allen B. Downey - * GNU General Public License v3.0 (http://www.gnu.org/copyleft/gpl.html) - * - * @author Allen B. Downey - */ - -import java.awt.Canvas; -import java.awt.Color; -import java.awt.Graphics; -import java.awt.Rectangle; -import javax.swing.JFrame; - - -public class Mickey extends Canvas { - - public void boxOval(Graphics g, Rectangle bb) { - g.fillOval(bb.x, bb.y, bb.width, bb.height); - } - - public void mickey(Graphics g, Rectangle bb) { - boxOval(g, bb); - - int dx = bb.width/2; - int dy = bb.height/2; - Rectangle half = new Rectangle(bb.x, bb.y, dx, dy); - - half.translate(-dx/2, -dx/2); - boxOval(g, half); - - half.translate(dx*2, 0); - boxOval(g, half); - } - - public void paint(Graphics g) { - Rectangle bb = new Rectangle(100, 150, 200, 200); - g.setColor(Color.gray); - mickey(g, bb); - } - - public static void main(String[] args) { - // make the frame - JFrame frame = new JFrame(); - frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); - - // add the canvas - Canvas canvas = new Mickey(); - canvas.setSize(400, 400); - canvas.setBackground(Color.white); - frame.getContentPane().add(canvas); - - // show the frame - frame.pack(); - frame.setVisible(true); - } -} diff --git a/code/Graphics/MickeySoln.java b/code/Graphics/MickeySoln.java deleted file mode 100644 index 12dfeea..0000000 --- a/code/Graphics/MickeySoln.java +++ /dev/null @@ -1,61 +0,0 @@ -/* - * Example code for Think Java (http://thinkapjava.com) - * - * Copyright(c) 2011 Allen B. Downey - * GNU General Public License v3.0 (http://www.gnu.org/copyleft/gpl.html) - * - * @author Allen B. Downey - */ - -import java.awt.Canvas; -import java.awt.Color; -import java.awt.Graphics; -import java.awt.Rectangle; -import javax.swing.JFrame; - - -public class MickeySoln extends Canvas { - - public void boxOval(Graphics g, Rectangle bb) { - g.fillOval(bb.x, bb.y, bb.width, bb.height); - } - - public void mickey(Graphics g, Rectangle bb) { - boxOval(g, bb); - if (bb.width < 3) { - return; - } - - int dx = bb.width/2; - int dy = bb.height/2; - Rectangle half = new Rectangle(bb.x, bb.y, dx, dy); - - half.translate(-dx/2, -dx/2); - mickey(g, half); - - half.translate(dx*2, 0); - mickey(g, half); - } - - public void paint(Graphics g) { - Rectangle bb = new Rectangle(100, 150, 200, 200); - g.setColor(Color.gray); - mickey(g, bb); - } - - public static void main(String[] args) { - // make the frame - JFrame frame = new JFrame(); - frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); - - // add the canvas - Canvas canvas = new MickeySoln(); - canvas.setSize(400, 400); - canvas.setBackground(Color.white); - frame.getContentPane().add(canvas); - - // show the frame - frame.pack(); - frame.setVisible(true); - } -} diff --git a/code/Graphics/Moire.java b/code/Graphics/Moire.java deleted file mode 100644 index 5dc0881..0000000 --- a/code/Graphics/Moire.java +++ /dev/null @@ -1,41 +0,0 @@ -/* - * Example code for Think Java (http://thinkapjava.com) - * - * Copyright(c) 2011 Allen B. Downey - * GNU General Public License v3.0 (http://www.gnu.org/copyleft/gpl.html) - * - * @author Allen B. Downey - */ - -import java.awt.Canvas; -import java.awt.Color; -import java.awt.Graphics; -import javax.swing.JFrame; - - -public class Moire extends Canvas { - - public void paint(Graphics g) { - int i = 90; - while (i < getWidth()) { - g.drawOval (0, 0, i, i); - i = i + 3; - } - } - - public static void main(String[] args) { - // make the frame - JFrame frame = new JFrame(); - frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); - - // add the canvas - Canvas canvas = new Moire(); - canvas.setSize(400, 400); - canvas.setBackground(Color.white); - frame.getContentPane().add(canvas); - - // show the frame - frame.pack(); - frame.setVisible(true); - } -} diff --git a/code/Graphics/MyCanvas.java b/code/Graphics/MyCanvas.java deleted file mode 100644 index 8f70ca7..0000000 --- a/code/Graphics/MyCanvas.java +++ /dev/null @@ -1,38 +0,0 @@ -/* - * Example code for Think Java (http://thinkapjava.com) - * - * Adapted from http://en.wikibooks.org/wiki/Java_Programming/Canvas - * - * Copyright(c) 2011 Allen B. Downey - * GNU General Public License v3.0 (http://www.gnu.org/copyleft/gpl.html) - * - * @author Allen B. Downey - */ - -import java.awt.Canvas; -import java.awt.Graphics; -import javax.swing.JFrame; - -public class MyCanvas extends Canvas { - - public static void main(String[] args) { - // make the frame - JFrame frame = new JFrame(); - frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); - - // add the canvas - Canvas canvas = new MyCanvas(); - canvas.setSize(400, 400); - frame.getContentPane().add(canvas); - - // show the frame - frame.pack(); - frame.setVisible(true); - } - - public void paint(Graphics g) { - // draw a circle - g.fillOval(100, 100, 200, 200); - } -} - diff --git a/code/Graphics/Snow.java b/code/Graphics/Snow.java deleted file mode 100644 index b84973b..0000000 --- a/code/Graphics/Snow.java +++ /dev/null @@ -1,112 +0,0 @@ -import java.awt.*; // Java abstract window toolkit - -public class Snow extends Frame { - - public static void main(String[] args) { - Snow c = new Snow (); // create a window - c.setSize (400, 400); // set its size - c.setBackground (Color.white); // set the background color - c.show (); // display the window - } - - public void paint (Graphics g) { - Rectangle bbox = getBounds (); // find the window size - paintBox (g, 0, 0, bbox.width, bbox.height); // draw something! - } - - public static void paintBox - (Graphics g, int x, int y, int width, int height) { - - // Mr. Snowperson - int personWidth = 30 * width / 100; - int personHeight = height; - int personx = x + 20 * width / 100; - int persony = y; - paintSnowperson (g, personx, persony, personWidth, personHeight); - - // Mrs. Snowperson - personWidth = 90 * personWidth / 100; - personHeight = 90 * height / 100; - personx = 50 * width / 100; - persony = height - personHeight; - paintSnowperson (g, personx, persony, personWidth, personHeight); - } - - public static void paintSnowperson - (Graphics g, int x, int y, int width, int height) { - - if (height < 10) return; // refuse to draw very small snowpeople - - int headheight = 20 * height / 100; - int midheight = 30 * height / 100; - int botheight = height - midheight - headheight; - - int headwidth = 30 * width / 100; - int midwidth = 60 * width / 100; - - int headgap = (width - headwidth) / 2; - int midgap = (width - midwidth) / 2; - - // top oval and face - g.drawOval (x + headgap, y, headwidth, headheight); - paintFace (g, x + headgap, y, headwidth, headheight); - - // middle oval and rings - g.drawOval (x + midgap, y + headheight, midwidth, midheight); - paintRings (g, x + midgap, y + headheight, midwidth, midheight); - - // bottom oval and baby snowpeople - y += headheight + midheight; - g.drawOval (x, y, width, botheight); - paintSnowperson (g, x + width/4, y, width/2, botheight); - } - - public static void paintFace - (Graphics g, int x, int y, int width, int height) { - int eyeheight = 20 * height / 100; - int eyewidth = 20 * width / 100; - int gap = (width - 2 * eyewidth) / 3; - int brow = 25 * height / 100; - - // just draw two eyes - g.fillOval (x + gap, y + brow, eyewidth, eyeheight); - g.fillOval (x + 2 * gap + eyewidth, y + brow, eyewidth, eyeheight); - } - - public static void paintRings - (Graphics g, int x, int y, int width, int height) { - // Polite methods avoid doing things like changing the current color, - // because the calling method might not like it. Before we change the - // color, we stow the old value. - Color old_color = g.getColor (); - - int ring_width = 30 * width/100; - int ring_height = 60 * height/100; - int gap = (width - 3 * ring_width) / 2; - - int xx = x; - int yy = y; - g.setColor (Color.blue); - g.drawOval (xx, yy, ring_width, ring_height); - - xx += ring_width + gap; - g.setColor (Color.black); - g.drawOval (xx, yy, ring_width, ring_height); - - xx += ring_width + gap; - g.setColor (Color.red); - g.drawOval (xx, yy, ring_width, ring_height); - - yy = y + height - ring_height; - xx = x + (width - 2 * ring_width - gap) / 2; - g.setColor (Color.yellow); - g.drawOval (xx, yy, ring_width, ring_height); - - xx += ring_width + gap; - g.setColor (Color.green); - g.drawOval (xx, yy, ring_width, ring_height); - - // before returning we restore the original color - g.setColor (old_color); - } -} diff --git a/code/Graphics/Snowperson.java b/code/Graphics/Snowperson.java deleted file mode 100644 index 564b868..0000000 --- a/code/Graphics/Snowperson.java +++ /dev/null @@ -1,123 +0,0 @@ -import java.awt.*; // Java abstract window toolkit - -public class Snowperson extends Frame { - - public static void main(String[] args) { - Snowperson c = new Snowperson (); // create a window - c.setSize (400, 400); // set its size - c.setBackground (Color.white); // set the background color - c.show (); // display the window - } - - public void paint (Graphics g) { - Rectangle bb = getBounds (); - bb.x = 0; - bb.y = 0; - paintBox (g, bb); - } - - public static void paintBox (Graphics g, Rectangle bb) { - - // Mr. Snowperson - int personWidth = 30 * bb.width / 100; - int personHeight = bb.height; - int personx = bb.x + 20 * bb.width / 100; - int persony = bb.y; - Rectangle mrbox = - new Rectangle (personx, persony, personWidth, personHeight); - paintSnowperson (g, mrbox); - - // Mrs. Snowperson - personWidth = 90 * personWidth / 100; - personHeight = 90 * bb.height / 100; - personx = 50 * bb.width / 100; - persony = bb.height - personHeight; - - Rectangle mrsbox = - new Rectangle (personx, persony, personWidth, personHeight); - paintSnowperson (g, mrsbox); - } - - public static void paintSnowperson (Graphics g, Rectangle bb) { - - if (bb.height < 10) return; // refuse to draw very small snowpeople - - int headheight = 20 * bb.height / 100; - int midheight = 30 * bb.height / 100; - int botheight = bb.height - midheight - headheight; - - int headwidth = 30 * bb.width / 100; - int midwidth = 60 * bb.width / 100; - - int headgap = (bb.width - headwidth) / 2; - int midgap = (bb.width - midwidth) / 2; - - // top oval and face - g.drawOval (bb.x + headgap, bb.y, headwidth, headheight); - Rectangle headBox = - new Rectangle (bb.x + headgap, bb.y, headwidth, headheight); - paintFace (g, headBox); - - // middle oval and rings - g.drawOval (bb.x + midgap, bb.y + headheight, midwidth, midheight); - Rectangle thoraxBox = - new Rectangle (bb.x + midgap, bb.y + headheight, midwidth, midheight); - paintRings (g, thoraxBox); - - // bottom oval and baby snowpeople - int abdomeny = bb.y + headheight + midheight; - g.drawOval (bb.x, abdomeny, bb.width, botheight); - Rectangle abdomenBox = - new Rectangle (bb.x + bb.width/3, abdomeny, bb.width/3, botheight); - paintSnowperson (g, abdomenBox); - } - - public static void paintFace (Graphics g, Rectangle bb) { - - int eyeheight = 20 * bb.height / 100; - int eyewidth = 20 * bb.width / 100; - int gap = (bb.width - 2 * eyewidth) / 3; - int brow = 25 * bb.height / 100; - - // just draw two eyes - g.fillOval (bb.x + gap, bb.y + brow, eyewidth, eyeheight); - g.fillOval (bb.x + 2 * gap + eyewidth, bb.y + brow, eyewidth, eyeheight); - } - - public static void paintRings (Graphics g, Rectangle bb) { - - // Polite methods avoid doing things like changing the current color, - // because the calling method might not like it. Before we change the - // color, we stow the old value. - Color oldColor = g.getColor (); - - int ringWidth = 30 * bb.width/100; - int ring_height = 60 * bb.height/100; - int gap = (bb.width - 3 * ringWidth) / 2; - - int xx = bb.x; - int yy = bb.y; - g.setColor (Color.blue); - g.drawOval (xx, yy, ringWidth, ring_height); - - xx += ringWidth + gap; - g.setColor (Color.black); - g.drawOval (xx, yy, ringWidth, ring_height); - - xx += ringWidth + gap; - g.setColor (Color.red); - g.drawOval (xx, yy, ringWidth, ring_height); - - yy = bb.y + bb.height - ring_height; - xx = bb.x + (bb.width - 2 * ringWidth - gap) / 2; - g.setColor (Color.yellow); - g.drawOval (xx, yy, ringWidth, ring_height); - - xx += ringWidth + gap; - g.setColor (Color.green); - g.drawOval (xx, yy, ringWidth, ring_height); - - // before returning we restore the original color - g.setColor (oldColor); - } -} diff --git a/code/Graphics/cardset-oxymoron/01c.gif b/code/Graphics/cardset-oxymoron/01c.gif deleted file mode 100644 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b/code/Graphics/cardset-oxymoron/13h.gif deleted file mode 100644 index 845a65d..0000000 Binary files a/code/Graphics/cardset-oxymoron/13h.gif and /dev/null differ diff --git a/code/Graphics/cardset-oxymoron/13s.gif b/code/Graphics/cardset-oxymoron/13s.gif deleted file mode 100644 index b719113..0000000 Binary files a/code/Graphics/cardset-oxymoron/13s.gif and /dev/null differ diff --git a/code/Graphics/cardset-oxymoron/COPYRIGHT b/code/Graphics/cardset-oxymoron/COPYRIGHT deleted file mode 100644 index 1c81a79..0000000 --- a/code/Graphics/cardset-oxymoron/COPYRIGHT +++ /dev/null @@ -1,10 +0,0 @@ -This PySol cardset was adapted from cards-2.0.tar.gz. -http://www.waste.org/~oxymoron/cards/ - -Copyright (C) 1998 Oliver Xymoron -Copyright (C) 1999 Markus F.X.J. Oberhumer - -This cardset is free software; you can redistribute it and/or -modify it under the terms of the GNU General Public License -as published by the Free Software Foundation; either version 2 of -the License, or (at your option) any later version. diff --git a/code/Graphics/cardset-oxymoron/back001.gif b/code/Graphics/cardset-oxymoron/back001.gif deleted file mode 100644 index 463c0b0..0000000 Binary files a/code/Graphics/cardset-oxymoron/back001.gif and /dev/null differ diff --git a/code/Graphics/cardset-oxymoron/back101.gif b/code/Graphics/cardset-oxymoron/back101.gif deleted file mode 100644 index 4bb2c95..0000000 Binary files a/code/Graphics/cardset-oxymoron/back101.gif and /dev/null differ diff --git a/code/Graphics/cardset-oxymoron/back102.gif b/code/Graphics/cardset-oxymoron/back102.gif deleted file mode 100644 index 82b25f7..0000000 Binary files a/code/Graphics/cardset-oxymoron/back102.gif and /dev/null differ diff --git a/code/Graphics/cardset-oxymoron/back111.gif 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and /dev/null differ diff --git a/code/GridWorldCode/gridworld.jar b/code/GridWorldCode/gridworld.jar deleted file mode 100644 index 07c32e4..0000000 Binary files a/code/GridWorldCode/gridworld.jar and /dev/null differ diff --git a/code/Makefile b/code/Makefile deleted file mode 100644 index cef92b8..0000000 --- a/code/Makefile +++ /dev/null @@ -1,21 +0,0 @@ -FILES = \ -Graphics/MyCanvas.java Graphics/MickeySoln.java Graphics/cardset.zip \ -Graphics/Mickey.java Graphics/Moire.java Graphics/CardTable.java \ -Graphics/GraphicsDemo.java Graphics/Snow.java Graphics/Snowperson.java \ -MyGridWorld/BoxBug.java MyGridWorld/GoodTermite.java \ -MyGridWorld/BoxBugRunner.java MyGridWorld/LangtonRunner.java \ -MyGridWorld/BugRunner.java MyGridWorld/LangtonTermite.java \ -MyGridWorld/ChaseRunner.java MyGridWorld/MyTermite.java \ -MyGridWorld/CircleBug.java MyGridWorld/Termite.java \ -MyGridWorld/CircleBugRunner.java MyGridWorld/TermiteRunner.java \ -MyGridWorld/DiamondTermite.java MyGridWorld/Termite.gif \ -MyGridWorld/BlueBug.java MyGridWorld/LifeRock.java \ -MyGridWorld/BlueBugRunner.java MyGridWorld/LifeRunner.java \ -MyGridWorld/EternalFlower.java \ -Cards/Card1.java Cards/Card3.java Cards/CardSoln3.java \ -Cards/Card2.java Cards/CardSoln2.java FileIO/Words.java FileIO/words.txt \ - -DEST = /home/downey/public_html/greent/thinkapjava/code - -all: - rsync -a $(FILES) $(DEST) diff --git a/code/MyGridWorld/BlueBug.java b/code/MyGridWorld/BlueBug.java deleted file mode 100644 index b7f7ad9..0000000 --- a/code/MyGridWorld/BlueBug.java +++ /dev/null @@ -1,78 +0,0 @@ -/* - * AP(r) Computer Science GridWorld Case Study: - * Copyright(c) 2005-2006 Cay S. Horstmann (http://horstmann.com) - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Cay Horstmann - * @author Chris Nevison - * @author Barbara Cloud Wells - */ - -import info.gridworld.actor.Actor; -import info.gridworld.actor.Bug; -import info.gridworld.actor.Rock; -import info.gridworld.grid.Grid; -import info.gridworld.grid.Location; - -import java.awt.Color; -import java.util.ArrayList; - -/** - * A BoxBug traces out a square "box" of a given size.
- * The implementation of this class is testable on the AP CS A and AB exams. - */ -public class BlueBug extends Bug -{ - /** - * Moves to the next location of the square. - */ - public void act() - { - randomTurn(); - if (!canMove()) { - return; - } - move(); - - Location loc = getLocation(); - Grid grid = getGrid(); - ArrayList neighbors = grid.getNeighbors(loc); - - for (int i=0; i - * This class is not tested on the AP CS A and AB exams. - */ -public class BlueBugRunner -{ - public static void main(String[] args) - { - ActorWorld world = new ActorWorld(); - BlueBug alice = new BlueBug(); - alice.setColor(Color.blue); - world.add(alice); - - for (int i=0; i<5; i++) { - world.add(new Rock()); - } - world.show(); - } -} \ No newline at end of file diff --git a/code/MyGridWorld/BoxBug.java b/code/MyGridWorld/BoxBug.java deleted file mode 100644 index 189ae51..0000000 --- a/code/MyGridWorld/BoxBug.java +++ /dev/null @@ -1,57 +0,0 @@ -/* - * AP(r) Computer Science GridWorld Case Study: - * Copyright(c) 2005-2006 Cay S. Horstmann (http://horstmann.com) - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Cay Horstmann - * @author Chris Nevison - * @author Barbara Cloud Wells - */ - -import info.gridworld.actor.Bug; - -/** - * A BoxBug traces out a square "box" of a given size.
- * The implementation of this class is testable on the AP CS A and AB exams. - */ -public class BoxBug extends Bug -{ - private int steps; - private int sideLength; - - /** - * Constructs a box bug that traces a square of a given side length - * @param length the side length - */ - public BoxBug(int length) - { - steps = 0; - sideLength = length; - } - - /** - * Moves to the next location of the square. - */ - public void act() - { - if (steps < sideLength && canMove()) - { - move(); - steps++; - } - else - { - turn(); - turn(); - steps = 0; - } - } -} diff --git a/code/MyGridWorld/BoxBugRunner.java b/code/MyGridWorld/BoxBugRunner.java deleted file mode 100644 index a82edfc..0000000 --- a/code/MyGridWorld/BoxBugRunner.java +++ /dev/null @@ -1,40 +0,0 @@ -/* - * AP(r) Computer Science GridWorld Case Study: - * Copyright(c) 2005-2006 Cay S. Horstmann (http://horstmann.com) - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Cay Horstmann - * @author Chris Nevison - * @author Barbara Cloud Wells - */ - -import info.gridworld.actor.ActorWorld; -import info.gridworld.grid.Location; - -import java.awt.Color; - -/** - * This class runs a world that contains box bugs.
- * This class is not tested on the AP CS A and AB exams. - */ -public class BoxBugRunner -{ - public static void main(String[] args) - { - ActorWorld world = new ActorWorld(); - BoxBug alice = new BoxBug(6); - alice.setColor(Color.ORANGE); - BoxBug bob = new BoxBug(3); - world.add(new Location(7, 8), alice); - world.add(new Location(5, 5), bob); - world.show(); - } -} \ No newline at end of file diff --git a/code/MyGridWorld/BugRunner.java b/code/MyGridWorld/BugRunner.java deleted file mode 100644 index 23f61a1..0000000 --- a/code/MyGridWorld/BugRunner.java +++ /dev/null @@ -1,95 +0,0 @@ -/* - * AP(r) Computer Science GridWorld Case Study: - * Copyright(c) 2005-2006 Cay S. Horstmann (http://horstmann.com) - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Cay Horstmann - * @author Allen Downey - * Modified by Allen Downey for an exercise in Think Java (thinkapjava.com) - */ - -import info.gridworld.actor.ActorWorld; -import info.gridworld.actor.Bug; -import info.gridworld.actor.Rock; - -import java.awt.Color; - -/** - * This class runs a world that contains a bug and a rock, added at random - * locations. Click on empty locations to add additional actors. Click on - * populated locations to invoke methods on their occupants.
- * To build your own worlds, define your own actors and a runner class. See the - * BoxBugRunner (in the boxBug folder) for an example.
- */ -public class BugRunner -{ - public static void moveBug(Bug bug, int n) { - if (n == 0) { - return; - } - if (bug.canMove()) { - bug.move(); - } else { - bug.turn(); - } - moveBug(bug, n-1); - } - - public static void randomBug(Bug bug, int n) { - if (n == 0) { - return; - } - int x = (int) (Math.random() * 4); - bug.setDirection(x * 90); - - if (bug.canMove()) { - bug.move(); - } - randomBug(bug, n-1); - } - - public static void colorBug(Bug bug) { - int x = bug.getLocation().getCol(); - int y = bug.getLocation().getRow(); - Color c = new Color(x*255/9, 0, y*255/9); - bug.setColor(c); - } - - public static void makeBugs(ActorWorld world, int n) { - if (n == 0) { - return; - } - Bug bug = new Bug(); - world.add(bug); - colorBug(bug); - makeBugs(world, n-1); - } - - public static void main(String[] args) - { - ActorWorld world = new ActorWorld(); - Bug redBug = new Bug(); - world.add(redBug); - moveBug(redBug, 10); - - Bug blueBug = new Bug(Color.blue); - world.add(blueBug); - randomBug(blueBug, 10); - - Color purple = new Color(148, 0, 211); - Bug purpleBug = new Bug(purple); - world.add(purpleBug); - - makeBugs(world, 3); - - world.show(); - } -} diff --git a/code/MyGridWorld/ChaseRunner.java b/code/MyGridWorld/ChaseRunner.java deleted file mode 100644 index 79d1e25..0000000 --- a/code/MyGridWorld/ChaseRunner.java +++ /dev/null @@ -1,92 +0,0 @@ -/* - * AP(r) Computer Science GridWorld Case Study: - * Copyright(c) 2005-2006 Cay S. Horstmann (http://horstmann.com) - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Cay Horstmann - * @author Allen Downey - * Modified by Allen Downey for an exercise in Think Java (thinkapjava.com) - */ - -import info.gridworld.actor.ActorWorld; -import info.gridworld.actor.Bug; -import info.gridworld.actor.Rock; - -import java.awt.Color; - -/** - * This class runs a world that contains a bug and a rock, added at random - * locations. Click on empty locations to add additional actors. Click on - * populated locations to invoke methods on their occupants.
- * To build your own worlds, define your own actors and a runner class. See the - * BoxBugRunner (in the boxBug folder) for an example.
- * This class is not tested on the AP CS A and AB exams. - */ -public class ChaseRunner -{ - public static int xdiff(Bug bug1, Bug bug2) { - int x1 = bug1.getLocation().getCol(); - int x2 = bug2.getLocation().getCol(); - return x2 - x1; - } - - public static int ydiff(Bug bug1, Bug bug2) { - int y1 = bug1.getLocation().getRow(); - int y2 = bug2.getLocation().getRow(); - return y2 - y1; - } - - public static double distance(Bug bug1, Bug bug2) { - int dx = xdiff(bug1, bug2); - int dy = ydiff(bug1, bug2); - return Math.sqrt(dx*dx + dy*dy); - } - - public static void turnToward(Bug bug1, Bug bug2) { - int dx = xdiff(bug1, bug2); - int dy = ydiff(bug1, bug2); - double angle = Math.atan2(dy, dx); - int degrees = (int) Math.round(angle * 180 / Math.PI); - bug1.setDirection(degrees + 90); - } - - public static void moveToward(Bug bug1, Bug bug2) { - turnToward(bug1, bug2); - if (bug1.canMove()) { - bug1.move(); - } - } - - public static void moveBugs(Bug bug1, Bug bug2, int n) { - while (n > 0) { - moveToward(bug1, bug2); - moveToward(bug2, bug1); - n = n-1; - } - } - - public static void main(String[] args) - { - ActorWorld world = new ActorWorld(); - - Bug redBug = new Bug(); - world.add(redBug); - - Bug blueBug = new Bug(Color.blue); - world.add(blueBug); - - System.out.println(distance(redBug, blueBug)); - moveBugs(redBug, blueBug, 5); - System.out.println(distance(redBug, blueBug)); - - world.show(); - } -} diff --git a/code/MyGridWorld/CircleBug.java b/code/MyGridWorld/CircleBug.java deleted file mode 100644 index 961c947..0000000 --- a/code/MyGridWorld/CircleBug.java +++ /dev/null @@ -1,56 +0,0 @@ -/* - * AP(r) Computer Science GridWorld Case Study: - * Copyright(c) 2005-2006 Cay S. Horstmann (http://horstmann.com) - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Cay Horstmann - * @author Chris Nevison - * @author Barbara Cloud Wells - */ - -import info.gridworld.actor.Bug; - -/** - * A CircleBug traces out a square "box" of a given size.
- * The implementation of this class is testable on the AP CS A and AB exams. - */ -public class CircleBug extends Bug -{ - private int steps; - private int sideLength; - - /** - * Constructs a box bug that traces a square of a given side length - * @param length the side length - */ - public CircleBug(int length) - { - steps = 0; - sideLength = length; - } - - /** - * Moves to the next location of the square. - */ - public void act() - { - if (steps < sideLength && canMove()) - { - move(); - steps++; - } - else - { - turn(); - steps = 0; - } - } -} diff --git a/code/MyGridWorld/CircleBugRunner.java b/code/MyGridWorld/CircleBugRunner.java deleted file mode 100644 index 088a1ea..0000000 --- a/code/MyGridWorld/CircleBugRunner.java +++ /dev/null @@ -1,40 +0,0 @@ -/* - * AP(r) Computer Science GridWorld Case Study: - * Copyright(c) 2005-2006 Cay S. Horstmann (http://horstmann.com) - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Cay Horstmann - * @author Chris Nevison - * @author Barbara Cloud Wells - */ - -import info.gridworld.actor.ActorWorld; -import info.gridworld.grid.Location; - -import java.awt.Color; - -/** - * This class runs a world that contains box bugs.
- * This class is not tested on the AP CS A and AB exams. - */ -public class CircleBugRunner -{ - public static void main(String[] args) - { - ActorWorld world = new ActorWorld(); - CircleBug alice = new CircleBug(6); - alice.setColor(Color.ORANGE); - CircleBug bob = new CircleBug(3); - world.add(new Location(7, 8), alice); - world.add(new Location(5, 5), bob); - world.show(); - } -} \ No newline at end of file diff --git a/code/MyGridWorld/DiamondTermite.java b/code/MyGridWorld/DiamondTermite.java deleted file mode 100644 index b1f4591..0000000 --- a/code/MyGridWorld/DiamondTermite.java +++ /dev/null @@ -1,51 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -import info.gridworld.actor.Actor; -import info.gridworld.actor.Bug; -import info.gridworld.actor.Flower; -import info.gridworld.grid.Grid; -import info.gridworld.grid.Location; - -/** - * A termite that picks up a flower if it sees one and - * drops a flower if it has one. - */ -public class DiamondTermite extends Termite { - - /* - * Does that thing that termites do. - */ - public void act() { - if (getGrid() == null) - return; - - if (hasFlower()) { - dropFlower(); - turn(45); - } - - if (seeFlower()) { - pickUpFlower(); - turn(-45); - } else { - createFlower(); - } - move(); - } -} diff --git a/code/MyGridWorld/EternalFlower.java b/code/MyGridWorld/EternalFlower.java deleted file mode 100644 index 52ebe8a..0000000 --- a/code/MyGridWorld/EternalFlower.java +++ /dev/null @@ -1,24 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -/** - * A flower that doesn't age. - */ -public class EternalFlower extends Flower { - public void act() {} -} diff --git a/code/MyGridWorld/GoodTermite.java b/code/MyGridWorld/GoodTermite.java deleted file mode 100644 index 9e47c93..0000000 --- a/code/MyGridWorld/GoodTermite.java +++ /dev/null @@ -1,51 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -import info.gridworld.actor.Actor; -import info.gridworld.actor.Bug; -import info.gridworld.actor.Flower; -import info.gridworld.grid.Grid; -import info.gridworld.grid.Location; - -/** - * A termite that picks up a flower if it sees one and - * drops a flower if it has one. - */ -public class GoodTermite extends Termite { - - /* - * Does that thing that termites do. - */ - public void act() { - if (getGrid() == null) - return; - - if (seeFlower()) { - if (hasFlower()) { - dropFlower(); - } else { - pickUpFlower(); - } - } - - if (canMove()) { - move(); - } - randomTurn(); - } -} diff --git a/code/MyGridWorld/LangtonRunner.java b/code/MyGridWorld/LangtonRunner.java deleted file mode 100644 index 95227ab..0000000 --- a/code/MyGridWorld/LangtonRunner.java +++ /dev/null @@ -1,40 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -import info.gridworld.actor.Actor; -import info.gridworld.actor.ActorWorld; -import info.gridworld.actor.Flower; -import info.gridworld.grid.UnboundedGrid; - -import java.awt.Color; - -/** - * This class runs a world that contains Termites.
- */ -public class LangtonRunner -{ - public static void main(String[] args) - { - ActorWorld world = new ActorWorld(new UnboundedGrid()); - - Termite alice = new LangtonTermite(); - world.add(alice); - - world.show(); - } -} diff --git a/code/MyGridWorld/LangtonTermite.java b/code/MyGridWorld/LangtonTermite.java deleted file mode 100644 index bffa9e0..0000000 --- a/code/MyGridWorld/LangtonTermite.java +++ /dev/null @@ -1,45 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -/** - * A termite that picks up a flower if it sees one and - * drops a flower if it has one. - */ -public class LangtonTermite extends Termite { - - /* - * Does that thing that termites do. - */ - public void act() { - if (getGrid() == null) - return; - - if (seeFlower()) { - flower = null; - pickUpFlower(); - turn(45); - } else { - if (!hasFlower()) { - createFlower(); - } - throwFlower(); - turn(-45); - } - move(); - } -} diff --git a/code/MyGridWorld/LifeRock.java b/code/MyGridWorld/LifeRock.java deleted file mode 100644 index 5d22da3..0000000 --- a/code/MyGridWorld/LifeRock.java +++ /dev/null @@ -1,121 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -import info.gridworld.actor.Actor; -import info.gridworld.actor.Rock; -import info.gridworld.grid.Grid; -import info.gridworld.grid.Location; - -import java.awt.Color; -import java.util.ArrayList; - - -/** - * Represents a Rock in Conway's Game of Life. - * - * The color of the rock represents whether the Rock is alive or dead. - * - * In order to implement simultaneous updates, act() has two phases: - * the first time it is invoked, it counts the neighbors; the second - * time it updates the status of the Rock. - */ -public class LifeRock extends Rock { - static final Color LIVE_COLOR = Color.blue; - static final Color DEAD_COLOR = Color.white; - - private int phase; - private int numNeighbors; - - /** - * Makes a dead rock. - */ - public LifeRock() { - super(); - phase = 1; - setDead(); - } - - /** - * Returns true if the Rock is alive. - */ - public boolean isAlive() { - return getColor() == LIVE_COLOR; - } - - /** - * Makes the Rock alive. - */ - public void setAlive() { - setColor(LIVE_COLOR); - } - - /** - * Makes the Rock dead. - */ - public void setDead() { - setColor(DEAD_COLOR); - } - - /** - * Check what phase we're in and calls the appropriate method. - * Moves to the next phase. - */ - public void act() { - if (phase == 1) { - numNeighbors = countLiveNeighbors(); - phase = 2; - } else { - updateStatus(); - phase = 1; - } - } - - /** - * Counts the number of live neighbors. - */ - public int countLiveNeighbors() { - Location loc = getLocation(); - Grid grid = getGrid(); - ArrayList neighbors = grid.getNeighbors(loc); - - int count = 0; - for (Actor neighbor: neighbors) { - LifeRock rock = (LifeRock) neighbor; - if (rock.isAlive()) { - count++; - } - } - return count; - } - - /** - * Updates the status of the Rock (live or dead) based on the number - * of neighbors. - */ - public void updateStatus() { - if (isAlive()) { - if (numNeighbors < 2 || numNeighbors > 3) { - setDead(); - } - } else { - if (numNeighbors == 3) { - setAlive(); - } - } - } -} diff --git a/code/MyGridWorld/LifeRunner.java b/code/MyGridWorld/LifeRunner.java deleted file mode 100644 index c84e957..0000000 --- a/code/MyGridWorld/LifeRunner.java +++ /dev/null @@ -1,81 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -import info.gridworld.actor.ActorWorld; -import info.gridworld.actor.Actor; -import info.gridworld.grid.Grid; -import info.gridworld.grid.BoundedGrid; -import info.gridworld.grid.Location; - -import java.awt.Color; -import java.util.ArrayList; - -/** - * - * This class is not tested on the AP CS A and AB exams. - */ -public class LifeRunner -{ - public static void main(String[] args) { - makeLifeWorld(9, 9); - } - - /** - * Makes a Game of Life grid with an r-pentomino. - */ - public static void makeLifeWorld(int rows, int cols) { - Grid grid = new BoundedGrid(rows, cols); - ActorWorld world = new ActorWorld(grid); - makeRocks(world); - makePentomino(world, rows/2, cols/2); - world.show(); - } - - /** - * Fills the grid with LifeRocks. - */ - public static void makeRocks(ActorWorld world) { - Grid grid = world.getGrid(); - int rows = grid.getNumRows(); - int cols = grid.getNumCols(); - for (int i=0; i grid = world.getGrid(); - ArrayList locs = new ArrayList(); - locs.add(new Location(x-1, y)); - locs.add(new Location(x-1, y+1)); - locs.add(new Location(x, y-1)); - locs.add(new Location(x, y)); - locs.add(new Location(x+1, y)); - - for (Location loc: locs) { - LifeRock rock = (LifeRock) grid.get(loc); - rock.setAlive(); - } - } -} \ No newline at end of file diff --git a/code/MyGridWorld/MyTermite.java b/code/MyGridWorld/MyTermite.java deleted file mode 100644 index bdabec9..0000000 --- a/code/MyGridWorld/MyTermite.java +++ /dev/null @@ -1,50 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -import info.gridworld.actor.Actor; -import info.gridworld.actor.Bug; -import info.gridworld.actor.Flower; -import info.gridworld.grid.Grid; -import info.gridworld.grid.Location; - -/** - * A termite that picks up a flower if it sees one and - * drops a flower if it has one. - */ -public class MyTermite extends Termite { - - /* - * Does that thing that termites do. - */ - public void act() { - if (getGrid() == null) - return; - - if (seeFlower()) { - pickUpFlower(); - } - if (hasFlower()) { - dropFlower(); - } - - if (canMove()) { - move(); - } - randomTurn(); - } -} diff --git a/code/MyGridWorld/Termite.gif b/code/MyGridWorld/Termite.gif deleted file mode 100644 index cc1b9e7..0000000 Binary files a/code/MyGridWorld/Termite.gif and /dev/null differ diff --git a/code/MyGridWorld/Termite.java b/code/MyGridWorld/Termite.java deleted file mode 100644 index 3cb8ee5..0000000 --- a/code/MyGridWorld/Termite.java +++ /dev/null @@ -1,202 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -import info.gridworld.actor.Actor; -import info.gridworld.actor.Bug; -import info.gridworld.actor.Flower; -import info.gridworld.grid.Grid; -import info.gridworld.grid.Location; - -/** - * - */ -public class Termite extends Bug { - Flower flower; - - Flower dropped = null; - Location dropLoc = null; - - /* - * Does that thing that termites do. - */ - public void act() { - if (getGrid() == null) - return; - - if (canMove()) { - move(); - } - randomTurn(); - } - - /* - * Turns left or right 45 degrees at random. - */ - public void randomTurn() { - if (Math.random() < 0.5) { - turn(-45); - } else { - turn(45); - } - } - - /* - * Turns the given number of degrees. - */ - public void turn(int degrees) { - setDirection(getDirection() + degrees); - } - - /* - * Checks whether the termite can move. - * Note: unlike most Bugs, termites can't move onto flowers. - */ - public boolean canMove() { - Location next = getNextLocation(); - return (isValid(next) && getNeighbor() == null); - } - - - /* - * Moves in the direction the termite is facing. - * Drops a flower, if one has been dropped, in the old location. - */ - public void move() { - Location next = getNextLocation(); - if (isValid(next)) { - moveTo(next); - } else { - removeSelfFromGrid(); - } - if (dropped != null) { - dropped.putSelfInGrid(getGrid(), dropLoc); - dropped = null; - } - } - - /* - * Returns true if the termite has a flower. - */ - public boolean hasFlower() { - return flower != null; - } - - /* - * Returns true if the termite is facing a flower. - */ - public boolean seeFlower() { - return getNeighbor() instanceof Flower; - } - - /* - * Creates a flower unless the termite already has one. - */ - public void createFlower() { - if (hasFlower()) { - System.out.println("createFlower? You already have one!"); - return; - } - flower = new Flower(); - } - - /* - * Drops the flower in the termites current location. - * - * Note: only one Actor can occupy a grid cell, so the effect of - * dropping a flower is delayed until the termite moves. - */ - public void dropFlower() { - if (!hasFlower()) { - System.out.println("dropFlower? You don't have one!"); - return; - } - dropped = flower; - dropLoc = getLocation(); - flower = null; - } - - /* - * Throws the flower into the location the termite is facing. - * - */ - public void throwFlower() { - if (!hasFlower()) { - System.out.println("throwFlower? You don't have one!"); - return; - } - if (getNeighbor() != null) { - System.out.println("throwFlower? There's someone there!"); - return; - } - Location next = getNextLocation(); - if (!isValid(next)) { - System.out.println("throwFlower? Invalid location!"); - return; - } - flower.putSelfInGrid(getGrid(), next); - flower = null; - } - - /* - * Picks up the flower the termite is facing, if there is one, - * and if the termite doesn't already have a flower. - */ - public void pickUpFlower() { - if (hasFlower()) { - System.out.println("pickUpFlower? You already have one!"); - return; - } - Actor neighbor = getNeighbor(); - if (neighbor instanceof Flower) { - flower = (Flower) neighbor; - flower.removeSelfFromGrid(); - } else { - System.out.println("pickUpFlower? There is no flower!"); - } - } - - /* - * Gets the location the termite is facing. - */ - private Location getNextLocation() { - Location loc = getLocation(); - Location next = loc.getAdjacentLocation(getDirection()); - return next; - } - - /* - * Gets the contents of the location the termite is facing. - * Returns null if the location is empty or invalid. - */ - private Actor getNeighbor() { - Location next = getNextLocation(); - if (getGrid().isValid(next)) { - return getGrid().get(next); - } else { - return null; - } - } - - /* - * Checks whether a location is valid in the termite's grid. - */ - private boolean isValid(Location loc) { - return getGrid().isValid(loc); - } - -} diff --git a/code/MyGridWorld/TermiteRunner.java b/code/MyGridWorld/TermiteRunner.java deleted file mode 100644 index 88d7230..0000000 --- a/code/MyGridWorld/TermiteRunner.java +++ /dev/null @@ -1,48 +0,0 @@ -/* - * This program is part of an exercise in Think Java (thinkapjava.com) - * Copyright(c) 2011 Allen B. Downey (http://allendowney.com) - * - * It is based on the AP(r) Computer Science GridWorld Case Study. - * - * This code is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation. - * - * This code is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * @author Allen B. Downey - */ - -import info.gridworld.actor.ActorWorld; -import info.gridworld.actor.Flower; - -import java.awt.Color; - -/** - * This class runs a world that contains Termites.
- */ -public class TermiteRunner { - - public static void main(String[] args) { - ActorWorld world = new ActorWorld(); - makeFlowers(world, 20); - - Termite alice = new Termite(); - world.add(alice); - - Termite bob = new Termite(); - bob.setColor(Color.blue); - world.add(bob); - - world.show(); - } - - public static void makeFlowers(ActorWorld world, int n) { - for (int i=0; i"); // print a prompt - String s = stdin.readLine(); // get input - if (s == null) break; - // check if s is "quit" - // print s - } - } -\end{verbatim} - -\item Identify helper methods you think will be useful, and -write and debug them in isolation. Suggestions: {\tt isOperator}, -{\tt isOperand}, {\tt parseExpression}, {\tt performOperation}. - -\item We know we want to push {\tt int} values onto the stack -and pop them off, which means we will have to use a wrapper class. -Make sure you know how to do that, and test those operations in -isolation. Maybe make them helper methods. - -\item Write a version of {\tt evaluate} that only handles one -kind of operator (like addition). Test it in isolation. - -\item Connect your evaluator to your input/output loop. - -\item Add the other operations. - -\item Once you have code that works, you might want to evaluate -the structural design. How should you divide the code into -classes? What instance variables should the classes have? What -parameters should be passed around? - -\item In addition to making the design elegant, you should also -make the code bulletproof, meaning that is should not cause an -exception under any circumstances, even if the user types something -weird. - -\end{enumerate} -\end{exercise} - - - -\beforechapter -\chapter{Queues and Priority Queues} -\label{chap16} -\label{queue} -\index{queue} -\index{ADT!Queue} -\index{priority queue} -\index{ADT!Priority Queue} -\index{FIFO} -\index{queueing discipline} -\index{priority queueing} - -This chapter presents two ADTs: Queues and Priority Queues. -In real life a {\bf queue} is a line of customers waiting for service -of some kind. In most cases, the first customer in line is the -next customer to be served. There are exceptions, though. For -example, at airports customers whose flight is leaving imminently -are sometimes taken from the middle of the queue. Also, at -supermarkets a polite customer might let someone with only a -few items go first. - -The rule that determines who goes next is called a -{\bf queueing discipline}. The simplest queueing discipline is -called {\bf FIFO}, for ``first-in-first-out.'' The most general -queueing discipline is {\bf priority queueing}, in which each customer -is assigned a priority, and the customer with the highest priority -goes first, regardless of the order of arrival. The reason I -say this is the most general discipline is that the priority -can be based on anything: what time a flight leaves, how many -groceries the customer has, or how important the customer is. -Of course, not all queueing disciplines are ``fair,'' but -fairness is in the eye of the beholder. - -The Queue ADT and the Priority Queue ADT have the same set -of operations and their interfaces are the same. The difference -is in the semantics of the operations: a Queue uses the FIFO -policy, and a Priority Queue (as the name suggests) uses the -priority queueing policy. - -As with most ADTs, there are a number of ways to implement queues. -Since a queue is a collection of items, we can use any of the basic -mechanisms for storing collections, including arrays and lists. -Our choice among them will be based in part on their performance--- -how long it takes to perform the operations we want to perform--- -and partly on ease of implementation. - -\index{collection} - - -\section{The queue ADT} -\index{ADT!Queue} -\index{Queue ADT} -\index{implementation!Queue} -\index{queue!List implementation} - -The queue ADT is defined by the following operations: - -\begin{description} - -\item[constructor:] Create a new, empty queue. - -\item[{\tt add}:] Add a new item to the queue. - -\item[{\tt remove}:] Remove and return an item from the queue. The item -that is returned is the first one that was added. - -\item[{\tt isEmpty}:] Check whether the queue is empty. - -\end{description} - -Here is an implementation of a generic Queue, based on the -built-in class {\tt java.util.LinkedList}: - -\begin{verbatim} -public class Queue { - private LinkedList list; - - public Queue () { - list = new LinkedList (); - } - - public boolean isEmpty () { - return list.isEmpty (); - } - - public void add (Object obj) { - list.addLast (obj); - } - - public Object remove () { - return list.removeFirst (); - } -} -\end{verbatim} -% -A queue object contains a single instance variable, which is -the list that implements it. For each of the other methods, -all we have to do is invoke one of the methods from the -{\tt LinkedList} class. - -We can write the same implementation a bit more concisely by taking -advantage of inheritance: - -\begin{verbatim} -public class Queue extends LinkedList { - - public Object remove () { - return removeFirst (); - } -} -\end{verbatim} -% -Ok, it's a lot more concise! Because {\tt Queue} extends {\tt LinkedList}, -we inherit the constructor, {\tt isEmpty} and {\tt add}. We also -inherit {\tt remove}, but the version of {\tt remove} we get from -the {\tt LinkedList} class doesn't do what we want; it removes -the {\em last} element in the list, not the first. We fix that -by providing a new version of {\tt remove}, which {\bf overrides} -the version we inherited. - -The choice between these implementations depends on several factors. -Inheritance can make an implementation more concise, as long as -there are methods in the parent class that are useful. But it can -also make an implementation more difficult to read and debug, because -the methods for the new class are not in one place. Also, it can -lead to unexpected behavior, because the new class inherits {\em all} -the methods from the parent class, not just the ones you need. -That means that the second version of {\tt Queue} -provides methods like {\tt removeLast} and {\tt clear} that -are not part of the Queue ADT. -The first implementation is safer; -by declaring a {\tt private} -instance variable, it prevents -clients from invoking methods on the {\tt LinkedList}. - -\index{instance variable!private} -\index{private instance variable} - - -\section{Veneer} -\index{veneer} -\index{performance hazard} -\index{performance analysis} - -By using a LinkedList to implement a Queue, we were able -to take advantage of existing code; the code we wrote just -translates LinkedList methods into Queue methods. -An implementation like this is called a {\bf veneer}. In -real life, veneer is a thin coating of good quality wood used -in furniture-making to hide lower quality wood underneath. -Computer scientists use this metaphor to describe a small -piece of code that hides the details of an implementation and -provides a simpler, or more standard, interface. - -The Queue example demonstrates one of the nice things about a -veneer, which is that it is easy to implement, and one of -the dangers of using a veneer, which is the {\bf performance -hazard}! - -Normally when we invoke a method we are not concerned with the -details of its implementation. But there is one ``detail'' -we might want to know---the performance characteristics of the -method. How long does it take, as a function of the number -of items in the list? - -To answer that question, we have to know more about the -implementation. If we assume that {\tt LinkedList} is really -implemented as a linked list, then the -implementation of {\tt removeFirst} probably looks something -like this: - -\begin{verbatim} - public Object removeFirst () { - Object result = head; - if (head != null) { - head = head.next; - } - return result.cargo; - } -\end{verbatim} -% -We assume that {\tt head} refers to the first node in the list, -and that each node contains {\tt cargo} and a reference to -the next node in the list. - -There are no loops or function calls here, so the run time of this -method is pretty much the same every time. Such a method is called a -{\bf constant time} operation. In reality, the method might be -slightly faster when the list is empty, since it skips the body of the -conditional, but that difference is not significant. - -\index{constant time} - -The performance of {\tt addLast} is very different. Here is -a hypothetical implementation: - -\begin{verbatim} - public void addLast (Object obj) { - // special case: empty list - if (head == null) { - head = new Node (obj, null); - return; - } - Node last; - for (last = head; last.next != null; last = last.next) { - // traverse the list to find the last node - } - last.next = new Node (obj, null); - } -\end{verbatim} -% -The first conditional handles the special case of adding a new node to -an empty list. In this case, again, the run time does not depend on -the length of the list. In the general case, though, we have to -traverse the list to find the last element so we can make it refer to -the new node. - -This traversal takes time proportional to the length of the -list. Since the run time is a linear function of the length, -we would say that this method is {\bf linear time}. Compared to -constant time, that's very bad. - -\index{linear time} - - -\section{Linked Queue} -\index{queue!linked implementation} -\index{linked queue} - -We would like an implementation of the Queue ADT that can -perform all operations in constant time. One way to -accomplish that is to implement a {\bf linked queue}, which -is similar to a linked list in the sense that it is made up -of zero or more linked {\tt Node} objects. The difference -is that the queue -maintains a reference to both the first and the last node, -as shown in the figure. - -\myfig{figure=figs/queue1.eps} - -Here's what a linked {\tt Queue} implementation looks like: - -\begin{verbatim} -public class Queue { - public Node first, last; - - public Queue () { - first = null; - last = null; - } - - public boolean isEmpty () { - return first == null; - } -} -\end{verbatim} -% -So far it is straightforward. In an empty queue, both {\tt first} -and {\tt last} are null. To check whether a list is empty, we only -have to check one of them. - -{\tt add} is a little more complicated because we have to -deal with several special cases. - -\begin{verbatim} - public void add (Object obj) { - Node node = new Node (obj, null); - if (last != null) { - last.next = node; - } - last = node; - if (first == null) { - first = last; - } - } -\end{verbatim} -% -The first condition checks to make sure that {\tt last} refers -to a node; if it does then we have to make it refer to the new -node. - -The second condition deals with the special case where the list -was initially empty. In this case both {\tt first} and {\tt last} -refer to the new node. - -{\tt remove} also deals with several special cases. - -\begin{verbatim} - public Object remove () { - Node result = first; - if (first != null) { - first = first.next; - } - if (first == null) { - last = null; - } - return result; - } -\end{verbatim} -% -The first condition checks whether there were any nodes in -the queue. If so, we have to copy the {\tt next} node into -{\tt first}. The second condition deals with the special -case that the list is now empty, in which case we have to -make {\tt last} null. - -As an exercise, draw diagrams showing these operations in -both the normal case and in the special cases, and convince -yourself that they are correct. - -Clearly, this implementation is more complicated than the -veneer implementation, and it is more difficult to demonstrate -that it is correct. The advantage is that we have achieved -the goal: {\tt add} and {\tt remove} are constant -time operations. - - -\section{Circular buffer} -\index{queue!circular buffer implementation} -\index{circular buffer} -\index{buffer!circular} - -Another common implementation of a queue is a {\bf circular -buffer}. ``Buffer'' is a general name for a temporary storage -location, although it often refers to an array, as it does in -this case. What it means to say a buffer is ``circular'' should -become clear in a minute. - -The implementation of a circular buffer is similar to the array -implementation of a stack in Section~\ref{arraystack}. The -queue items are stored in an array, and we use indices to -keep track of where we are in the array. In the stack implementation, -there was a single index that pointed to the next available space. -In the queue implementation, there are two indices: {\tt first} -points to the space in the array that contains the first customer -in line and {\tt next} points to the next available space. - -The following figure shows a queue with two items (represented -by dots). - -\myfig{figure=figs/queue2.eps} - -There are two ways to think of the variables {\tt first} and -{\tt last}. Literally, they are integers, and their values are -shown in boxes on the right. Abstractly, though, they are -indices of the array, and so they are often drawn as arrows -pointing to locations in the array. The arrow representation is -convenient, but you should remember that the indices are not -references; they are just integers. - -Here is an incomplete array implementation of a queue: - -\begin{verbatim} -public class Queue { - public Object[] array; - public int first, next; - - public Queue () { - array = new Object[128]; - first = 0; - next = 0; - } - - public boolean isEmpty () { - return first == next; - } -\end{verbatim} -% -The instance variables and the constructor are straightforward, -although again we have the problem that we have to choose an -arbitrary size for the array. Later we will solve that problem, -as we did with the stack, by resizing the array if it gets full. - -The implementation of {\tt isEmpty} is a little surprising. You might -have thought that {\tt first == 0} would indicate an empty queue, but -that neglects the fact that the head of the queue is not necessarily -at the beginning of the array. Instead, we know that the queue is -empty if {\tt head} equals {\tt next}, in which case there are no -items left. Once we see the implementation of {\tt add} and {\tt -remove}, that condition will make more sense. - -\begin{verbatim} - public void add (Object item) { - array[next] = item; - next++; - } - - public Object remove () { - Object result = array[first]; - first++; - return result; - } -\end{verbatim} -% -{\tt add} looks very much like {\tt push} in Section~\ref{arraystack}; -it puts the new item in the next available space and then increments -the index. - -{\tt remove} is similar. It takes the first item from the queue -and then increments {\tt first} so it refers to the new head of the queue. -The following figure shows what the queue looks like after both -items have been removed. - -\myfig{figure=figs/queue3.eps} - -It is always true that {\tt next} points to an available space. -If {\tt first} catches up with {\tt next} and points to the same -space, then {\tt first} is referring to an ``empty'' location, -and the queue is empty. I put ``empty'' in quotation marks because -it is possible that the location that {\tt first} points to actually -contains a value (we do nothing to ensure that empty locations contain -{\tt null}); on the other hand, since we know the queue is empty, we -will never read this location, so we can think of it, abstractly, -as empty. - -\begin{exercise} -Modify {\tt remove} so that it returns {\tt null} -if the queue is empty. -\end{exercise} - -The next problem with this implementation is that eventually it -will run out of space. When we add an item we increment {\tt next} -and when we remove an item we increment {\tt first}, but we never -decrement either. What happens when we get to the end of the -array? - -The following figure shows the queue after we add four more items: - -\myfig{figure=figs/queue4.eps} - -The array is now full. There is no ``next available space,'' so there -is nowhere for {\tt next} to point. One possibility is that we could -resize the array, as we did with the stack implementation. But in that -case the array would keep getting bigger regardless of how many items -were actually in queue. A better solution is to wrap around to the -beginning of the array and reuse the spaces there. This ``wrap around'' -is the reason this implementation is called a circular buffer. - -One way to wrap the index around is to add a special case whenever -we increment an index: - -\begin{verbatim} - next++; - if (next == array.length) next = 0; -\end{verbatim} -% -A fancy alternative is to use the modulus operator: - -\begin{verbatim} - next = (next + 1) % array.length; -\end{verbatim} -% -Either way, we have one last problem to solve. How do we know -if the queue is {\em really} full, meaning that we cannot add -another item? The following figure shows what the queue looks -like when it is ``full.'' - -\myfig{figure=figs/queue5.eps} - -There is still one empty space in the array, but the queue is -full because if we add another item, then we have to increment -{\tt next} such that {\tt next == first}, and in that case it -would appear that the queue was empty! - -To avoid that, we sacrifice one space in the array. So how -can we tell if the queue is full? - -\begin{verbatim} - if ((next + 1) % array.length == first) -\end{verbatim} -% -And what should we do if the array is full? In that case resizing -the array is probably the only option. - -\begin{exercise} -Write an implementation of a queue using a circular buffer that -resizes itself when necessary. -\end{exercise} - - -\section{Priority queue} -\index{priority queue!ADT} -\index{ADT!Priority Queue} - -The Priority Queue ADT has the same interface as -the Queue ADT, but different semantics. The interface is: - -\begin{description} - -\item[constructor:] Create a new, empty queue. - -\item[{\tt add}:] Add a new item to the queue. - -\item[{\tt remove}:] Remove and return an item from the queue. The item -that is returned is the one with the highest priority. - -\item[{\tt isEmpty}:] Check whether the queue is empty. - -\end{description} - -The semantic difference is that the item that is removed from -the queue is not necessarily the first one that was added. Rather, -it is whatever item in the queue has the highest priority. -What the priorities are, and how they compare to each other, are not -specified by the Priority Queue implementation. It depends on -what the items are that are in the queue. - -For example, if the items in the queue have names, we might choose -them in alphabetical order. If they are bowling scores, we might -choose from highest to lowest, but if they are golf scores, we would -go from lowest to highest. - -\index{generic} -\index{data structure!generic} - -So we face a new problem. We would like an implementation of -Priority Queue that is generic---it should work with any kind -of object---but at the same time the code that implements Priority -Queue needs to have the ability to compare the objects it contains. - -We have seen a way to implement generic data structures using -{\tt Objects}, but that does not solve this problem, because -there is no way to compare {\tt Objects} unless we know what type -they are. - -The answer lies in a Java feature called a {\bf metaclass}. - - -\section {Metaclass} -\index{metaclass} -\index{Comparable} -\index{metaclass!Comparable} - -A metaclass is a set of classes that provide a common set of methods. -The metaclass definition specifies the requirements a class must -satisfy to be a member of the set. - -Often metaclasses have names that end in ``able'' to indicate -the fundamental capability the metaclass requires. For -example, any class that provides a method named {\tt draw} can -be a member of the metaclass named {\tt Drawable}. Any -class that contains a method named {\tt start} can be a member -of the metaclass {\tt Runnable}. - -Java provides a built-in metaclass that we can use in an -implementation of a Priority Queue. It is called {\tt Comparable}, -and it means what it says. Any class that belongs to the {\tt -Comparable} metaclass has to provide a method named {\tt compareTo} -that compares two objects and returns a value indicating whether one -is larger or smaller than the other, or whether they are the same. - -Many of the built-in Java classes are members of the {\tt Comparable} -metaclass, including numeric wrapper classes like {\tt Integer} -and {\tt Double}. - -In the next section I will show how to write an ADT that manipulates -a metaclass. Then we will see how to write a new -class that belongs to an existing metaclass. In the -next chapter we will see how to define a new metaclass. - - -\section{Array implementation of Priority Queue} -\index{implementation!Priority Queue} -\index{priority queue!array implementation} - -In the implementation of the Priority Queue, every time we specify -the type of the items in the queue, we specify the metaclass -{\tt Comparable}. For example, the instance variables are an -array of {\tt Comparables} and an integer: - -\begin{verbatim} -public class PriorityQueue { - private Comparable[] array; - private int index; -} -\end{verbatim} -% -As usual, {\tt index} is the index of the next available location in the -array. The instance variables are declared {\tt private} so that -other classes cannot have direct access to them. - -\index{instance variable!private} -\index{private instance variable} - -The constructor and {\tt isEmpty} are similar to what we have seen -before. The initial size of the array is arbitrary. - -\begin{verbatim} - public PriorityQueue () { - array = new Comparable [16]; - index = 0; - } - - public boolean isEmpty () { - return index == 0; - } -\end{verbatim} -% -{\tt add} is similar to {\tt push}: - -\begin{verbatim} - public void add (Comparable item) { - if (index == array.length) { - resize (); - } - array[index] = item; - index++; - } -\end{verbatim} -% -The only substantial method in the class is {\tt remove}, which has -to traverse the array to find and remove the largest item: - -\begin{verbatim} - public Comparable remove () { - if (index == 0) return null; - - int maxIndex = 0; - - // find the index of the item with the highest priority - for (int i=1; i 0) { - maxIndex = i; - } - } - Comparable result = array[maxIndex]; - - // move the last item into the empty slot - index--; - array[maxIndex] = array[index]; - return result; - } -\end{verbatim} -% -As we traverse the array, {\tt maxIndex} keeps track of the -index of the largest element we have seen so far. What it -means to be the ``largest'' is determined by {\tt compareTo}. -In this case the {\tt compareTo} method is provided by the -{\tt Integer} class, and it does what we expect---larger -(more positive) numbers win. - - -\section {A Priority Queue client} -\index{client} -\index{metaclass} - -The implementation of Priority Queue is written entirely -in terms of {\tt Comparable} objects, but there is no -such thing as a {\tt Comparable} object! Go ahead, try -to create one: - -\begin{verbatim} - Comparable comp = new Comparable (); // ERROR -\end{verbatim} -% -You'll get a compile-time message that says something like -``java.lang.Comparable is an interface. It can't be instantiated.'' -In Java, metaclasses are called {\bf interfaces}. I have -avoided this word so far because it also means several other -things, but now you have to know. - -\index{interface} - -Why can't metaclasses be instantiated? Because a metaclass -only specifies requirements (you must have a {\tt compareTo} -method); it does not provide an implementation. - -To create a {\tt Comparable} object, you have to create one of the -objects that belongs to the {\tt Comparable} set, like {\tt Integer}. -Then you can use that object anywhere a {\tt Comparable} is called -for. - -\begin{verbatim} - PriorityQueue pq = new PriorityQueue (); - Integer item = new Integer (17); - pq.add (item); -\end{verbatim} -% -This code creates a new, empty Priority Queue and a new {\tt Integer} -object. Then it adds the {\tt Integer} into the queue. {\tt -add} is expecting a {\tt Comparable} as a parameter, so it is -perfectly happy to take an {\tt Integer}. If we try to pass a {\tt -Rectangle}, which does not belong to {\tt Comparable}, we get a -compile-time message like, ``Incompatible type for method. Explicit -cast needed to convert java.awt.Rectangle to java.lang.Comparable.'' - -That's the compiler telling us that if we want to make that conversion, -we have to do it explicitly. We might try to do what it says: - -\begin{verbatim} - Rectangle rect = new Rectangle (); - pq.add ((Comparable) rect); -\end{verbatim} -% -But in that case we get a run-time error, a {\tt ClassCastException}. -When the {\tt Rectangle} tries to pass as a {\tt Comparable}, the -run-time system checks whether it satisfies the requirements, and -rejects it. So that's what we get for following the compiler's advice. - -\index{ClassCastException} -\index{exception!ClassCastException} - -To get items out of the queue, we have to reverse the process: - -\begin{verbatim} - while (!pq.isEmpty ()) { - item = (Integer) pq.remove (); - System.out.println (item); - } -\end{verbatim} -% -This loop removes all the items from the queue and prints them. -It assumes that the items in the queue are {\tt Integers}. -If they were not, we would get a {\tt ClassCastException}. - - -\section{The {\tt Golfer} class} -\index{Golfer} -\index{class!Golfer} -\index{metaclass!implementing} -\index{Comparable} - -Finally, let's look at how we can make a new class that belongs to -{\tt Comparable}. As an example of something with an unusual definition -of ``highest'' priority, we'll use golfers: - -\begin{verbatim} -public class Golfer implements Comparable { - String name; - int score; - - public Golfer (String name, int score) { - this.name = name; - this.score = score; - } -} -\end{verbatim} -% -The class definition and the constructor are pretty much the same as -always; the difference is that we have to declare that {\tt Golfer -implements Comparable}. In this case the keyword {\tt implements} -means that {\tt Golfer} implements the interface specified by {\tt -Comparable}. - -If we try to compile {\tt Golfer.java} at -this point, we get something like ``class Golfer must be declared -abstract. It does not define int compareTo(java.lang.Object) from -interface java.lang.Comparable.'' In other words, to be a {\tt Comparable}, -{\tt Golfer} has to provide a method named {\tt compareTo}. So -let's write one: - -\begin{verbatim} - public int compareTo (Object obj) { - Golfer that = (Golfer) obj; - - int a = this.score; - int b = that.score; - - // for golfers, low is good! - if (ab) return -1; - return 0; - } -\end{verbatim} -% -Two things here are a little surprising. First, the parameter -is an {\tt Object}. That's because in general the caller doesn't -know what type the objects are that are being compared. For -example, in {\tt PriorityQueue.java} when we invoke {\tt compareTo}, -we pass a {\tt Comparable} as a parameter. We don't have to -know whether it is an {\tt Integer} or a {\tt Golfer} or whatever. - -Inside {\tt compareTo} we have to convert the parameter from -an {\tt Object} to a {\tt Golfer}. As usual, there is a risk -when we do this kind of cast: if we cast to the wrong type we -get an exception. - -Finally, we can create some golfers: - -\begin{verbatim} - Golfer tiger = new Golfer ("Tiger Woods", 61); - Golfer phil = new Golfer ("Phil Mickelson", 72); - Golfer hal = new Golfer ("Hal Sutton", 69); -\end{verbatim} -% -And put them in the queue: - -\begin{verbatim} - pq.add (tiger); - pq.add (phil); - pq.add (hal); -\end{verbatim} -% -When we pull them out: - -\begin{verbatim} - while (!pq.isEmpty ()) { - golfer = (Golfer) pq.remove (); - System.out.println (golfer); - } -\end{verbatim} -% -They appear in descending order (for golfers): - -\begin{verbatim} - Tiger Woods 61 - Hal Sutton 69 - Phil Mickelson 72 -\end{verbatim} -% -When we switched from {\tt Integers} to {\tt Golfers}, we didn't -have to make any changes in {\tt PriorityQueue.java} at all. So -we succeeded in maintaining a barrier between {\tt PriorityQueue} -and the classes that use it, allowing us to reuse the code without -modification. Furthermore, we were able to give the client code -control over the definition of {\tt compareTo}, making this -implementation of {\tt PriorityQueue} more versatile. - - - -\section{Glossary} -\index{queue} -\index{queueing discipline} -\index{FIFO} -\index{priority queue} -\index{veneer} -\index{constant time} -\index{linear time} -\index{performance hazard} -\index{linked queue} -\index{circular buffer} -\index{metaclass} -\index{interface} - -\begin{description} - -\item[queue:] An ordered set of objects waiting for a service of -some kind. - -\item[queueing discipline:] The rules that determine which member -of a queue is removed next. - -\item[FIFO:] ``first in, first out,'' a queueing discipline in which -the first member to arrive is the first to be removed. - -\item[priority queue:] A queueing discipline in which -each member has a priority determined by external factors. -The member with the highest priority is the first to be removed. - -\item[Priority Queue:] An ADT that defines the operations one -might perform on a priority queue. - -\item[veneer:] A class definition that implements an ADT with -method definitions that are invocations of other methods, sometimes -with simple transformations. The veneer does no significant work, -but it improves or standardizes the interface seen by the client. - -\item[performance hazard:] A danger associated with a veneer that -some of the methods might be implemented inefficiently in a way -that is not apparent to the client. - -\item[constant time:] An operation whose run time does not -depend on the size of the data structure. - -\item[linear time:] An operation whose run time is a linear -function of the size of the data structure. - -\item[linked queue:] An implementation of a queue using a linked -list and references to the first and last nodes. - -\item[circular buffer:] An implementation of a queue using an -array and indices of the first element and the next available space. - -\item[metaclass:] A set of classes. The metaclass specification -lists the requirements a class must satisfy to be included in the set. - -\item[interface:] The Java word for a metaclass. Not to be -confused with the more broad meaning of the word interface. - - -\end{description} - - -\section{Exercises} - -\begin{exercise} -This question is based on Exercise~\ref{ex.rational}. - -Write a {\tt compareTo} method for the {\tt Rational} class -that would allow {\tt Rational} to implement {\tt Comparable}. -Hint: don't forget that the parameter is an {\tt Object}. -\end{exercise} - - -\begin{exercise} -Write a class definition for {\tt SortedList}, which extends -{\tt LinkedList}. A SortedList is similar to a LinkedList; the -difference is that the elements have to be Comparable, and the -list is sorted in decreasing order. - -Write an object method for {\tt SortedList} -called {\tt add} that takes a Comparable as a parameter and that -adds the new object into the list, -at the appropriate place so -that the list stays sorted. - -If you want, you can write a helper method in the {\tt Node} class. -\end{exercise} - - -\begin{exercise} -Write an object method for the {\tt LinkedList} class -named {\tt maximum} that can be invoked on a -{\tt LinkedList} object, and that returns the largest cargo -object in the list, or null if the list is empty. - -You can assume that every cargo element belongs to a class that -belongs to the metaclass {\tt Comparable}, and that any two -elements can be compared to each other. -\end{exercise} - - - -\begin{exercise} -Write an implementation of a Priority Queue using -a linked list. There are three ways you might proceed: - -\begin{itemize} - -\item A Priority Queue might contain a LinkedList object as an -instance variable. - -\item A Priority Queue might contain a reference to the -first Node object in a linked list. - -\item A Priority Queue might extend (inherit from) the existing -LinkedList class. - -\end{itemize} -% -Think about the pros and cons of each and choose one. Also, you -can choose whether to keep the list sorted (slow add, fast remove) -or unsorted (slow remove, fast add). -\end{exercise} - - -\begin{exercise} -An event queue is a data structure that keeps track of a set -of events, where each event has a time associated with it. -The ADT is: - -\begin{description} - -\item[constructor:] make a new, empty event queue - -\item[{\tt add}:] put a new event in the queue. The parameters are -the event, which is an Object, and the time the event occurs, which -is a {\tt Date} object. The event Object must not be null. - -\item[{\tt nextTime}:] return the {\tt Date} at which the next event -occurs, where the ``next'' event is the one in the queue with the -earliest time. Do not remove the event from the queue. Return -null if the queue is empty. - -\item[{\tt nextEvent}:] return the next event (an {\tt Object}) from -the queue and remove it from the queue. Return null if the queue is -empty. - -%\item[{\tt events}:] return an {\tt Iterator} that includes all the -%events in the queue, ordered from lowest to highest. Do not modify -%the queue. - -\end{description} - -The {\tt Date} class is defined in {\tt java.util} and it implements -{\tt Comparable}. According to the documentation, its {\tt compareTo} -method returns ``the value 0 if the argument Date is equal to this -Date; a value less than 0 if this Date is before the Date argument; -and a value greater than 0 if this Date is after the Date argument.'' - -Write an implementation of an event queue using the PriorityQueue -ADT. You should not make any assumptions about how the PriorityQueue -is implemented. - -HINT: create a class named {\tt Event} that contains a {\tt Date} -and an event {\tt Object}, and that implements {\tt Comparable} -appropriately. -\end{exercise} - - -\beforechapter -\chapter{Trees} -\label{chap17} -\index{tree} -\index{ADT} -\index{data structure} - -\section{A tree node} -\index{node} -\index{tree node} -\index{cargo} -\index{embedded reference} -\index{implementation!Tree} -\index{binary tree} - -Like lists, trees are made up of nodes. A common kind of tree is -a {\bf binary tree}, in which each node contains a reference to two -other nodes (possibly null). The class definition looks like this: - -\begin{verbatim} -public class Tree { - Object cargo; - Tree left, right; -} -\end{verbatim} -% -Like list nodes, tree nodes contain cargo: in this case a generic {\tt -Object}. The other instance variables are named {\tt left} and {\tt -right}, in accordance with a standard way to represent trees -graphically: - -\myfig{figure=figs/tree1.eps} - -The top of the tree (the node referred to by {\tt tree}) is -called the {\bf root}. In keeping with the tree -metaphor, the other nodes are called branches and the nodes -at the tips with null references are called {\bf leaves}. It -may seem odd that we draw the picture with the root at the top -and the leaves at the bottom, but that is not the strangest thing. - -\index{root node} -\index{leaf node} -\index{parent node} -\index{child node} -\index{level} - -To make things worse, computer scientists mix in yet another -metaphor: the family tree. The top node is sometimes called -a {\bf parent} and the nodes it refers to are its {\bf children}. -Nodes with the same parent are called {\bf siblings}, and so on. - -Finally, there is also a geometric vocabulary for taking -about trees. I already mentioned left and right, but there is -also ``up'' (toward the parent/root) and down (toward the -children/leaves). Also, all the nodes that are the same -distance from the root comprise a {\bf level} of the tree. - -I don't know why we need three metaphors for talking about trees, -but there it is. - - -\section {Building trees} -\index{tree!linked implementation} - -The process of assembling tree nodes is similar -to the process of assembling lists. -We have a constructor for tree nodes that initializes the instance -variables. - -\begin{verbatim} - public Tree (Object cargo, Tree left, Tree right) { - this.cargo = cargo; - this.left = left; - this.right = right; - } -\end{verbatim} -% -We allocate the child nodes first: - -\begin{verbatim} - Tree left = new Tree (new Integer(2), null, null); - Tree right = new Tree (new Integer(3), null, null); -\end{verbatim} -% -We can create the parent node and link it to the children -at the same time: - -\begin{verbatim} - Tree tree = new Tree (new Integer(1), left, right); -\end{verbatim} -% -This code produces the state shown in the previous figure. - - -\section {Traversing trees} -\index{tree!traversal} -\index{traverse} - -The most natural -way to traverse a tree is recursively. For example, to -add up all the integers in a tree, we could write this class -method: - -\begin{verbatim} - public static int total (Tree tree) { - if (tree == null) return 0; - Integer cargo = (Integer) tree.cargo; - return cargo.intValue() + total (tree.left) + total (tree.right); - } -\end{verbatim} -% -This is a class method because we would like to use {\tt null} to -represent the empty tree, and make the empty tree the base case of the -recursion. If the tree is empty, the method returns {\tt 0}. -Otherwise it makes two recursive calls to find the total value of its -two children. Finally, it adds in its own cargo and returns the -total. - -\index{tree!empty} - -Although this method works, there is some difficulty fitting it into -an object-oriented design. -It should not appear in the {\tt Tree} class because it -requires the cargo to be {\tt Integer} objects. If we make that -assumption in {\tt Tree.java} then we lose the advantages of a generic -data structure. - -On the other hand, this code accesses the instance variables -of the {\tt Tree} nodes, so it ``knows'' more than it should about -the implementation of the tree. If we change that implementation -later this code will break. - -Later in this chapter we will develop ways to solve this problem, -allowing client code to traverse trees containing any kinds of objects -without breaking the abstraction barrier between the client code and -the implementation. Before we get there, let's look at an -application of trees. - - -\section {Expression trees} -\index{tree!expression} -\index{expression tree} -\index{postfix} -\index{infix} - -A tree is a natural way to represent the structure of a -mathematical expression. -Unlike other notations, it can represent the computation unambiguously. -For example, the infix expression {\tt 1 + 2 * 3} is ambiguous unless -we know that the multiplication happens before the addition. - -The following figure represents the same computation: - -\myfig{figure=figs/tree2.eps} - -The nodes can be operands like {\tt 1} and {\tt 2} or operators -like {\tt +} and {\tt *}. Operands are leaf nodes; operator nodes -contain references to their operands (all of these operators -are {\bf binary}, meaning they have exactly two operands). - -Looking at this figure, there is no question what the order of -operations is: the multiplication happens first in order to compute -the first operand of the addition. - -Expression trees like this have many uses. The example we are -going to look at is translation from one format (postfix) to -another (infix). Similar trees are used inside compilers to parse, -optimize and translate programs. - - -\section {Traversal} -\index{tree!traversal} -\index{traverse} -\index{recursion} -\index{preorder} -\index{postorder} -\index{inorder} - -I already pointed out that recursion provides a natural way to -traverse a tree. We can print the contents of an expression tree -like this: - -\begin{verbatim} - public static void print (Tree tree) { - if (tree == null) return; - System.out.print (tree + " "); - print (tree.left); - print (tree.right); - } -\end{verbatim} -% -In other words, to print a tree, first print the contents of -the root, then print the entire left subtree, then print the -entire right subtree. This way of traversing a tree is called -a {\bf preorder}, because the contents of the root appear before -the contents of the children. - -For the example expression the output is {\tt + 1 * 2 3}. This -is different from both postfix and infix; it is a new notation called -{\bf prefix}, in which the operators appear before their operands. - -You might suspect that if we traverse the tree in a -different order we get the expression in a different -notation. For example, if we print the subtrees first, and then -the root node: - -\begin{verbatim} - public static void printPostorder (Tree tree) { - if (tree == null) return; - printPostorder (tree.left); - printPostorder (tree.right); - System.out.print (tree + " "); - } -\end{verbatim} -% -We get the expression in postfix ({\tt 1 2 3 * +})! As the -name of the method implies, this order of traversal -is called {\bf postorder}. Finally, to traverse a tree {\bf inorder}, -we print the left tree, then the root, then the right tree: - -\begin{verbatim} - public static void printInorder (Tree tree) { - if (tree == null) return; - printInorder (tree.left); - System.out.print (tree + " "); - printInorder (tree.right); - } -\end{verbatim} -% -The result is {\tt 1 + 2 * 3}, which is the expression in infix. - -To be fair, I have to point out that I omitted an -important complication. Sometimes when we write an expression -in infix we have to use parentheses to preserve the order of -operations. So an inorder traversal is not quite sufficient to -generate an infix expression. - -Nevertheless, with a few improvements, the expression tree -and the three recursive traversals provide -a general way to translate expressions from one format to -another. - - -\section {Encapsulation} -\index{encapsulation} -\index{client} -\index{provider} -\index{metaclass} - -As I mentioned before, there is a problem with the way we have been -traversing trees: it breaks down the barrier between the client code -(the application that uses the tree) and the provider code (the Tree -implementation). Ideally, tree code should be general; it shouldn't -know anything about expression trees. And the code that generates and -traverses the expression tree shouldn't know about the implementation -of the trees. This design criterion is called {\bf object -encapsulation} to distinguish it from the encapsulation we saw in -Section~\ref{encapsulation}, which we might call {\bf method -encapsulation}. - -In the current version, the {\tt Tree} code knows too much about -the client. Instead, the {\tt Tree} class should provide -the general capability of traversing a tree in various ways. As -it traverses, it should perform operations on each node that are -specified by the client. - - -\index{Visitable} -\index{metaclass!Visitable} - -To facilitate this separation of interests, we will -create a new metaclass, called {\tt Visitable}. The items -stored in a tree will be required to be visitable, which means -that they define a method named {\tt visit} that does whatever -the client wants done to each node. That way the -Tree can perform the traversal and the client can perform -the node operations. - -Here are the steps we have to perform to wedge a metaclass -between a client and a provider: - -\begin{enumerate} - -\item Define a metaclass that specifies the methods -the provider code will need to invoke on its components. - -\item Write the provider code in terms of the new metaclass, -as opposed to generic {\tt Objects}. - -\item Define a class that belongs to the metaclass -and that implements the required methods -as appropriate for the client. - -\item Write the client code to use the new class. - -\end{enumerate} - -The next few sections demonstrate these steps. - - -\section {Defining a metaclass} -\index{metaclass!defining} -\index{interface} - -There are actually two ways to implement a metaclass in Java, -an an {\bf interface} or as an {\bf abstract class}. The differences -between them aren't important for now, so we'll start by -defining an interface. - -An interface definition looks a lot like a class -definition, with two differences: - -\begin{itemize} - -\item The keyword {\tt class} is replaced with {\tt interface}, and - -\item The method definitions have no bodies. - -\end{itemize} - -An interface definition specifies the methods a class has to -implement in order to be in the metaclass. The specification -includes the name, parameter -types, and return type of each method. - -The definition of {\tt Visitable} is - -\begin{verbatim} -public interface Visitable { - public void visit (); -} -\end{verbatim} -% -That's it! The definition of {\tt visit} looks like any other -method definition, except that it has no body. This definition -specifies that any class that implements {\tt Visitable} has to have -a method named {\tt visit} that takes no parameters and that returns -{\tt void}. - -\index{body!method} - -Like other class definitions, interface definitions go in a file -with the same name as the class (in this case {\tt Visitable.java}). - - -\section {Implementing a metaclass} -\index{metaclass!implementing} -\index{Token class} -\index{class!Token} - -If we are using an expression tree to generate infix, then -``visiting'' a node means printing its contents. Since the -contents of an expression tree are tokens, we'll create a new -class called {\tt Token} that implements {\tt Visitable} - -\begin{verbatim} -public class Token implements Visitable { - String str; - - public Token (String str) { - this.str = str; - } - - public void visit () { - System.out.print (str + " "); - } -} -\end{verbatim} -% -When we compile this class definition (which is in a file named {\tt -Token.java}), the compiler checks whether the methods provided satisfy -the requirements specified by the metaclass. If not, it will -produce an error message. For example, if we misspell the name of the -method that is supposed to be {\tt visit}, we might get -something like, ``class Token must be declared abstract. It does not -define void visit() from interface Visitable.'' This is one of -many error messages where the solution suggested by the compiler -is wrong. When it says the class ``must be declared abstract,'' -what it means is that you have to fix the class so that it implements -the interface properly. Sometimes I think the people who write -these messages should be beaten. - -The next step is to modify the parser to put {\tt Token} objects -into the tree instead of {\tt Strings}. Here is a small example: - -\begin{verbatim} - String expr = "1 2 3 * +"; - StringTokenizer st = new StringTokenizer (expr, " +-*/", true); - String token = st.nextToken(); - Tree tree = new Tree (new Token (token), null, null)); -\end{verbatim} -% -This code takes the first token in the string and wraps it in -a {\tt Token} object, then puts the {\tt Token} into a tree node. -If the {\tt Tree} requires the cargo to be {\tt Visitable}, it -will convert the {\tt Token} to be a {\tt Visitable} object. -When we remove the {\tt Visitable} from the tree, we will have -to cast it back into a {\tt Token}. - -\begin{exercise} -Write a version of {\tt printPreorder} called -{\tt visitPreorder} that traverses the tree and invokes -{\tt visit} on each node in preorder. -\end{exercise} - -The flow of execution for methods like {\tt visitPreorder} is -unusual. The client invokes a method provided by the Tree -implementation, and then the tree implementation invokes a -method provided by the client. This pattern is called a -{\bf callback}; it is a good way to make provider code more -general without breaking down the abstraction barrier. - -\index{callback} - - -\section {The {\tt Vector} class} -\label{vector} -\index{Vector class} -\index{class!Vector} - -The {\tt Vector} is a built-in Java class in the {\tt java.util} -package. It is an implementation of an array of {\tt Objects}, -with the added feature that it can resize itself automatically, -so we don't have to. - -Before using the {\tt Vector} class, you should understand -a few concepts. Every {\tt Vector} has a -capacity, which is the amount of space that has been allocated -to store values, and a size, which is the number of values that -are actually in the vector. - -The following figure is a simple diagram of a {\tt Vector} -that contains three elements, but it has a capacity of seven. - -\myfig{figure=figs/vector.eps} - -There are two sets of methods for accessing the elements of -a vector. They provide different semantics and different -error-checking capabilities, and they are easy to get confused. - -The simpler accessors methods are {\tt get} and {\tt set}, which -provide semantics similar to the array index operator {\tt []}. -{\tt get} takes an integer index and returns the element at the -indicated position. {\tt set} takes an index and an element, -and stores the new element at the indicated position, replacing -the existing element. - -{\tt get} and {\tt set} do not change the size of the vector (number -of elements). It is the responsibility of the client code to make -sure that the vector has sufficient size before invoking {\tt set} or -{\tt get}. The {\tt size} method returns the number of elements in -the Vector. If you try to access an element that does not exist (in -this case the elements with indices 3 through 6), you will get an {\tt -ArrayIndexOutOfBounds} exception. - -\index{exception!ArrayIndexOutOfBounds} -\index{ArrayIndexOutOfBounds} - -The other set of methods includes several versions -of {\tt add} and {\tt remove}. These methods change the size -of the Vector and, if necessary, the capacity. One version -of {\tt add} takes an element as a parameter and adds it to the -end of the Vector. This method is safe in the sense that it -will not cause an exception. - -Another version of {\tt add} -takes an index and an element and, like {\tt set}, it puts -the new element at the given position. The difference is -that {\tt add} doesn't replace the existing element; it -increases the size of the Vector and shifts elements to the -right to make room for the new one. Thus, the invocation -{\tt v.add (0, elt)} add the new element at the beginning -of the Vector. Unfortunately, this method is neither -safe nor efficient; it can cause an {\tt ArrayIndexOutOfBounds} -exception and, in most implementations, it is linear time -(proportional to the size of the Vector). - -Most of the time the client doesn't have to worry about -capacity. Whenever the size of the {\tt Vector} changes, -the capacity is updated automatically. -For performance reasons, some applications take -control of this function, which is why there are additional methods -for increasing and decreasing capacity. - -Because the client code has no access to the implementation of -a vector, it is not clear how we should traverse one. Of course, -one possibility is to use a loop variable as an index into the -vector: - -\begin{verbatim} - for (int i=0; i a} and -{\tt a > b}. - -Now that the subtree is reheapified, we can work our way up -the tree until we reach the root. - - -\section {Performance of heaps} -\index{Heap!analysis} -\index{analysis!Heap} - -For both add and remove, we perform a constant time operation -to do the actual addion and removal, but then we have to -reheapify the tree. In one case we start at the root and work -our way down, comparing items and then recursively reheapifying -one of the subtrees. In the other case we start at a leaf and -work our way up, again comparing elements at each level of -the tree. - -As usual, there are several operations we might want to count, -like comparisons and swaps. Either choice would work; the -real issue is the number of levels of the tree we examine -and how much work we do at each level. In both cases we -keep examining levels of the tree until we restore the heap -property, which means we might only visit one, or in the worst -case we might -have to visit them all. Let's consider the worst case. - -At each level, we perform only constant time operations -like comparisons and swaps. So the total amount of work is -proportional to the number of levels in the tree, a.k.a. -the height. - -So we might say that these operations are linear with respect to -the height of the tree, but the ``problem size'' we are interested -in is not height, it's the number of items in the heap. - -As a function of $n$, the height of the tree is $log_2 n$. -This is not true for all trees, but it is true for complete -trees. To see why, think of the number of nodes on each level -of the tree. The first level contains 1, the second contains 2, -the third contains 4, and so on. The $i$th level contains -$2^i$ nodes, and the total number in all levels up to $i$ is -$2^i - 1$. In other words, $2^h = n$, which means that -$h = log_2 n$. - -\index{logarithmic time} - -Thus, both add and remove take {\bf logarithmic} time. -To add and remove $n$ items takes time proportional to -$n \log_2 n$. - - -\section{Heapsort} -\index{heapsort} -\index{sorting} -\index{analysis!heapsort} - -The result of the previous section suggests yet another algorithm -for sorting. Given $n$ items, we add them into a Heap and -then remove them. Because of the Heap semantics, they come -out in order. We have already shown that this algorithm, which -is called {\bf heapsort}, takes time proportional to $n \log_2 n$, -which is better than selection sort and the same as mergesort. - -As the value of $n$ gets large, we expect heapsort to be faster -than selection sort, but performance analysis gives us no way -to know whether it will be faster than mergesort. We would say -that the two algorithms have the same {\bf order of growth} because -their runtimes grow with the same functional form. Another way to -say the same thing is that they belong to the same {\bf complexity -class}. - -\index{big-O notation} -\index{complexity class} -\index{order of growth} -\index{constant time} -\index{linear time} -\index{quadratic time} -\index{logarithmic time} - -Complexity classes are sometimes written in ``big-O notation''. -For example, $\mathcal{O} (n^2)$, pronounced ``oh of -en squared'' is the set of all functions that grow no faster -than $n^2$ for large values of $n$. To say that an algorithm -is $\mathcal{O} (n^2)$ is the same as saying that it -is quadratic. The other complexity classes we have seen, -in decreasing order of performance, are: - -\vspace {0.2in} -\begin{tabular}{ll} -$\mathcal{O} (1)$ & constant time \\ -$\mathcal{O} (\log n)$ & logarithmic \\ -$\mathcal{O} (n)$ & linear \\ -$\mathcal{O} (n \log n)$ & ``en log en'' \\ -$\mathcal{O} (n^2)$ & quadratic \\ -$\mathcal{O} (2^n)$ & exponential -\end{tabular} -\vspace {0.2in} - -So far none of the algorithms we have looked at are {\bf exponential}. -For large values of $n$, these algorithms quickly become impractical. -Nevertheless, the phrase ``exponential growth'' appears frequently in -even non-technical language. It is frequently misused so I wanted to -include its technical meaning. - -People often use ``exponential'' to describe any curve that is -increasing and accelerating (that is, one that has positive slope and -curvature). Of course, there are many other curves that fit this -description, including quadratic functions (and higher-order -polynomials) and even functions as undramatic as $n \log n$. Most -of these curves do not have the (often detrimental) explosive -behavior of exponentials. - - -\section{Glossary} -\index{selection sort} -\index{mergesort} -\index{heapsort} -\index{complexity class} -\index{order of growth} -\index{overhead} - -\begin{description} - -\item[selection sort:] The simple sorting algorithm in Section~\ref{sorting}. - -\item[mergesort:] A better sorting algorithm from Section~\ref{mergesort}. - -\item[heapsort:] Yet another sorting algorithm. - -\item[complexity class:] A set of algorithms whose performance -(usually run time) has the same order of growth. - -\item[order of growth:] A set of functions with the same leading-order -term, and therefore the same qualitative behavior for large values -of $n$. - -\item[overhead:] Additional time or resources consumed by a program -performing operations other than the abstract operations considered -in performance analysis. - -\end{description} - - -\section{Exercises} - -\begin{exercise} -\begin{enumerate} - -\item Draw the Heap represented by the following array. - -\myfig{figure=figs/heap.eps} - -\item Show what the array would look like after the value -68 is added to the Heap. - -\end{enumerate} -\end{exercise} - -\begin{exercise} -Assume that there are $n$ elements in a Heap. To find -the median value of the elements, we could remove $n/2-1$ elements -and then return the value of the $n/2$-eth element. Then we -would have to put $n/2$ elements back into the Heap. What would -be the order of growth of this algorithm? -\end{exercise} - -\begin{exercise} -How many times will the following loop -execute? Express your answer as a function of {\tt n}: - -\begin{verbatim} -while (n > 1) { - n = n / 2; -} -\end{verbatim} -\end{exercise} - - -\begin{exercise} -How many recursive calls will zippo make? Express -your answer as a function of {\tt x} or {\tt n} or both. - -\begin{verbatim} -public static double zippo (double x, int n) { - if (n == 0) return 1.0; - return x * zippo (x, n-1); -} -\end{verbatim} -\end{exercise} - - -\begin{exercise} -Write an implementation of a Heap based on the array implementation -of a tree. The run time of the {\tt add} and {\tt remove} operations -should be proportional to $\log n$, where $n$ is the number of elements -in the Heap. -\end{exercise} - - - -\beforechapter -\chapter{Maps} -\label{chap19} - -\section {Arrays, Vectors and Maps} -\index{array} -\index{Vector} -\index{map} - -Arrays are a generally useful data structure, but they suffer -from two important limitations: - -\begin{itemize} - -\item The size of the array does not depend on the number of -items in it. If the array is too big, it wastes space. If -it is too small it might cause an error, or we might have to -write code to resize it. - -\item Although the array can contain any type of item, the -indices of the array have to be integers. We cannot, for -example, use a String to specify an element of an array. - -\end{itemize} - -In Section~\ref{vector} we saw how the built-in {\tt Vector} class -solves the first problem. As the client code adds items the Vector -expands automatically. It is also possible to shrink a Vector so that -the capacity is the same as the current size. - -But {\tt Vectors} don't help with the second problem. The indices are -still integers. That's where the Map ADT comes in. A Map is similar -to a Vector; the difference is that it can use any object type as an -index. These generalized indices are called {\bf keys}. - -Just as you use an index to access a value in a Vector, you use a key -to access a value in a Map. Each key is associated with a value, -which is why Maps are sometimes called {\bf associative arrays}. The -association of a particular key with a particular value is called an -{\bf entry}. - -\index{dictionary} -\index{associative array} -\index{key} -\index{entry} -\index{index} - -A common example of a map is a dictionary, which maps -words (the keys) onto their definitions (the -values). Because of this example Maps are also sometimes called -Dictionaries. And, just for completeness, Maps are also sometimes -called Tables. - - -\section {The Map ADT} -\label{map} -\index{Map ADT} -\index{ADT!Map} - -Like the other ADTs we have looked at, Maps are defined -by the set of operations they support: - -\begin{description} - -\item[constructor:] Make a new, empty map. - -\item[{\tt put}:] Create an entry that associates a value with a key. - -\item[{\tt get}:] For a given key, find the corresponding value. - -\item[{\tt containsKey}:] Return {\tt true} if there -is an entry in the Map with the given Key. - -\item[{\tt keySet}]: Returns a Set that contains all the keys -in the Map. - -\end{description} - - -\section {The built-in HashMap} -\index{HashMap} -\index{class!HashMap} - -Java provides an implementation of the Map ADT called -{\tt java.util.HashMap}. -Later in the chapter we'll see why it is called {\tt HashMap}. - -To demonstrate the use of a HashMap we'll write -a short program that traverses a String and counts the number -of times each word appears. - -We'll create a new class called {\tt WordCount} that will -build the Map and then print its contents. Each -{\tt WordCount} object contains a {\tt HashMap} as an -instance variable: - -\begin{verbatim} -public class WordCount { - HashMap map; - - public WordCount () { - map = new HashMap (); - } -} -\end{verbatim} -% -The only public methods for {\tt WordCount} are {\tt processLine}, -which takes a String and adds its words to the Map, and {\tt print}, -which prints the results at the end. - -{\tt processLine} breaks the String into words using a -{\tt StringTokenizer} and passes each word to {\tt processWord}. - -\begin{verbatim} - public void processLine (String s) { - StringTokenizer st = new StringTokenizer (s, " ,."); - while (st.hasMoreTokens()) { - String word = st.nextToken(); - processWord (word.toLowerCase ()); - } - } -\end{verbatim} -% -The interesting work is in {\tt processWord}. - -\begin{verbatim} - public void processWord (String word) { - if (map.containsKey (word)) { - Integer i = (Integer) map.get (word); - Integer j = new Integer (i.intValue() + 1); - map.put (word, j); - } else { - map.put (word, new Integer (1)); - } - } -\end{verbatim} -% -If the word is already in the map, we {\tt get} its counter, -increment it, and {\tt put} the new value. Otherwise, we just -{\tt put} a new entry in the map with the counter set to {\tt 1}. - - -\index{The keySet} -\index{{\tt keySet}} -\index{traverse} - -To print the entries in the map, we need to be able to traverse the -keys in the map. Fortunately, {\tt HashMap} -provides a method, {\tt keySet}, that returns a {\tt Set} -object, and {\tt Set} provides a method {\tt iterator} that returns -(you guessed it) an Iterator. - -Here's how to use {\tt keySet} to print the contents of the {\tt -HashMap}: - -\begin{verbatim} -public void print () { - Set set = map.keySet(); - Iterator it = set.iterator(); - while (it.hasNext ()) { - String key = (String) it.next (); - Integer value = (Integer) map.get (key); - System.out.println ("{ " + key + ", " + value + " }"); - } -} -\end{verbatim} -% -Each of the elements of the Iterator is an Object, -but since we know they are keys, we typecast them to be Strings. -When we get the values from the Map, they are also Objects, -but we know they are counters, so we typecast them to be Integers. - -Finally, to count the words in a string: - -\begin{verbatim} - WordCount wc = new WordCount (); - wc.processLine ("you spin me right round baby " + - "right round like a record baby " + - "right round round round"); - wc.print (); -\end{verbatim} -% -The output is - -\begin{verbatim} -{ you, 1 } -{ round, 5 } -{ right, 3 } -{ me, 1 } -{ like, 1 } -{ baby, 2 } -{ spin, 1 } -{ record, 1 } -{ a, 1 } -\end{verbatim} -% -The elements of the Iterator are not in any particular order. -The only guarantee is that all the keys in the map will appear. - - -\section {A Vector implementation} -\index{implementation!Map} -\index{map!vector implementation} -\index{Entry} - -An easy way to implement the Map ADT is to use a {\tt Vector} -of entries, where each Entry is an object that contains a key -and a value. -A class definition for {\tt Entry} might look like -this: - -\begin{verbatim} -class Entry { - Object key, value; - - public Entry (Object key, Object value) { - this.key = key; - this.value = value; - } - - public String toString () { - return "{ " + key + ", " + value + " }"; - } -} -\end{verbatim} -% -Then the implementation of Map looks like this: - -\begin{verbatim} -public class MyMap { - Vector entries; - - public Map () { - entries = new Vector (); - } -} -\end{verbatim} - -To put a new entry in the map, we just {\tt add} a new -{\tt Entry} to the {\tt Vector}: - -\begin{verbatim} - public void put (Object key, Object value) { - entries.add (new Entry (key, value)); - } -\end{verbatim} - -Then to look up a key in the Map we have to traverse the -Vector and find an Entry with a matching -key: - -\begin{verbatim} - public Object get (Object key) { - Iterator it = entries.iterator (); - while (it.hasNext ()) { - Entry entry = (Entry) it.next (); - if (key.equals (entry.key)) { - return entry.value; - } - } - return null; - } -\end{verbatim} -% -The idiom to traverse a {\tt Vector} is the one we saw in -Section~\ref{iterator}. When we compare keys, we use deep -equality (the {\tt equals} method) rather than shallow -equality (the {\tt ==} operator). This allows the key class -to specify the definition of equality. In the example, the -keys are Strings, so {\tt get} will use the {\tt equals} -method in the {\tt String} class. - -\index{traverse} -\index{deep equality} -\index{quality!deep} -\index{shallow equality} -\index{quality!shallow} - -For most of the built-in classes, the {\tt equals} method -implements deep equality. For some classes, though, it is -not easy to define what that means. For example, see the -documentation of {\tt equals} for {\tt Doubles}. - -\index{equals} -\index{equality} - -Because {\tt equals} is an object method, this implementation -of {\tt get} does not work if a key is {\tt null}. In order to -handle {\tt null} keys, we would have to add a special case to -{\tt get} or write a class method that compares keys and handles -{\tt null} parameters safely. But we will skip this detail. - -Now that we have {\tt get}, we can write a version of {\tt put} that -is more complete. If there is already an entry in the map with the -given key, {\tt put} is supposed to update it (give it a new value), -and return the old value (or {\tt null} if there was none). Here is -an implementation that provides this feature: - -\begin{verbatim} - public Object put (Object key, Object value) { - Object result = get (key); - if (result == null) { - Entry entry = new Entry (key, value); - entries.add (entry); - } else { - update (key, value); - } - return result; - } - - private void update (Object key, Object value) { - Iterator it = entries.iterator (); - while (it.hasNext ()) { - Entry entry = (Entry) it.next (); - if (key.equals (entry.key)) { - entry.value = value; - break; - } - } - } -\end{verbatim} - -The {\tt update} method is not part of the Map ADT, so -it is declared {\tt private}. It traverses the vector until -it finds the right {\tt Entry} and then it updates -the {\tt value} field. Notice that we don't modify -the {\tt Vector} itself, just one of the objects it contains. - -The only methods we haven't implemented are {\tt containsKey} and {\tt -keySet}. The {\tt containsKey} method is almost identical to {\tt get} -except that it returns {\tt true} or {\tt false} instead of an object -reference or {\tt null}. - -\begin{exercise} -Implement {\tt keySet} by building and returning a {\tt TreeSet} -object. Use your implementation of {\tt TreeSet} from -Exercise~\ref{ex.treeset} or the built-in implementation {\tt -java.util.TreeSet}. -\end{exercise} - - -\section{The {\tt List} metaclass} -\index{metaclass!List} \index{List metaclass} - -The {\tt java.util} package defines a metaclass called -{\tt List} that specifies the set of operations a class has to -implement in order to be considered (very abstractly) a list. -This does not mean, of course, that every class that implements -{\tt List} has to be a linked list. - -Not surprisingly, the built-in {\tt LinkedList} class is a member of -the {\tt List} metaclass. Surprisingly, so is {\tt Vector}. - -The methods in the {\tt List} definition include {\tt add}, {\tt get} -and {\tt iterator}. In fact, all the methods from the {\tt Vector} -class that we used to implement {\tt Map} are defined in the {\tt -List} metaclass. That means that instead of a {\tt Vector}, we could -have used any {\tt List} class. In our implementation of {\tt Map} we -can replace {\tt Vector} with {\tt LinkedList}, and the program still -works! - -This kind of type generality can be useful for tuning -the performance of a program. You can write the program in -terms of a metaclass like {\tt List} and then test the -program with several different implementations to see which -yields the best performance. - - -\section{HashMap implementation} -\index{implementation!Map} -\index{implementation!HashMap} -\index{HashMap!implementation} -\index{map!HashMap implementation} - -The reason that the built-in implementation of the Map ADT -is called {\tt HashMap} is that it uses a particularly efficient -implementation of a Map called a hash table. - -In order to understand the hash table implementation, and why it is -considered efficient, we'll start by analyzing the performance of the -{\tt List} implementation. - -Looking at the implementation of {\tt put}, we see that there are -two cases. If the key is not already in the map, then we -only have to create a new entry and {\tt add} it to -the {\tt List}. Both of these are constant-time operations. - -In the other case, we have to traverse the {\tt List} to find -the existing entry. That's a linear time operation. -For the same reason, {\tt get} and {\tt containsKey} are also -linear. - -Although linear operations are often good enough, we can do -better. It turns out that there is a way to implement the -Map ADT so that both {\tt put} and {\tt get} are constant time -operations! - -The key is to realize that traversing a list takes time -proportional to the length of the list. If we can put an upper -bound on the length of the list, then we can put an upper -bound on the traverse time, and anything with a fixed upper -bound is considered constant time. - -\index{analysis!hash table} - -But how can we limit the length of the lists without limiting -the number of items in the map? By increasing the number -of lists. Instead of one long list, we'll keep many short -lists. - -As long as we know which list to search, we can put a bound -on the amount of searching. - - -\section{Hash Functions} -\index{hash function} -\index{mapping} - -And that's where hash functions come in. We need some way to look at -a key and know, without searching, which list it will be in. We'll -assume that the lists are in an array (or {\tt Vector}) so we can -refer to them by index. - -The solution is to come up with some mapping---almost any -mapping---between the key values and the indices of the lists. -For every possible key there has to be a single index, but -there might be many keys that map to the same index. - -For example, imagine an array of 8 Lists and a map made -up of keys that are {\tt Integers} and values that are -{\tt Strings}. It might be tempting to use the -{\tt intValue} of the {\tt Integers} as indices, since they -are the right type, but there are a whole lot of integers -that do not fall between 0 and 7, which are the only legal -indices. - -\index{modulus} -\index{operator!modulus} - -The modulus operator provides a simple -(in terms of code) and efficient (in terms of run time) way -to map {\em all} the integers into the range $(0, 7)$. -The expression - -\begin{verbatim} - key.intValue() % 8 -\end{verbatim} -% -is guaranteed to produce a value in the range from -7 to 7 (including -both). If you take its absolute value (using {\tt Math.abs}) you -will get a legal index. - -For other types, we can play similar games. For example, -to convert a {\tt Character} to an integer, we can use -the built-in method {\tt Character.getNumericValue} and -for {\tt Doubles} there is {\tt intValue}. - -\index{shifted sum} - -For {\tt Strings} we could get the numeric value of each character and -add them up, or instead we might use a {\bf shifted sum}. To -calculate a shifted sum, you alternate between adding new values to -the accumulator and shifting the accumulator to the left. By ``shift -to the left'' I mean ``multiply by a constant.'' - -To see how this works, take the list of numbers -${ 1, 2, 3, 4, 5, 6 }$ and compute their shifted sum as -follows. First, initialize the accumulator to 0. Then, - -\begin{enumerate} - -\item Multiply the accumulator by 10. - -\item Add the next element of the list to the accumulator. - -\item Repeat until the list is finished. - -\end{enumerate} - -As an exercise, write a method that calculates the shifted sum -of the numeric values of the characters in a {\tt String} using -a multiplier of 16. - -For each type, we can come up with a function that takes values of that -type and generates a corresponding integer value. These -functions are called {\bf hash functions}, because they often -involve making a hash of the components of the object. The -integer value for each object is called its {\bf hash code}. - -There is one other way we might generate a hash code for Java objects. -Every Java object provides a method called {\tt hashCode} that returns -an integer that corresponds to that object. For the built-in types, -the {\tt hashCode} method is implemented so that if two objects -contain the same data (deep equality), they will have the same hash -code. The documentation of these methods explains what the hash -function is. You should check them out. - -\index{deep equality} -\index{hash function} -\index{hash code} - -For user-defined types, it is up to the implementor to provide -an appropriate hash function. The default hash function, provided -in the {\tt Object} class, often uses the location of the -object to generate a hash code, so its notion of ``sameness'' -is shallow equality. Most often when we are searching a -Map for a key, shallow equality is not what we want. - -Regardless of how the hash code is generated, the last step -is to use modulus and absolute value functions to map the hash code -into the range of legal indices. - - -\section{Resizing a hash map} -\index{resizing} -\index{hash map!resizing} - -Let's review. A hash table consists of an array (or Vector) -of {\tt Lists}, where each {\tt List} contains a small number -of entries. To add a new entry to a map, we calculate -the hash code of the new key and add the entry to the -corresponding {\tt List}. - -To look up a key, we hash it again and search the corresponding list. -If the lengths of the lists are bounded then the search time is -bounded. - -So how do we keep the lists short? Well, one goal is to keep -them as balanced as possible, so that there are no very long -lists at the same time that others are empty. -This is not easy to do perfectly---it depends on how well we -chose the hash function---but we can usually do a pretty good -job. - -Even with perfect balance, the average list length -grows linearly with the number of entries, and we have to put -a stop to that. - -The solution is to keep track of the average number of entries -per list, which is called the {\bf load factor}; -if the load factor gets too high, we have to resize the hash table. - -\index{load factor} -\index{rehashing} - -To resize, we create a new hash table, usually twice as big as the -original, take all the entries out of the old one, hash them again, -and put them in the new hash table. Usually we can get away with -using the same hash function; we just use a different value for the -modulus operator. - - -\section{Performance of resizing} -\index{analysis!HashMap} - -How long does it take to resize the hash table? Clearly it is linear -with the number of entries. That means that {\em most} of the -time {\tt put} takes constant time, but every once in a while ----when we resize---it takes linear time. - -At first that sounds bad. Doesn't that undermine my -claim that we can perform {\tt put} in constant time? Well, -frankly, yes. But with a little wheedling, we can fix it. - -Since some {\tt put} operations take longer than others, let's -figure out the {\em average} time for a put operation. The -average is going to be $c$, the constant time for a simple -{\tt put}, plus an additional term of $p$, the percentage of -the time I have to resize, times $kn$, the cost -of resizing. -% -\begin{equation} -t(n) = c + p \cdot kn -\end{equation} -% -We don't know what $c$ and $k$ are, but we can figure out what -$p$ is. Imagine that we have just resized the hash map by -doubling its size. If there are $n$ entries, then we can add an -addition $n$ entries before we have to resize again. So the -percentage of the time we have to resize is $1/n$. - -Plugging into the equation, we get -% -\begin{equation} -t(n) = c + 1/n \cdot kn = c + k -\end{equation} -% -In other words, $t(n)$ is constant time! - - -\section{Glossary} -\index{map} -\index{entry} -\index{key} -\index{value} -\index{dictionary} -\index{associative array} -\index{hash map} -\index{hash function} -\index{hash code} -\index{shifted sum} -\index{load factor} - -\begin{description} - -\item[map:] An ADT that defines operations on a collection of -entries. - -\item[entry:] An element in a map that contains a key and a value. - -\item[key:] An index, of any type, used to look up values in a map. - -\item[value:] An element, of any type, stored in a map. - -\item[dictionary:] Another name for a map. - -\item[associative array:] Another name for a dictionary. - -\item[hash map:] A particularly efficient implementation of a map. - -\item[hash function:] A function that maps values of a certain type -onto integers. - -\item[hash code:] The integer value that corresponds to a given value. - -\item[shifted sum:] A simple hash function often used for compounds -objects like {\tt Strings}. - -\item[load factor:] The number of entries in a hashmap divided -by the number of lists in the hashmap; i.e. the average number -of entries per list. - - -\end{description} - -\section{Exercises} - -\begin{exercise} -\begin{enumerate} -\item Compute the shifted sum of the numbers 1, 2, 3, 4, 5, 6 using -a multiplier of 10. - -\item Compute the shifted sum of the numbers 11, 12, 13, 14, 15, 16 using -a multiplier of 100. - -\item Compute the shifted sum of the numbers 11, 12, 13, 14, 15, 16 using -a multiplier of 10. -\end{enumerate} -\end{exercise} - - -\begin{exercise} -Imagine you have a hash table that -contains 100 lists. If you are asked to {\tt get} the value associated -with a certain key, and the hash code for that key is 654321, what is -the index of the list where the key will be (if it is in the map)? -\end{exercise} - - -\begin{exercise} -If there are 100 lists and there are 89 entries in the -map and the longest list contains 3 entries, and the median -list length is 1 and 19\% of the lists are empty, what is the load -factor? -\end{exercise} - - -\begin{exercise} -Imagine that there are a large number of people at a party. -You would like to know whether any two of them have the same -birthday. First, you design a new kind of Java object that -represents birthdays with two instance variables: -{\tt month}, which is an integer between 1 and 12, and -{\tt day}, which is an integer between 1 and 31. - -Next, you create an array of {\tt Birthday} objects that -contains one object for each person at the party, and you -get someone to help type in all the birthdays. - -\begin{enumerate} - -\item Write an {\tt equals} method for {\tt Birthday} so that -Birthdays with the same month and day are equal. - -\item Write a method called {\tt hasDuplicate} that takes -an array of {\tt Birthdays} and returns {\tt true} if there -are two or more people with the same birthday. -Your algorithm should only traverse the array of -{\tt Birthdays} once. - -\item Write a method called {\tt randomBirthdays} that takes -an integer {\tt n} and returns an array with {\tt n} random -{\tt Birthday} objects. To keep things simple, you can pretend -that all months have 30 days. - -\item Generate 100 random arrays of 10 {\tt Birthdays} each, and -see how many of them contain duplicates. - -\item If there are 20 people at a party, what is the probability -that two or more of them have the same birthday? - -\end{enumerate} -\end{exercise} - - -\begin{exercise} -A Map is said to be {\bf invertible} if each key and each value -appears only once. In a HashMap, it is always true that each -key appears only once, but it is possible for the same value to -appear many times. Therefore, some HashMaps are invertible -and some are not. - -Write a method called {\tt isInvertible} that takes a {\tt HashMap} -and returns true if the map is invertible and false otherwise. -\end{exercise} - - -\begin{exercise} - -The goal of this exercise is to find the 20 most common words in this -book. Type in the code from the book that uses the built-in {\tt -HashMap} to count word frequencies. Download the text of the book -from \url{http://thinkapjava.com/thinkapjava.txt}. - -The plain text version of the book is generated automatically by a -program called {\tt detex} that tries to strip out all the typesetting -commands, but it leaves behind assorted junk. Think about how your -program should handle punctuation and any other wierdness that appears -in the file. - -Write programs to answer the following questions: - -\begin{enumerate} - -\item How many words are there in the book? - -\item How many {\em different} words are there in the book? For -purposes of comparison, there are (very roughly) 500,000 words in -English, of which (very roughly) 50,000 are in current use. What -percentage of this vast lexicon did I find fit to use? - -\item How many times does the word ``encapsulation'' appear? - -\item What are the 20 most common words in the book? HINT: there is -another data structure that might help with this part of the exercise. - -\end{enumerate} -\end{exercise} - - -\begin{exercise} -Write a method for the {\tt LinkedList} class that checks whether -the list contains a loop. You should not assume that the length -field is correct. -Your method should be linear in the -number of nodes. -\end{exercise} - - -\begin{exercise} -Write a hash table implementation of the Map ADT (as defined in -Section~\ref{map}). Test it by using it with any of the programs -you have written so far. Hints: - -\begin{enumerate} - -\item Start with the {\tt Vector} implementation in the book -and make sure it works with existing programs. - -\item Modify the implementation to use either an array of -LinkedLists or a Vector of LinkedLists, whichever you prefer. - -\end{enumerate} -\end{exercise} - - -\begin{exercise} -Write an implementation of the {\tt Set} interface using a -{\tt HashMap}. -\end {exercise} - - -\begin{exercise} -\index{tree!search} -\index{search tree} -\index{binary search tree} - -The {\tt java.util} package provides two implementations of the -{\tt Map} interface, called {\tt HashMap} and {\tt TreeMap}. -{\tt HashMap} is based on a hash table like the one described -in this chapter. {\tt TreeMap} is based on a red-black tree, which -is similar to the search tree in Exercise~\ref{ex.searchtree}. - -Although these implementations provide the same interface, we -expect them to achieve different performance. As the number of -entries, $n$, increases, we expect {\tt add} and {\tt contains} -to take constant time for the hash table implementation, and -logarithmic time for the tree implementation. - -Perform an experiment to confirm (or refute!) these performance -predictions. Write a program that adds $n$ entries to a -{\tt HashMap} or {\tt TreeMap}, then invokes {\tt contains} on -each of the keys. Record the runtime of the program for a range -of values of $n$ and make a plot of runtime versus $n$. Is -the performance behavior in line with our expectations. -\end {exercise} - - -\chapter{Markov analysis} -\label{markov} - -Translate the random text example from Think Python into Java. - - -\chapter{Huffman code} -\label{huffman} - -\section{Variable-length codes} - -If you are familiar with Morse code, you know that it is a system -for encoding the letters of the alphabet as a series of dots and -dashes. For example, the famous signal {\tt ...---...} represents -the letters SOS, which comprise an internationally-recognized call -for help. This table shows the rest of the codes: - -\begin{verbatim} - A .- N -. 1 .---- . .-.-.- - B -... O --- 2 ..--- , --..-- - C -.-. P .--. 3 ...-- ? ..--.. - D -.. Q --.- 4 ....- ( -.--. - E . R .-. 5 ..... ) -.--.- - F ..-. S ... 6 -.... - -....- - G --. T - 7 --... " .-..-. - H .... U ..- 8 ---.. _ ..--.- - I .. V ...- 9 ----. ' .----. - J .--- W .-- 0 ----- : ---... - K -.- X -..- / -..-. ; -.-.-. - L .-.. Y -.-- + .-.-. $ ...-..- - M -- Z --.. = -...- -\end{verbatim} - -\index{Morse code} -\index{code!Morse} - -Notice that some codes are longer than others. By design, the -most common letters have the shortest codes. Since there are a -limited number of short codes, that means that less common -letters and symbols have longer codes. A typical message will -have more short codes than long ones, which minimizes the average -transmission time per letter. - -\index{Huffman code} -\index{code!Huffman} -\index{variable-length code} -\index{code!variable-length} - -Codes like this are called variable-length codes. In this chapter, -we will look at an algorithm for generating a variable-length code -called a {\bf Huffman code}. It is an interesting algorithm in -its own right, but it also makes a useful exercise because its -implementation uses many of the data structures we have been studying. - -Here is an outline of the next few sections: - -\begin{itemize} - -\item First, we will use a sample of English text to generate -a frequency table. A frequency table is like a histogram; it counts -the number of times each letter appears in the sample text. - -\item The heart of a Huffman code is the Huffman tree. We will -use the frequency table to build the Huffman tree, and then use -the tree to encode and decode sequences. - -\item Finally, we will traverse the Huffman tree and built a code -table, which contains the sequence of dots and dashes for each letter. - -\end{itemize} - - -\section {The frequency table} -\label{freqtab} - -\index{Poe, Edgar Allen} -\index{Gold Bug, The} -\index{frequency} - -Since the goal is to give short codes to common letters, we have to -know how often each letter occurs. In Edgar Allen Poe's short story -``The Gold Bug,'' one of the characters uses letter frequencies to -crack a cypher. He explains, - -\begin{quote} -``Now, in English, the letter which most frequently occurs is -e. Afterwards, the succession runs thus: a o i d h n -r s t u y c f g l m w b k p q x z. E however -predominates so remarkably that an individual -sentence of any length is rarely seen, in which it is -not the prevailing character.'' -\end{quote} - -So our first mission is to see whether Poe got it right. To check, -I chose as my sample the text of ``The Gold Bug'' itself, which -I downloaded from one of the Web sites that take advantage -of its entry into the public domain. - -\begin{exercise} -Write a class called {\tt FreqTab} that counts the number of -times each letter appears in a sample text. Download the text -of your favorite public-domain short story, and analyse the frequency -of the letters. - -\index{HashMap} -\index{class!HashMap} - -I found it most convenient to make {\tt FreqTab} extend -{\tt HashMap}. Then I wrote a method called {\tt increment} -that takes a letter as a parameter and either adds or updates -an entry in the HashMap for each letter. - -You can use {\tt keySet} to get the entries from the HashMap, -and print a list of letters with their frequencies. Unfortunately, -they will not appear in any particular order. The next exercise -solves that problem. -\end{exercise} - - -\begin{exercise} -\label{ex.pair} -Write a class called {\tt Pair} that represents a letter-frequency -pair. Pair objects should contain a letter and a frequency as -instance variables. {\tt Pair} should implement {\tt Comparable}, -where the Pair with the higher frequency wins. - -\index{Pair} -\index{class!Pair} - -Now sort the letter-frequency pairs from the HashMap by traversing the -set of keys, building {\tt Pair} objects, adding the Pairs to a -PriorityQueue, removing the Pairs from the PriorityQueue, and printing -them in descending order by frequency. - -How good was Poe's guess about the most frequent letters? -\end{exercise} - - -\section{The Huffman Tree} -\label{hufftree} - -The next step is to assemble the Huffman tree. Each node -of the tree contains a letter and its frequency, and pointers to -the left and right nodes. - -To assemble the Huffman tree, we start by creating a set of -singleton trees, one for each entry in the frequency table. -Then we build the tree from the bottom up, starting with the -least-frequent letters and iteratively joining subtrees until -we have a single tree that contains all the letters. - -Here is the algorithm in more detail. - -\begin{enumerate} - -\item For each entry in the frequency table, create a singleton -Huffman tree and add it to a PriorityQueue. When we remove a tree from -the PriorityQueue, we get the one with the lowest frequency. - -\item Remove two trees from the PriorityQueue and join them by creating -a new parent node that refers to the removed nodes. The frequency -of the parent node is the sum of the frequencies of the children. - -\item If the PriorityQueue is empty, we are done. Otherwise, put the -new tree into the PriorityQueue and go to Step 2. - -\end{enumerate} - -An example will make this clearer. To keep things managable, -we will use a sample text that only contains the letters -{\tt adenrst}: - -\begin{quote} -Eastern Tennessee anteaters ensnare and eat red ants, detest ant -antennae (a tart taste) and dread Antarean anteater-eaters. -Rare Andean deer eat tender sea reeds, aster seeds and rats' -ears. Dessert? Rats' asses. -\end{quote} - -This eloquent treatise on the eating habits of various fauna -yields the following frequency table: - -\begin{verbatim} -e 40 -a 32 -t 24 -s 22 -n 20 -r 19 -d 13 -\end{verbatim} - -So after Step 1, the PriorityQueue looks like this: - -\myfig{figure=figs/huff0.eps,width=2.0in} - -In Step 2, we remove the two trees with the lowest frequency -({\tt r} and {\tt d}) and join them by creating a parent node -with frequency 32. The letter value for the internal nodes is -irrelevant, so it is omitted from the figures. When we put the -new tree back in the PriorityQueue, the result looks like this: - -\myfig{figure=figs/huff1.eps,width=2.0in} - -Now we repeat the process, combining {\tt s} and {\tt n}: - -\myfig{figure=figs/huff2.eps,width=2.0in} - -After the next interation, we have the following collection of -trees. By the way, a collection of trees is called a {\bf forest}. - -\index{forest} - -\myfig{figure=figs/huff3.eps,width=2.0in} - -%\myfig{figure=figs/huff4.eps,width=2.0in} -%\myfig{figure=figs/huff5.eps,width=2.0in} - -After two more iterations, there is only one tree left: - -\myfig{figure=figs/huff6.eps,width=2.0in} - -This is the Huffman tree for the sample text. Actually, it is not the -only one, because each time we join two trees, we choose arbitrarily -which goes on the left and which on the right, and when there is a tie -in the PriorityQueue, the choice is arbitrary. So there may be many -possible trees for a given sample. - -So how to we get a code from the Huffman tree? The code -for each letter is determined by the path from the root of the tree -to the leaf that contains the letter. For example, the path -from the root to {\tt s} is left-right-left. If we represent -a left with {\tt .} and a right with {\tt -} (another arbitrary -choice) we get the following code table. - -\begin{verbatim} -e -. -a -- -t ..- -s .-. -n .-- -r .... -d ...- -\end{verbatim} - -Notice that we have achieved the goal: the most frequent letters -have the shortest codes. - -\begin{exercise} -By hand, figure out a Huffman tree for the following frequency -table: - -\begin{verbatim} -e 93 -s 71 -r 57 -t 53 -n 49 -i 44 -d 43 -o 37 -\end{verbatim} -\end{exercise} - - -\section{The {\tt super} method} - -One way to implement {\tt HuffTree} is to extend {\tt Pair} -from Exercise~\ref{ex.pair}. - -\begin{verbatim} -public class HuffTree extends Pair implements Comparable { - HuffTree left, right; - - public HuffTree (int freq, String letter, - HuffTree left, HuffTree right) { - this.freq = freq; - this.letter = letter; - this.left = left; - this.right = right; - } -} -\end{verbatim} - -{\tt HuffTree} implements {\tt Comparable} so we can put HuffTrees -into a PriorityQueue. In order to implement {\tt Comparable}, we have to -provide a {\tt compareTo} method. We could write one from scratch, -but it is easier to take advantage of the version of {\tt compareTo} -in the {\tt Pair} class. - -Unfortunately, the existing method doesn't do exactly what we want. -For Pairs, we give priority to the higher frequency. For HuffTrees, -we want to give priority to the lower frequency. Of course, we could -write a new version of {\tt compareTo}, but that would override the -version in the parent class, and we would like to be able to invoke -the version in the parent class. - -\index{Catch 22} - -Apparently we are not the first people to encounter this little -{\bf Catch 22}, because the nice people who invented Java have provided -a solution. The keyword {\tt super} allows us to invoke a method -that has been overridden. It's called {\tt super} because parent -classes are sometimes called {\bf superclasses}. - -\index{superclass} -\index{{\tt super}} - -Here's an example from my implementation of {\tt HuffTree}: - -\begin{verbatim} - public int compareTo (Object obj) { - return -super.compareTo (obj); - } -\end{verbatim} - -When {\tt compareTo} is invoked on a {\tt HuffTree}, it turns -around and invokes the overridden version of {\tt compareTo}, -and then negates the result, which has the effect of reversing -the order of priority. - -\index{parent class} -\index{child class} -\index{subclass} - -When a child class (also called a {\bf subclass}) overrides -a constructor, it can invoke the parent's constructor using -{\tt super}: - -\begin{verbatim} - public HuffTree (int freq, String letter, - HuffTree left, HuffTree right) { - super (freq, letter); - this.left = left; - this.right = right; - } -\end{verbatim} - -In this example, the parent's constructor initializes {\tt freq} -and {\tt letter}, and then the child's constructor initializes -{\tt left} and {\tt right}. - -Although this feature is useful, it is also error prone. There -are some odd restrictions---the parent's constructor has to be -invoked first, before the other instance variables are -initialized---and there are some gotchas you don't even want to -know about. In general, this mechanism is like a first aid kit. -If you get into real trouble, it can help you out. But you -know what's even better? Don't get into trouble. In this case, -it is simpler to initialize all four instance variables in -the child's constructor. - -\begin{exercise} -Type in the {\tt HuffTree} class definition from this section -and add a class method called {\tt build} that takes a {\tt FreqTab} -and returns a {\tt HuffTree}. Use the algorithm in Section~\ref{hufftree}. -\end{exercise} - - -\section{Decoding} - -When we receive an encoded message, we use the Huffman tree to -decode it. Here is the algorithm: - -\begin{enumerate} - -\item Start at the root of the HuffTree. - -\item If the next symbol is {\tt .}, go to the left child; otherwise, -go to the right child. - -\item If you are at a leaf node, get the letter from the node and -append it to the result. Go back to the root. - -\item Go to Step 2. - -\end{enumerate} - -Consider the code {\tt ..--.--}, as an example. Starting at the -top of the tree, we go left-left-right and get to the letter {\tt t}. -Then we start at the root again, go right-left and get to the -letter {\tt e}. Back to the top, then right-right, and we get -the letter {\tt a}. If the code is well-formed, we should be -at a leaf node when the code ends. In this case the message -is my beverage of choice, tea. - -\begin{exercise} -Use the example HuffTree to decode the following words: - -\begin{enumerate} - -\item {\tt .-.--.--..---} - -\item {\tt .-...--.-......-.} - -\item {\tt ...--.-.....} - -\item {\tt -.--.-...-} - -Notice that until you start decoding, you can't tell how many -letters there are or where the boundaries fall. -\end{enumerate} -\end{exercise} - - -\begin{exercise} -Write a class definition for {\tt Huffman}. The constructor should -take a string that contains sample text, and it should build a -frequency table and a Huffman tree. - -Write a method called {\tt decode} that takes a String of dots -and dashes and that uses the Huffman tree to decode the String -and return the result. - -Note: even if you use the sample string in Section~\ref{freqtab}, -you won't necessarily get the same HuffTree as in Section~\ref{hufftree}, -so you (probably) won't be able to use your program to decode -the examples in the previous exercise. -\end{exercise} - - -\section{Encoding} -\label{codetab} - -In a sense, encoding a message is harder than decoding, because for a -given letter we might have to search the tree to find the leaf node -that contains the letter, and then figure out the path from the root -to that node. - -This process is much more efficient if we traverse the tree once, -compute all the codes, and build a Map from letters to -codes. - -By now we have seen plenty of tree traversals, but this one is -unusual because as we move around the tree, we want to keep track -of the path we are on. At first, that might seem hard, but there -is a natural way to perform this computation recursively. Here -is the key observation: if the path from the root to a given node -is represented by a string of dots and dashes called {\tt path}, -then the path to the left child of the node is {\tt path + '-'} -and the path to the right child is {\tt path + '.'}. - -\begin{exercise} -\begin{enumerate} -\item Write a class definition for {\tt CodeTab}, which extends -{\tt HashMap}. - -\item In the CodeTab definition, -write a recursive method called {\tt getCodes} that traverses -a HuffTree in any order. When it reaches a leaf node, it should -print the letter in the node and the code that represents the path -from the root to the node. - -\item Once {\tt getCodes} is working, modify it so that when it -reaches a leaf node, it makes an entry in the HashMap, with -the letter as the key and the code as the value. - -\item Write a constructor for {\tt CodeTab} that takes a HuffTree as -a parameter and that invokes {\tt getCodes} to build the code -table. - -\item In the {\tt Huffman} class, write a method called {\tt encode} -that traverses a string, looks up each character in the code -table, and returns the encoding of the string. Test this method -by passing the result to {\tt decode} and see if you get the -original string back. - -\end{enumerate} - -\end{exercise} - -\section{Glossary} -\index{superclass} -\index{subclass} -\index{{\tt super}} -\index{forest} - -\begin{description} - -\item[forest:] A collection of trees (duh!). - -\item[Catch 22:] A situation in which the apparent solution to -a problem seems inevitably to preclude any solution to the problem. -The term comes from Joseph Heller's book of the same title (and -the excellent movie directed by Stanley Kubrick). - -\index{Heller, Joseph} -\index{Kubrick, Stanley} - -\item[superclass:] Another name for a parent class. - -\item[subclass:] Another name for a child class. - -\item[{\tt super}:] A keyword that can be used to invoke an overridden -method from a superclass. - -\end{description} - - diff --git a/figs/LifeRunner.eps b/figs/LifeRunner.eps deleted file mode 100644 index e08ea83..0000000 --- a/figs/LifeRunner.eps +++ /dev/null @@ -1,21318 +0,0 @@ -%!PS-Adobe-3.0 EPSF-3.0 -%%Creator: (ImageMagick) -%%Title: (LifeRunner.eps) -%%CreationDate: (2011-07-28T14:33:11-04:00) -%%BoundingBox: 0 0 479 571 -%%HiResBoundingBox: 0 0 479 571 -%%DocumentData: Clean7Bit -%%LanguageLevel: 1 -%%Pages: 1 -%%EndComments - -%%BeginDefaults -%%EndDefaults - -%%BeginProlog -% -% Display a color image. 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image. - % - % Parameters: - % class: 0-PseudoClass or 1-Grayscale. - % - currentfile buffer readline pop - token pop /class exch def pop - class 0 gt - { - currentfile buffer readline pop - token pop /depth exch def pop - /grays columns 8 add depth sub depth mul 8 idiv string def - columns rows depth - [ - columns 0 0 - rows neg 0 rows - ] - { currentfile grays readhexstring pop } image - } - { - % - % Parameters: - % colors: number of colors in the colormap. - % colormap: red, green, blue color packets. - % - currentfile buffer readline pop - token pop /colors exch def pop - /colors colors 3 mul def - /colormap colors string def - currentfile colormap readhexstring pop pop - systemdict /colorimage known - { - columns rows 8 - [ - columns 0 0 - rows neg 0 rows - ] - { PseudoClassPacket } false 3 colorimage - } - { - % - % No colorimage operator; convert to grayscale. - % - columns rows 8 - [ - columns 0 0 - rows neg 0 rows - ] - { GrayPseudoClassPacket } image - } ifelse - } ifelse -} bind def - -/DisplayImage -{ - % - % Display a DirectClass or PseudoClass image. - % - % Parameters: - % x & y translation. - % x & y scale. - % label pointsize. - % image label. - % image columns & rows. - % class: 0-DirectClass or 1-PseudoClass. - % compression: 0-none or 1-RunlengthEncoded. - % hex color packets. - % - gsave - /buffer 512 string def - /byte 1 string def - /color_packet 3 string def - /pixels 768 string def - - currentfile buffer readline pop - token pop /x exch def - token pop /y exch def pop - x y translate - currentfile buffer readline pop - token pop /x exch def - token pop /y exch def pop - currentfile buffer readline pop - token pop /pointsize exch def pop - /Times-Roman findfont pointsize scalefont setfont - x y scale - currentfile buffer readline pop - token pop /columns exch def - token pop /rows exch def pop - currentfile buffer readline pop - token pop /class exch def pop - currentfile buffer readline pop - token pop /compression exch def pop - class 0 gt 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-% arrowhead -n 4653 1620 m 4773 1650 l 4653 1680 l col0 s -% Polyline -gs clippath -6003 1620 m 6123 1650 l 6003 1680 l 6165 1680 l 6165 1620 l cp -clip -n 5775 1650 m 6150 1650 l gs col0 s gr gr - -% arrowhead -n 6003 1620 m 6123 1650 l 6003 1680 l col0 s -% Polyline -gs clippath -3453 1620 m 3573 1650 l 3453 1680 l 3615 1680 l 3615 1620 l cp -clip -n 3300 1650 m 3600 1650 l gs col0 s gr gr - -% arrowhead -n 3453 1620 m 3573 1650 l 3453 1680 l col0 s -% Polyline -n 3600 1125 m 4425 1125 l 4425 2175 l 3600 2175 l cp gs col0 s gr -/Helvetica ff 180.00 scf sf -1200 1425 m -gs 1 -1 sc (source) col0 sh gr -/Helvetica ff 180.00 scf sf -1200 1650 m -gs 1 -1 sc (code) col0 sh gr -/Helvetica ff 180.00 scf sf -2400 1725 m -gs 1 -1 sc (compiler) col0 sh gr -/Helvetica ff 180.00 scf sf -3750 1650 m -gs 1 -1 sc (code) col0 sh gr -/Helvetica ff 180.00 scf sf -3750 1425 m -gs 1 -1 sc (byte) col0 sh gr -/Helvetica ff 180.00 scf sf -1200 2100 m -gs 1 -1 sc (x.java) col0 sh gr -/Helvetica ff 180.00 scf sf -3750 2100 m -gs 1 -1 sc (x.class) col0 sh gr -/Helvetica ff 180.00 scf sf -2700 2625 m -gs 1 -1 sc (... and generates) col0 sh gr -/Helvetica ff 180.00 scf sf -2700 2850 m -gs 1 -1 sc (Java byte code.) col0 sh gr -/Helvetica ff 180.00 scf sf -4575 2775 m -gs 1 -1 sc (reads the byte) col0 sh gr -/Helvetica ff 180.00 scf sf -4575 3000 m -gs 1 -1 sc (code...) col0 sh gr -/Helvetica ff 180.00 scf sf -4875 1725 m -gs 1 -1 sc (interpreter) col0 sh gr -/Helvetica ff 180.00 scf sf -4575 2550 m -gs 1 -1 sc (A Java interpreter) col0 sh gr -$F2psEnd -rs diff --git a/figs/java.fig b/figs/java.fig deleted file mode 100644 index 8793f95..0000000 --- a/figs/java.fig +++ /dev/null @@ -1,60 +0,0 @@ -#FIG 3.2 -Portrait -Center -Inches -Letter -100.00 -Single --2 -1200 2 -6 6150 1200 7350 2100 -1 1 0 1 0 7 0 0 -1 0.000 1 0.0000 6750 1650 300 300 6750 1650 7050 1950 -1 4 0 1 0 7 0 0 -1 0.000 1 0.0000 6637 1537 54 54 6600 1500 6675 1575 -1 4 0 1 0 7 0 0 -1 0.000 1 0.0000 6862 1537 54 54 6825 1500 6900 1575 -2 4 0 1 0 7 0 0 -1 0.000 0 0 7 0 0 5 - 7350 2100 7350 1200 6150 1200 6150 2100 7350 2100 -3 0 0 1 0 7 0 0 -1 0.000 0 0 0 3 - 6600 1725 6750 1800 6900 1725 - 0.000 1.000 0.000 --6 -6 1050 2400 2250 3000 -4 0 0 0 0 16 12 0.0000 4 180 1080 1050 2550 The compiler\001 -4 0 0 0 0 16 12 0.0000 4 135 780 1050 2775 reads the\001 -4 0 0 0 0 16 12 0.0000 4 135 1185 1050 3000 source code...\001 --6 -6 6600 2400 7950 3000 -4 0 0 0 0 16 12 0.0000 4 135 1335 6600 2550 ... and the result\001 -4 0 0 0 0 16 12 0.0000 4 150 945 6600 2775 appears on\001 -4 0 0 0 0 16 12 0.0000 4 135 930 6600 3000 the screen.\001 --6 -1 1 0 1 0 7 0 0 -1 0.000 1 0.0000 2772 1644 528 306 2772 1644 3300 1950 -1 1 0 1 0 7 0 0 -1 0.000 1 0.0000 5269 1641 506 309 5269 1641 5775 1950 -2 2 0 1 0 7 0 0 -1 0.000 0 0 -1 0 0 5 - 1050 1125 1875 1125 1875 2175 1050 2175 1050 1125 -2 1 0 1 0 7 0 0 -1 0.000 0 0 -1 1 0 2 - 0 0 1.00 60.00 120.00 - 1875 1650 2250 1650 -2 1 0 1 0 7 0 0 -1 0.000 0 0 -1 1 0 2 - 0 0 1.00 60.00 120.00 - 4425 1650 4800 1650 -2 1 0 1 0 7 0 0 -1 0.000 0 0 -1 1 0 2 - 0 0 1.00 60.00 120.00 - 5775 1650 6150 1650 -2 1 0 1 0 7 0 0 -1 0.000 0 0 -1 1 0 2 - 0 0 1.00 60.00 120.00 - 3300 1650 3600 1650 -2 2 0 1 0 7 0 0 -1 0.000 0 0 -1 0 0 5 - 3600 1125 4425 1125 4425 2175 3600 2175 3600 1125 -4 0 0 0 0 16 12 0.0000 4 105 570 1200 1425 source\001 -4 0 0 0 0 16 12 0.0000 4 135 420 1200 1650 code\001 -4 0 0 0 0 16 12 0.0000 4 180 705 2400 1725 compiler\001 -4 0 0 0 0 16 12 0.0000 4 135 420 3750 1650 code\001 -4 0 0 0 0 16 12 0.0000 4 180 360 3750 1425 byte\001 -4 0 0 0 0 16 12 0.0000 4 180 495 1200 2100 x.java\001 -4 0 0 0 0 16 12 0.0000 4 135 570 3750 2100 x.class\001 -4 0 0 0 0 16 12 0.0000 4 180 1395 2700 2625 ... and generates\001 -4 0 0 0 0 16 12 0.0000 4 180 1365 2700 2850 Java byte code.\001 -4 0 0 0 0 16 12 0.0000 4 180 1200 4575 2775 reads the byte\001 -4 0 0 0 0 16 12 0.0000 4 135 555 4575 3000 code...\001 -4 0 0 0 0 16 12 0.0000 4 180 840 4875 1725 interpreter\001 -4 0 0 0 0 16 12 0.0000 4 180 1515 4575 2550 A Java interpreter\001 diff --git a/figs/java.pdf b/figs/java.pdf deleted file mode 100644 index a87e87f..0000000 Binary files a/figs/java.pdf and /dev/null differ diff --git a/figs/mickey.eps b/figs/mickey.eps deleted file mode 100644 index 70513fa..0000000 --- a/figs/mickey.eps +++ /dev/null @@ -1,4330 +0,0 @@ -%!PS-Adobe-3.0 EPSF-3.0 -%%Creator: (ImageMagick) -%%Title: (mickey.eps) -%%CreationDate: (2011-07-21T15:46:16-04:00) -%%BoundingBox: 0 0 392 372 -%%HiResBoundingBox: 0 0 392 372 -%%DocumentData: Clean7Bit -%%LanguageLevel: 1 -%%Pages: 1 -%%EndComments - -%%BeginDefaults -%%EndDefaults - -%%BeginProlog -% -% Display a color image. The image is displayed in color on -% Postscript viewers or printers that support color, otherwise -% it is displayed as grayscale. -% -/DirectClassPacket -{ - % - % Get a DirectClass packet. - % - % Parameters: - % red. - % green. - % blue. - % length: number of pixels minus one of this color (optional). - % - currentfile color_packet readhexstring pop pop - compression 0 eq - { - /number_pixels 3 def - } - { - currentfile byte readhexstring pop 0 get - /number_pixels exch 1 add 3 mul def - } ifelse - 0 3 number_pixels 1 sub - { - pixels exch color_packet putinterval - } for - pixels 0 number_pixels getinterval -} bind def - -/DirectClassImage -{ - % - % Display a DirectClass image. - % - systemdict /colorimage known - { - columns rows 8 - [ - columns 0 0 - rows neg 0 rows - ] - { DirectClassPacket } false 3 colorimage - } - { - % - % No colorimage operator; convert to grayscale. - % - columns rows 8 - [ - columns 0 0 - rows neg 0 rows - ] - { GrayDirectClassPacket } image - } ifelse -} bind def - -/GrayDirectClassPacket -{ - % - % Get a DirectClass packet; convert to grayscale. - % - % Parameters: - % red - % green - % blue - % length: number of pixels minus one of this color (optional). - % - currentfile color_packet readhexstring pop pop - color_packet 0 get 0.299 mul - color_packet 1 get 0.587 mul add - color_packet 2 get 0.114 mul add - cvi - /gray_packet exch def - compression 0 eq - { - /number_pixels 1 def - } - { - currentfile byte readhexstring pop 0 get - /number_pixels exch 1 add def - } ifelse - 0 1 number_pixels 1 sub - { - pixels exch gray_packet put - } for - pixels 0 number_pixels getinterval -} bind def - -/GrayPseudoClassPacket -{ - % - % Get a PseudoClass packet; convert to grayscale. - % - % Parameters: - % index: index into the colormap. - % length: number of pixels minus one of this color (optional). - % - currentfile byte readhexstring pop 0 get - /offset exch 3 mul def - /color_packet colormap offset 3 getinterval def - color_packet 0 get 0.299 mul - color_packet 1 get 0.587 mul add - color_packet 2 get 0.114 mul add - cvi - /gray_packet exch def - compression 0 eq - { - /number_pixels 1 def - } - { - currentfile byte readhexstring pop 0 get - /number_pixels exch 1 add def - } ifelse - 0 1 number_pixels 1 sub - { - pixels exch gray_packet put - } for - pixels 0 number_pixels getinterval -} bind def - -/PseudoClassPacket -{ - % - % Get a PseudoClass packet. - % - % Parameters: - % index: index into the colormap. - % length: number of pixels minus one of this color (optional). - % - currentfile byte readhexstring pop 0 get - /offset exch 3 mul def - /color_packet colormap offset 3 getinterval def - compression 0 eq - { - /number_pixels 3 def - } - { - currentfile byte readhexstring pop 0 get - /number_pixels exch 1 add 3 mul def - } ifelse - 0 3 number_pixels 1 sub - { - pixels exch color_packet putinterval - } for - pixels 0 number_pixels getinterval -} bind def - -/PseudoClassImage -{ - % - % Display a PseudoClass image. - % - % Parameters: - % class: 0-PseudoClass or 1-Grayscale. - % - currentfile buffer readline pop - token pop /class exch def pop - class 0 gt - { - currentfile buffer readline pop - token pop /depth exch def pop - /grays columns 8 add depth sub depth mul 8 idiv string def - columns rows depth - [ - columns 0 0 - rows neg 0 rows - ] - { currentfile grays readhexstring pop } image - } - { - % - % Parameters: - % colors: number of colors in the colormap. - % colormap: red, green, blue color packets. - % - currentfile buffer readline pop - token pop /colors exch def pop - /colors colors 3 mul def - /colormap colors string def - currentfile colormap readhexstring pop pop - systemdict /colorimage known - { - columns rows 8 - [ - columns 0 0 - rows neg 0 rows - ] - { PseudoClassPacket } false 3 colorimage - } - { - % - % No colorimage operator; convert to grayscale. - % - columns rows 8 - [ - columns 0 0 - rows neg 0 rows - ] - { GrayPseudoClassPacket } image - } ifelse - } ifelse -} 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Downey - -% Permission is granted to copy, distribute, transmit and adapt -% this work under a Creative Commons -% Attribution-NonCommercial-ShareAlike 3.0 Unported License: -% http://creativecommons.org/licenses/by-nc-sa/3.0/ - -% If you are interested in distributing a commercial version of this -% work, please contact Allen B. Downey. - -% The original form of this book is LaTeX source code. Compiling this -% LaTeX source has the effect of generating a device-independent -% representation of the book, which can be converted to other formats -% and printed. - -% The LaTeX source for this book is available from http://thinkapjava.com -% and http://code.google.com/p/thinkapjava/source/checkout - -% This book was typeset using LaTeX . The illustrations were -% drawn in xfig. All of these are free, open-source programs. - -%%---------------------------------------------------------------- - -% How to compile this document: -% If your environment provides latex, makeindex, and dvips, -% the following commands should produce a Postscript version -% of the book. - -% latex book -% makeindex book -% latex book -% dvips -o book.ps book - -% You will also need the following (fairly standard) latex -% packages: url, epsfig, makeidx, fancyhdr - -% This distribution also includes a Makefile that should -% compile both the Postscript and PDF versions of the book. - -%%----------------------------------------------------------------- - -\documentclass[12pt]{book} - -\usepackage{amsmath} -\usepackage{amsthm} -\usepackage{amssymb} -\usepackage{makeidx} -\usepackage{url} -\usepackage{fancyhdr} -\usepackage{verbatim} -\usepackage{moreverb} -\usepackage{hevea} -\usepackage{upquote} -\usepackage{graphicx} - - -\newcommand{\thetitle}{Think Java: How to Think Like a Computer Scientist} -\newcommand{\theversion}{5.1.2} - -\newif\ifplastex -\plastexfalse - -\ifplastex -% PLASTEX ONLY - \usepackage{localdef} - \maketitle - -\else - -% LATEX AND HTML - -\newtheoremstyle{exercise} - {\topsep} % space above - {\topsep} % space below - {} % body font - {} % indent amount - {\bfseries} % head font - {.} % punctuation - {5pt} % head space - {} % custom head -\theoremstyle{exercise} -\newtheorem{exercise}{Exercise}[chapter] - -\title{\thetitle} - -\author{Allen B. 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Downey} - -Version \theversion - -\setcounter{chapter}{-1} - -\end{htmlonly} - -% BEGINNING OF LATEXONLY - -\input{latexonly} - -\begin{latexonly} - -%-half title-------------------------------------------------- - -%\thispagestyle{empty} -% -%\begin{flushright} -%\vspace*{2.5in} -% -%{\huge Think Java} -% -%\vspace{1in} -% -%{\LARGE How to Think Like a Computer Scientist} -% -%\vfill -% -%\end{flushright} - -%--verso------------------------------------------------------ - -%%\clearemptydoublepage -%\cleardoublepage - -%--title page-------------------------------------------------- -\pagebreak -\thispagestyle{empty} - -\begin{flushright} -\vspace*{2.5in} - -{\huge Think Java} - -\vspace{0.25in} - -{\LARGE How to Think Like a Computer Scientist} - -\vspace{1in} - -{\Large -Allen B. Downey -} - - -\vspace{1in} - -{\Large \theversion} - -\vfill - -\end{flushright} - - -%--copyright-------------------------------------------------- -\pagebreak -\thispagestyle{empty} - -Copyright \copyright ~2012 Allen Downey. - -\vspace{0.25in} - -Permission is granted to copy, distribute, transmit and adapt -this work under a Creative Commons -Attribution-NonCommercial-ShareAlike 3.0 Unported License: -\url{http://creativecommons.org/licenses/by-nc-sa/3.0/} - -If you are interested in distributing a commercial version of this -work, please contact Allen B. Downey. - -The original form of this book is \LaTeX\ source code. Compiling this -\LaTeX\ source has the effect of generating a device-independent -representation of the book, which can be converted to other formats -and printed. - -The \LaTeX\ source for this book is available from: -\url{http://thinkapjava.com} - -This book was typeset using \LaTeX . The illustrations were -drawn in xfig. All of these are free, open-source programs. - -\vspace{0.25in} - - -%----------------------------------------------------------------- - -\end{latexonly} - -\fi -% END OF THE PART WE SKIP FOR PLASTEX - -\chapter{Preface} - -\begin{quote} -``As we enjoy great Advantages from the Inventions of others, -we should be glad of an Opportunity to serve others by any -Invention of ours, and this we should do freely and generously.'' - ----Benjamin Franklin, quoted in {\em Benjamin Franklin} by -Edmund S. Morgan. -\end{quote} - -\subsection*{Why I wrote this book} - -This is the fifth edition of a book I started writing in 1999, -when I was teaching at Colby College. I had taught an introductory -computer science class using the Java programming language, but I -had not found a textbook I was happy with. For one thing, -they were all too big! There was no way my students would read -800 pages of dense, technical material, even if I wanted them to. -And I didn't want them to. Most of the material was too -specific---details about Java and its libraries that would be obsolete -by the end of the semester, and that obscured the material I really -wanted to get to. - -The other problem I found was that the introduction to object-oriented -programming was too abrupt. Many students who were otherwise -doing well just hit a wall when we got to objects, whether we did -it at the beginning, middle or end. - -So I started writing. I wrote a chapter a day for 13 days, and on -the 14th day I edited. Then I sent it to be photocopied and bound. -When I handed it out on the first day of class, I told the students -that they would be expected to read one chapter a week. In other -words, they would read it seven times slower than I wrote it. - - -\subsection*{The philosophy behind it} - -Here are some of the ideas that make the book the way it is: - -\begin{itemize} - -\item Vocabulary is important. Students need to be able to talk -about programs and understand what I am saying. I try to -introduce the minimum number of terms, to define them carefully -when they are first used, and to organize them in glossaries -at the end of each chapter. In my class, I include vocabulary -questions on quizzes and exams, and require students to use -appropriate terms in short-answer responses. - -\item To write a program, students have to understand the -algorithm, know the programming language, and they have to be -able to debug. I think too many books neglect debugging. This -book includes an appendix on debugging and an appendix on program -development (which can help avoid debugging). I recommend that -students read this material early and come back to it often. - -\item Some concepts take time to sink in. Some of the more -difficult ideas in the book, like recursion, appear several times. -By coming back to these ideas, I am trying to give students a -chance to review and reinforce or, if they missed it the first time, -a chance to catch up. - -\item I try to use the minimum amount of Java to get the -maximum amount of programming power. The purpose of this book -is to teach programming and some introductory ideas from computer -science, not Java. I left out some language features, like -the {\tt switch} statement, that are unnecessary, and avoided -most of the libraries, especially the ones like the AWT that have been -changing quickly or are likely to be replaced. - -\end{itemize} - -The minimalism of my approach has some advantages. -Each chapter is about ten pages, not including the exercises. -In my classes I ask students to read each chapter before we -discuss it, and I have found that they are willing to do that -and their comprehension is good. Their preparation makes -class time available for discussion of the more abstract material, -in-class exercises, and additional topics that aren't in the -book. - -But minimalism has some disadvantages. There is not much here -that is intrinsically fun. Most of my examples demonstrate the -most basic use of a language feature, and many of the exercises -involve string manipulation and mathematical ideas. I think some -of them are fun, but many of the things that excite students -about computer science, like graphics, sound and network applications, -are given short shrift. - -The problem is that many of the more exciting features involve -lots of details and not much concept. Pedagogically, that means -a lot of effort for not much payoff. So there is a tradeoff between -the material that students enjoy and the material that is most -intellectually rich. I leave it to individual teachers to find -the balance that is best for their classes. To help, the book -includes appendices that cover graphics, keyboard input and -file input. - -\subsection*{Object-oriented programming} - -Some books introduce objects immediately; others warm up with a more -procedural style and develop object-oriented style more gradually. -This book uses the ``objects late'' approach. - -Many of Java's object-oriented features are motivated -by problems with previous languages, and their implementations -are influenced by this history. Some of these features are -hard to explain if students aren't familiar with the problems -they solve. - -It wasn't my intention to postpone object-oriented programming. -On the contrary, I got to it as quickly as I could, limited by -my intention to introduce concepts one at a time, as clearly -as possible, in a way that allows students to practice each -idea in isolation before adding the next. But I have to admit -that it takes some time to get there. - -\subsection*{The Computer Science AP Exam} - -Naturally, when the College Board announced that the AP Exam -would switch to Java, I made plans to update the Java version of -the book. Looking at the proposed AP Syllabus, I saw that their -subset of Java was all but identical to the subset I had chosen. - -During January 2003, I worked on the Fourth Edition of the book, -making these changes: - -\begin{itemize} - -\item I added sections to improve coverage of the AP syllabus. - -\item I improved the appendices on debugging and program development. - -\item I collected the exercises, quizzes, and exam questions I -had used in my classes and put them at the end of the appropriate -chapters. I also made up some problems that are intended to -help with AP Exam preparation. - -\end{itemize} - -Finally, in August 2011 I wrote the fifth edition, adding -coverage of the GridWorld Case Study that is part of the AP Exam. - - -\subsection*{Free books!} - -Since the beginning, this book has been under a license that allows users -to copy, distribute and modify the book. Readers can download the -book in a variety of formats and read it on screen or print it. -Teachers are free to print as many copies as they need. And anyone is -free to customize the book for their needs. - -People have translated the book into other computer languages -(including Python and Eiffel), and other natural languages (including -Spanish, French and German). Many of these derivatives are also -available under free licenses. - -Motivated by Open -Source Software, I adopted the philosophy of releasing the -book early and updating it often. I do my best to minimize the -number of errors, but I also depend on readers to help out. - -The response has been great. I get messages almost every day from -people who have read the book and liked it enough to take the trouble -to send in a ``bug report.'' Often I can correct an error -and post an updated version within a few minutes. I think of the -book as a work in progress, improving a little whenever I have time -to make a revision, or when readers send feedback. - -\subsection*{Oh, the title} - -I get a lot of grief about the title of the book. Not everyone -understands that it is---mostly---a joke. -Reading this book will probably not make you think like a computer -scientist. That takes time, experience, and probably a few more -classes. - -But there is a kernel of truth in the title: this book is not -about Java, and it is only partly about programming. If it is -successful, this book is about a way of thinking. Computer scientists -have an approach to problem-solving, and a way of crafting solutions, -that is unique, versatile and powerful. I hope that this book -gives you a sense of what that approach is, and that at some -point you will find yourself thinking like a computer scientist. - -\vspace{0.2in} - -\begin{flushleft} -Allen Downey\\ -Needham, Massachusetts\\ -July 13, 2011 -\end{flushleft} - - -\section*{Contributors List} - -When I started writing free books, it didn't occur to me to keep -a contributors list. When Jeff Elkner suggested it, it seemed so -obvious that I am embarassed by the omission. This list starts -with the 4th Edition, so it omits many people who contributed -suggestions and corrections to earlier versions. - -If you have additional comments, please send them to: \\ -\href{mailto:feedback@greenteapress.com}{feedback@greenteapress.com} - -\begin{itemize} - -\item Ellen Hildreth used this book to teach Data Structures at -Wellesley College, and she gave me a whole stack of corrections, -along with some great suggestions. - -\item Tania Passfield pointed out that the glossary of Chapter 4 -has some leftover terms that no longer appear in the text. - -\item Elizabeth Wiethoff noticed that my series expansion of -$\exp(-x^2)$ was wrong. She is also working on a Ruby version of -the book! - -\item Matt Crawford sent in a whole patch file full of corrections! - -\item Chi-Yu Li pointed out a typo and an error in one of the code -examples. - -\item Doan Thanh Nam corrected an example in Chapter 3. - -\item Stijn Debrouwere found a math typo. - -\item Muhammad Saied translated the book into Arabic, and found -several errors. - -\item Marius Margowski found an inconsistency in a code example. - -\item Guy Driesen found several typos. - -\item Leslie Klein discovered yet another error in the series expansion -of $\exp(-x^2)$, identified typos in the card array figures, and gave -helpful suggestions to clarify several exercises. - -\end{itemize} - -Finally, I wish to acknowledge Chris Mayfield for his significant -contribution to version 5.1 of this book. His careful review -lead to over one hundred corrections and improvements throughout. -Several new features include embedded hypertext links and cross -references, consistent layout of all exercises, and Java syntax -highlighting in code examples. - -% endcontrib - -% table of contents - -\setcounter{tocdepth}{1} -\tableofcontents - -% main matter -\mainmatter - -\chapter{The way of the program} -\label{chap01} - -The goal of this book is to teach you to think like a -computer scientist. I like the way computer scientists think because -they combine some of the best features of Mathematics, Engineering, -and Natural Science. Like mathematicians, computer scientists use formal -languages to denote ideas (specifically computations). Like -engineers, they design things, assembling components into systems and -evaluating tradeoffs among alternatives. Like scientists, -they observe the behavior of complex systems, form hypotheses, and test -predictions. - -The single most important skill for a computer scientist is {\bf -problem-solving}. By that I mean the ability to formulate problems, -think creatively about solutions, and express a solution clearly and -accurately. As it turns out, the process of learning to program is an -excellent opportunity to practice problem-solving skills. That's why -this chapter is called ``The way of the program.'' - -On one level, you will be learning to program, which is a useful -skill by itself. On another level you will use programming -as a means to an end. As we go along, that end will -become clearer. - -\section{What is a programming language?} -\index{programming language} -\index{language!programming} - -The programming language you will be learning is Java, which is -relatively new (Sun released the first version in May, 1995). Java is -an example of a {\bf high-level language}; other high-level languages -you might have heard of are Python, C or C++, and Perl. - -As you might infer from the name ``high-level language,'' there are -also {\bf low-level languages}, sometimes called machine -language or assembly language. Loosely-speaking, computers can only -run programs written in low-level languages. Thus, programs -written in a high-level language have to be translated before they can -run. This translation takes time, which is a small disadvantage -of high-level languages. - -\index{portable} -\index{high-level language} -\index{low-level language} -\index{language!high-level} -\index{language!low-level} - -The advantages are enormous. First, -it is {\em much} easier to program in a high-level language: -the program takes less time to write, -it's shorter and easier to read, and it's more likely to be -correct. Second, high-level languages are {\bf portable}, -meaning that they can run on different kinds of computers with -few or no modifications. Low-level programs can only run -on one kind of computer, and have to be rewritten to run on -another. - -Due to these advantages, almost all programs are written in -high-level languages. Low-level languages are only used for -a few special applications. - -\index{compile} -\index{interpret} - -There are two ways to translate a program; -{\bf interpreting} and {\bf compiling}. An interpreter -is a program that reads a high-level program -and does what it says. In effect, it translates -the program line-by-line, alternately reading lines and -carrying out commands. - -A compiler is a program that reads a high-level program and -translates it all at once, before running any of the commands. -Often you compile the program as a separate step, and then -run the compiled code later. In this case, the high-level -program is called the {\bf source code}, and the translated -program is called the {\bf object code} or the {\bf executable}. - -Java is both compiled and -interpreted. Instead of translating programs into -machine language, the Java compiler generates {\bf byte code}. -Byte code is easy (and fast) to interpret, like machine language, -but it is also portable, like a high-level language. Thus, -it is possible to compile a program on one machine, -transfer the byte code to another machine, -and then interpret the byte code on the other machine. This -ability is an advantage of Java over many other -high-level languages. - - -\includegraphics{figs/java.pdf} - - -Although this process may seem complicated, in most program -development environments these steps -are automated for you. Usually you will only have to write a program -and press a button or type a single command to compile and run it. On -the other hand, it is useful to know what steps are -happening in the background, so if something goes wrong you can -figure out what it is. - - - -\section{What is a program?} - -A program is a sequence of instructions that specifies how to perform -a computation\footnote{This definition does not apply to all - programming languages; for alternatives, see - \url{http://en.wikipedia.org/wiki/Declarative_programming}.}. The -computation might be something mathematical, like solving a system of -equations or finding the roots of a polynomial, but it can also be a -symbolic computation, like searching and replacing text in a document -or (strangely enough) compiling a program. - -\index{statement} - -The instructions, which we will call {\bf statements}, look different -in different programming languages, but there are a few basic -operations most languages perform: - -\begin{description} - -\item[input:] Get data from the keyboard, or a file, or some -other device. - -\item[output:] Display data on the screen or send data to a -file or other device. - -\item[math:] Perform basic mathematical operations like addition and -multiplication. - -\item[testing:] Check for certain conditions and run the -appropriate sequence of statements. - -\item[repetition:] Perform some action repeatedly, usually with -some variation. - -\end{description} - -That's pretty much all there is to it. -Every program you've ever used, no matter how complicated, is -made up of statements that perform these operations. Thus, -one way to describe programming is the process of breaking a -large, complex task up into smaller and smaller subtasks -until the subtasks are simple enough to be performed -with one of these basic operations. - - -\section{What is debugging?} -\index{debugging} -\index{bug} - -For whimsical reasons, -programming errors are called {\bf bugs} and the process -of tracking them down and correcting them is called -{\bf debugging}. - -There are three kinds of errors that can occur -in a program, and it is useful to distinguish them -to track them down more quickly. - -\subsection{Syntax errors} -\index{syntax error} -\index{error!syntax} - -The compiler can only translate a program if the program is -syntactically correct; otherwise, the compilation fails and -you will not be able to run your program. {\bf Syntax} -refers to the structure of your program and the rules about -that structure. -\index{syntax} - -For example, in English, a sentence must begin with a capital -letter and end with a period. this sentence contains a syntax -error. So does this one - -For most readers, a few syntax errors are not a significant -problem, which is why we can read the poetry of e e cummings -without spewing error messages. - -Compilers are not so forgiving. If there is a single syntax -error anywhere in your program, the compiler will print an -error message and quit, and you will not be able to run -your program. - -To make matters worse, there are more syntax rules in Java -than there are in English, and the error messages you get from -the compiler are often not very helpful. During the first -weeks of your programming career, you will probably -spend a lot of time tracking down syntax errors. As you -gain experience, you will make fewer errors and find -them faster. - -\subsection{Run-time errors} -\label{run-time} -\index{run-time error} -\index{error!run-time} -\index{exception} -\index{safe language} -\index{language!safe} - -The second type of error is a run-time error, so-called because -the error does not appear until you run the program. In Java, -run-time errors occur when the interpreter is running the byte -code and something goes wrong. - -Java tends to be a {\bf safe} -language, which means that the compiler catches a lot of errors. -So run-time errors are rare, especially -for simple programs. - -In Java, run-time errors are called {\bf exceptions}, -and in most environments they appear as windows or dialog -boxes that contain information about what happened and what -the program was doing when it happened. This information is -useful for debugging. - -\subsection{Logic errors and semantics} -\index{semantics} -\index{logic error} -\index{error!logic} - -The third type of error is the {\bf logic} or {\bf semantic} error. -If there is a logic error in your program, it will compile and run -without generating error messages, but it will not do the right thing. -It will do something else. Specifically, it will do what you told it -to do. - -The problem is that the program you wrote is not the program you -wanted to write. The semantics, or meaning of the program, are wrong. -Identifying logic errors can be tricky because you have to work -backwards, looking at the output of the program and trying to figure -out what it is doing. - -\subsection{Experimental debugging} - -One of the most important skills you will acquire in this -class is debugging. Although debugging can be frustrating, it -is one of the most interesting, challenging, and -valuable parts of programming. - -Debugging is like detective work. You are -confronted with clues and you have to infer the processes -and events that lead to the results you see. - -Debugging is also like an experimental science. Once you have an idea -what is going wrong, you modify your program and try again. If your -hypothesis was correct, then you can predict the result of the -modification, and you take a step closer to a working program. If -your hypothesis was wrong, you have to come up with a new one. As -Sherlock Holmes pointed out, ``When you have eliminated the -impossible, whatever remains, however improbable, must be the truth.'' -(From A.~Conan Doyle's {\em The Sign of Four}.) - -\index{Holmes, Sherlock} -\index{Doyle, Arthur Conan} - -For some people, programming and debugging are the -same thing. That is, programming is the process of gradually -debugging a program until it does what you want. The idea -is that you should always start with a working program that -does {\em something}, and make small modifications, debugging -them as you go, so that you always have a working program. - -For example, Linux is an operating system that contains thousands of -lines of code, but it started out as a simple program Linus Torvalds -used to explore the Intel 80386 chip. According to Larry Greenfield, -``One of Linus's earlier projects was a program that would switch -between printing AAAA and BBBB. This later evolved to Linux'' -(from {\em The Linux Users' Guide} Beta Version 1). - -\index{Linux} -\index{Torvalds, Linux} -\index{Greenfield, Larry} - -In later chapters I make more suggestions about debugging -and other programming practices. - -\section{Formal and natural languages} -\index{formal language} -\index{natural language} -\index{language!formal} -\index{language!natural} - -{\bf Natural languages} are the languages that people speak, -like English, Spanish, and French. They were not designed -by people (although people try to impose order on them); -they evolved naturally. - -{\bf Formal languages} are languages designed by people for -specific applications. For example, the notation that mathematicians -use is a formal language that is particularly good at denoting -relationships among numbers and symbols. Chemists use a formal -language to represent the chemical structure of molecules. And -most importantly: - -\begin{quote} -{\bf Programming languages are formal languages that have been -designed to express computations.} -\end{quote} - -Formal languages have strict rules -about syntax. For example, $3+3=6$ is a syntactically correct -mathematical statement, but $3 \$ =$ is not. Also, $H_2O$ is a -syntactically correct chemical name, but $_2Zz$ is not. - -Syntax rules come in two flavors, pertaining to tokens and structure. -Tokens are the basic elements of the language, like words and numbers -and chemical elements. One of the problems with $3 \$ =$ is that -$\$$ is not a legal token in mathematics (at least as far as I -know). Similarly, $_2Zz$ is not legal because there is no element with -the abbreviation $Zz$. - -The second type of syntax rule pertains to the structure of a -statement; that is, the way the tokens are arranged. The statement -$3 \$ =$ is structurally illegal, because you can't have an equals -sign at the end of an equation. Similarly, molecular formulas -have to have subscripts after the element name, not before. - -When you read a sentence in English or a statement in a formal -language, you have to figure out what the structure of the sentence is -(although in a natural language you do this unconsciously). This -process is called {\bf parsing}. - -\index{parse} - -Although formal and natural languages have features in -common---tokens, structure, syntax and semantics---there are -differences. - -\index{ambiguity} -\index{redundancy} -\index{literalness} - -\begin{description} - -\item[ambiguity:] Natural languages are full of ambiguity, which - people deal with by using contextual clues and other information. - Formal languages are designed to be unambiguous, which means that - any statement has exactly one meaning, regardless of context. - -\item[redundancy:] To make up for ambiguity and reduce - misunderstandings, natural languages are often redundant. Formal - languages are more concise. - -\item[literalness:] Natural languages are full of idiom and -metaphor. Formal languages mean exactly what they say. - -\end{description} - -People who grow up speaking a natural language (everyone) often have a -hard time adjusting to formal languages. In some ways the difference -between formal and natural language is like the difference between -poetry and prose, but more so: - -\index{poetry} -\index{prose} - -\begin{description} - -\item[Poetry:] Words are used for their sounds as well as for -their meaning, and the whole poem together creates an effect or -emotional response. Ambiguity is common and deliberate. - -\item[Prose:] The literal meaning of words is more important -and the structure contributes more meaning. - -\item[Programs:] The meaning of a computer program is unambiguous -and literal, and can be understood entirely by analysis of the -tokens and structure. - -\end{description} - -Here are some suggestions for reading programs (and other formal -languages). First, remember that formal languages are much more dense -than natural languages, so it takes longer to read them. Also, the -structure is important, so it is usually not a good idea to read -from top to bottom, left to right. Instead, learn to parse the -program in your head, identifying the tokens and interpreting the -structure. Finally, remember that the details matter. Little things -like spelling errors and bad punctuation, which you can get away -with in natural languages, can make a big difference in a formal -language. - -\section{The first program} -\label{hello} -\index{hello world} - -Traditionally the first program people write in a new language -is called ``hello world'' because all it does is display the -words ``Hello, World.'' In Java, this program looks like: - -\begin{lstlisting} -class Hello { - - // main: generate some simple output - - public static void main(String[] args) { - System.out.println("Hello, world."); - } -} -\end{lstlisting} -% -This program includes features that are hard to explain to -beginners, but it provides a preview of topics we -will see in detail later. - -Java programs are made up of {\bf class definitions}, which have -the form: - -\index{class definition} -\index{definition!class} - -\begin{lstlisting} -class CLASSNAME { - - public static void main (String[] args) { - STATEMENTS - } -} -\end{lstlisting} -% -Here {\tt CLASSNAME} indicates a name chosen by the programmer. -The class name in the example is {\tt Hello}. - -\index{class!name} -\index{public} -\index{static} - -{\tt main} is a {\bf method}, which is a named collection of -statements. The name {\tt main} is special; it marks the place in the -program where execution begins. When the program runs, it starts at -the first statement in {\tt main} and ends when it finishes the last -statement. - -\index{method} -\index{print} -\index{statement!print} - -{\tt main} can have any number of statements, but the example has one. -It is a {\bf print statement}, meaning that it displays a message on -the screen. Confusingly, ``print'' can mean ``display something on -the screen,'' or ``send something to the printer.'' In this book I -won't say much about sending things to the printer; we'll do all our -printing on the screen. The print statement ends with a semi-colon -({\tt ;}). - -{\tt System.out.println} is a method provided by one of Java's -libraries. A {\bf library} is a collection of class and method -definitions. -\index{library} - -Java uses squiggly-braces (\{ and \}) to group things together. The -outermost squiggly-braces (lines 1 and 8) contain the class -definition, and the inner braces contain the definition of {\tt main}. - -\index{braces, squiggly} -\index{squiggly braces} -\index{comment} -\index{statement!comment} - -Line 3 begins with {\tt //}. That means it's -a {\bf comment}, which is a bit of -English text that you can put a program, -usually to explain what it does. When the compiler -sees {\tt //}, it ignores everything from there until the end -of the line. - - -\section{Glossary} - -\begin{description} - -\item[problem-solving:] The process of formulating a problem, finding -a solution, and expressing the solution. - -\item[high-level language:] A programming language like Java that -is designed to be easy for humans to read and write. - -\item[low-level language:] A programming language that is designed -to be easy for a computer to run. Also called ``machine -language'' or ``assembly language.'' - -\item[formal language:] Any of the languages people have designed -for specific purposes, like representing mathematical ideas or -computer programs. All programming languages are formal languages. - -\item[natural language:] Any of the languages people speak that -have evolved naturally. - -\item[portability:] A property of a program that can run on more -than one kind of computer. - -\item[interpret:] To run a program in a high-level language -by translating it one line at a time. - -\item[compile:] To translate a program in a high-level language -into a low-level language, all at once, in preparation for later -execution. - -\item[source code:] A program in a high-level language, before -being compiled. - -\item[object code:] The output of the compiler, after translating -the program. - -\item[executable:] Another name for object code that is ready -to run. - -\item[byte code:] A special kind of object code used for Java -programs. Byte code is similar to a low-level language, but it is -portable, like a high-level language. - -\item[statement:] A part of a program that specifies a computation. - -\item[print statement:] A statement that causes output to be displayed - on the screen. - -\item[comment:] A part of a program that contains information -about the program, but that has no effect when the program runs. - -\item[method:] A named collection of statements. - -\item[library:] A collection of class and method definitions. - -\item[bug:] An error in a program. - -\item[syntax:] The structure of a program. - -\item[semantics:] The meaning of a program. - -\item[parse:] To examine a program and analyze the syntactic structure. - -\item[syntax error:] An error in a program that makes it impossible -to parse (and therefore impossible to compile). - -\item[exception:] An error in a program that makes it fail at -run-time. Also called a run-time error. - -\item[logic error:] An error in a program that makes it do something -other than what the programmer intended. - -\item[debugging:] The process of finding and removing any of -the three kinds of errors. - -\index{problem-solving} -\index{high-level language} -\index{low-level language} -\index{formal language} -\index{natural language} -\index{interpret} -\index{compile} -\index{syntax} -\index{semantics} -\index{parse} -\index{exception} -\index{error} -\index{debugging} -\index{statement} -\index{comment} - -\end{description} - -\section{Exercises} - -\begin{exercise} - -Computer scientists have the annoying habit of using common -English words to mean something other than their common -English meaning. For example, in English, statements and -comments are the same thing, but in programs they are different. - -The glossary at the end of each chapter is intended to highlight -words and phrases that have special meanings in computer science. -When you see familiar words, don't assume that you know what -they mean! - -\begin{enumerate} - -\item In computer jargon, what's the difference between a statement -and a comment? - -\item What does it mean to say that a program is portable? - -\item What is an executable? - -\end{enumerate} - -\end{exercise} - -\begin{exercise} - -Before you do anything else, find out how to compile and run a Java -program in your environment. Some environments provide sample programs -similar to the example in Section~\ref{hello}. - -\begin{enumerate} - -\item Type in the ``Hello, world'' program, then compile and run it. - -\item Add a print statement that prints a second message after -the ``Hello, world!''. Something witty like, ``How are you?'' -Compile and run the program again. - -\item Add a comment to the program (anywhere), recompile, and run -it again. The new comment should not affect the result. - -\end{enumerate} - -This exercise may seem trivial, but it is the starting place for many -of the programs we will work with. To debug with confidence, -you have to have confidence in your programming environment. In some -environments, it is easy to lose track of which program is executing, -and you might find yourself trying to debug one program while you are -accidentally running another. Adding (and changing) print statements -is a simple way to be sure that the program you are looking at is -the program you are running. - -\end{exercise} - - -\begin{exercise} - -It is a good idea to commit as many errors as you can think of, -so that you see what error messages the compiler produces. -Sometimes the compiler tells you exactly what is wrong, and all -you have to do is fix it. But sometimes the error messages are -misleading. You will develop a sense for when you can -trust the compiler and when you have to figure things out yourself. - -\begin {enumerate} - -\item Remove one of the open squiggly-braces. - -\item Remove one of the close squiggly-braces. - -\item Instead of {\tt main}, write {\tt mian}. - -\item Remove the word {\tt static}. - -\item Remove the word {\tt public}. - -\item Remove the word {\tt System}. - -\item Replace {\tt println} with {\tt Println}. - -\item Replace {\tt println} with {\tt print}. This one is -tricky because it is a logic error, not a syntax error. -The statement {\tt System.out.print} is legal, but it may or may -not do what you expect. - -\item Delete one of the parentheses. Add an extra one. - -\end {enumerate} -\end{exercise} - - - - - - -\chapter{Variables and types} -\label{chap02} - -\section{More printing} -\index{print} -\index{statement!print} - -You can put as many -statements as you want in {\tt main}; for example, to -print more than one line: - -\begin{lstlisting} -class Hello { - - // Generates some simple output. - - public static void main(String[] args) { - System.out.println("Hello, world."); // print one line - System.out.println("How are you?"); // print another - } -} -\end{lstlisting} -% -As this example demonstrates, you can put comments at the -end of a line, as well as on a line by themselves. - -\index{String} -\index{type!String} - -The phrases that appear in quotation marks are called {\bf strings}, -because they are made up of a sequence (string) of characters. -Strings can contain any combination of letters, numbers, punctuation -marks, and other special characters. - -\index{newline} - -{\tt println} is short for ``print line,'' because after each -line it adds a special character, called a {\bf newline}, that -moves the cursor to the next line of the display. -The next time {\tt println} is invoked, the new text appears -on the next line. - -To display the output from multiple print -statements all on one line, use {\tt print}: - -\begin{lstlisting} -class Hello { - - // Generates some simple output. - - public static void main(String[] args) { - System.out.print("Goodbye, "); - System.out.println("cruel world!"); - } -} -\end{lstlisting} -% -The output appears on a single line as -{\tt Goodbye, cruel world!}. There is a space -between the word ``Goodbye'' and the second quotation mark. -This space appears in the output, so it affects the behavior -of the program. - -Spaces that appear outside of quotation marks generally do -not affect the behavior of the program. For example, I -could have written: - -\begin{lstlisting} -class Hello { -public static void main(String[] args) { -System.out.print("Goodbye, "); -System.out.println("cruel world!"); -} -} -\end{lstlisting} -% -This program would compile and run just as well as the original. -The breaks at the ends of lines (newlines) do not affect -the program's behavior either, so I could have written: - -\begin{lstlisting} -class Hello { public static void main(String[] args) { -System.out.print("Goodbye, "); System.out.println -("cruel world!");}} -\end{lstlisting} -% -That would work, too, but -the program is getting harder and harder to read. Newlines and -spaces are useful for organizing your program visually, making -it easier to read the program and locate errors. - - -\section {Variables} -\index{variable} -\index{value} - -One of the most powerful features of a programming language is the -ability to manipulate {\bf variables}. A variable is a named location -that stores a {\bf value}. Values are things that can be printed, stored -and (as we'll see later) operated on. The strings we have been -printing ({\tt "Hello, World."}, {\tt "Goodbye, "}, etc.) are values. - -To store a value, you have to create a variable. Since -the values we want to store are strings, we declare that -the new variable is a string: - -\begin{lstlisting} - String bob; -\end{lstlisting} -% -This statement is a {\bf declaration}, because it declares that the -variable named {\tt bob} has the type {\tt String}. Each variable -has a type that determines what kind of values it can store. For -example, the {\tt int} type can store integers, and the {\tt String} -type can store strings. - -\index{declaration} -\index{statement!declaration} - -Some types begin with a capital letter and some -with lower-case. We will learn the significance of this distinction -later, but for now you should take care to get it right. There is no -such type as {\tt Int} or {\tt string}, and the compiler will object -if you try to make one up. - -To create an integer variable, the syntax is {\tt int bob;}, -where {\tt bob} is the arbitrary name you made up for the -variable. In general, you will want to make up variable names -that indicate what you plan to do with the variable. For -example, if you saw these variable declarations: - -\begin{lstlisting} - String firstName; - String lastName; - int hour, minute; -\end{lstlisting} -% -you could guess what values -would be stored in them. This example -also demonstrates the syntax for declaring multiple variables -with the same type: {\tt hour} and {\tt second} -are both integers ({\tt int} type). - -\section{Assignment} -\index{assignment} -\index{statement!assignment} - -Now that we have created variables, we want to -store values. We do that with an {\bf assignment -statement}. - -\begin{lstlisting} - bob = "Hello."; // give bob the value "Hello." - hour = 11; // assign the value 11 to hour - minute = 59; // set minute to 59 -\end{lstlisting} -% -This example shows three assignments, and the comments show -three different ways people sometimes talk about assignment -statements. The vocabulary can be confusing here, but the -idea is straightforward: - -\begin{itemize} - -\item When you declare a variable, you create a named storage location. - -\item When you make an assignment to a variable, you give it a value. - -\end{itemize} - -A common way to represent variables on paper is to draw a box -with the name of the variable on the outside and the value -of the variable on the inside. This figure shows -the effect of the three assignment statements: - - -\includegraphics{figs/assign.pdf} - - -As a general rule, -a variable has to have the same type as the -value you assign it. You cannot store a {\tt String} in {\tt minute} or an -integer in {\tt bob}. - -On the other hand, that rule can be confusing, because there are many -ways that you can convert values from one type to another, and Java -sometimes converts things automatically. For now you should -remember the general rule, and we'll talk about exceptions later. - -Another source of confusion is that some strings {\em look} -like integers, but they are not. For example, {\tt bob} -can contain the string {\tt "123"}, which is made up of the -characters {\tt 1}, {\tt 2} and {\tt 3}, but that is not -the same thing as the {\em number} {\tt 123}. - -\begin{lstlisting} - bob = "123"; // legal - bob = 123; // not legal -\end{lstlisting} - - -\section{Printing variables} -\label{printing} - -You can print the value of a variable using {\tt println} or -{\tt print}: - -\begin{lstlisting} -class Hello { - public static void main(String[] args) { - String firstLine; - firstLine = "Hello, again!"; - System.out.println(firstLine); - } -} -\end{lstlisting} -% -This program creates a variable named {\tt firstLine}, assigns -it the value {\tt "Hello, again!"} and then prints that value. -When we talk about ``printing a variable,'' we mean printing -the {\em value} of the variable. To print the {\em name} of -a variable, you have to put it in quotes. -For example: {\tt System.out.println("firstLine");} - -For example, you can write - -\begin{lstlisting} - String firstLine; - firstLine = "Hello, again!"; - System.out.print("The value of firstLine is "); - System.out.println(firstLine); -\end{lstlisting} -% -The output of this program is - -\begin{lstlisting} -The value of firstLine is Hello, again! -\end{lstlisting} -% -I am happy to report that the syntax for printing a variable -is the same regardless of the variable's type. - -\begin{lstlisting} - int hour, minute; - hour = 11; - minute = 59; - System.out.print("The current time is "); - System.out.print(hour); - System.out.print(":"); - System.out.print(minute); - System.out.println("."); -\end{lstlisting} -% -The output of this program is {\tt The current time is 11:59.} - -WARNING: To put multiple values -on the same line, is common to use several {\tt print} statements -followed by a {\tt println}. -But you have to remember -the {\tt println} at the end. In many environments, the -output from {\tt print} is stored without being displayed until -{\tt println} is invoked, at which point the entire -line is displayed at once. If you omit {\tt println}, the -program may terminate without displaying the stored output! - - -\section{Keywords} -\index{keyword} - -A few sections ago, I said that you can make up any name you -want for your variables, but that's not quite true. There -are certain words that are reserved in Java because they are -used by the compiler to parse the structure of your program, -and if you use them as variable names, it will get confused. -These words, called {\bf keywords}, include {\tt public}, -{\tt class}, {\tt void}, {\tt int}, and many more. - -The complete list is available at \url{http://download.oracle.com/javase/tutorial/java/nutsandbolts/_keywords.html}. -This site, provided by Oracle, includes Java documentation I refer to -throughout the book. - -Rather than memorize the list, I suggest you -take advantage of a feature provided in many Java development -environments: code highlighting. As you type, -parts of your program should appear in different colors. For -example, keywords might be blue, strings red, and other code -black. If you type a variable name and it turns blue, watch -out! You might get some strange behavior from the compiler. - - -\section{Operators} -\index{operator} - -{\bf Operators} are symbols used to represent -computations like addition and multiplication. Most -operators in Java do what you expect them -to do because they are common mathematical symbols. For -example, the operator for addition is {\tt +}. Subtraction -is {\tt -}, multiplication is {\tt *}, and division is {\tt /}. - -\begin{lstlisting} -1+1 hour-1 hour*60 + minute minute/60 -\end{lstlisting} -% -Expressions can contain both variable -names and numbers. Variables are -replaced with their values before the computation is performed. - -\index{expression} - -Addition, subtraction and multiplication all do what you -expect, but you might be surprised by division. For example, -this program: - -\begin{lstlisting} - int hour, minute; - hour = 11; - minute = 59; - System.out.print("Number of minutes since midnight: "); - System.out.println(hour*60 + minute); - System.out.print("Fraction of the hour that has passed: "); - System.out.println(minute/60); -\end{lstlisting} -% -generates this output: - -\begin{verbatimtab} -Number of minutes since midnight: 719 -Fraction of the hour that has passed: 0 -\end{verbatimtab} -% -The first line is expected, but the second line is -odd. The value of {\tt minute} is 59, and -59 divided by 60 is 0.98333, not 0. The problem is that -Java is performing {\bf integer division}. - -\index{type!int} -\index{integer division} -\index{arithmetic!integer} -\index{division!integer} -\index{operand} - -When both {\bf operands} are integers (operands are the things -operators operate on), the result is also an integer, -and by convention integer division always rounds {\em down}, -even in cases like this where the next integer is so close. - -An alternative is to calculate a percentage -rather than a fraction: - -\begin{lstlisting} - System.out.print("Percentage of the hour that has passed: "); - System.out.println(minute*100/60); -\end{lstlisting} -% -The result is: - -\begin{verbatimtab} -Percentage of the hour that has passed: 98 -\end{verbatimtab} -% -Again the result is rounded down, but at least now the answer -is approximately correct. To get a more accurate -answer, we can use a different type of variable, called -floating-point, that can store fractional values. -We'll get to that in the next chapter. - - -\section{Order of operations} -\index{precedence} -\index{order of operations} - -When more than one operator appears in an expression, the order -of evaluation depends on the rules of {\bf precedence}. A -complete explanation of precedence can get complicated, but -just to get you started: - -\begin{itemize} - -\item Multiplication and division happen before -addition and subtraction. So {\tt 2*3-1} yields 5, not 4, and -{\tt 2/3-1} yields -1, not 1 (remember that in integer division -{\tt 2/3} is 0). - -\item If the operators have the same precedence they are evaluated -from left to right. So in the expression {\tt minute*100/60}, -the multiplication happens first, yielding {\tt 5900/60}, which -in turn yields {\tt 98}. If the operations had gone from right -to left, the result would be {\tt 59*1} which is {\tt 59}, which -is wrong. - -\item Any time you want to override the rules of precedence (or -you are not sure what they are) you can use parentheses. Expressions -in parentheses are evaluated first, so {\tt 2 *(3-1)} is 4. -You can also use parentheses to make an expression easier to -read, as in {\tt(minute * 100) / 60}, even though it doesn't -change the result. - -\end{itemize} - - -\section{Operators for {\tt Strings}} -\index{string operator} -\index{operator!string} - -In general you cannot perform mathematical operations on {\tt String}s, -even if the strings look like numbers. The following are -illegal (if we know that bob has type {\tt String}) - -\begin{verbatimtab} -bob - 1 "Hello"/123 bob * "Hello" -\end{verbatimtab} -% -By the way, can you tell by looking at those expressions -whether {\tt bob} is an integer or a string? Nope. -The only way to tell the type of a variable is to look at -the place where it is declared. - -\index{concatenate} - -Interestingly, the {\tt +} operator {\em does} work with -{\tt String}s, but it might not do what you expect. -For {\tt String}s, the {\tt +} operator represents {\bf concatenation}, -which means joining up the two operands by linking them -end-to-end. So {\tt "Hello, " + "world."} yields the string -{\tt "Hello, world."} and {\tt bob + "ism"} adds the suffix -{\em ism} to the end of whatever {\tt bob} is, which is -handy for naming new forms of bigotry. - - -\section{Composition} -\index{composition} -\index{expression} - -So far we have looked at the elements of a programming -language---variables, expressions, and statements---in -isolation, without talking about how to combine them. - -One of the most useful features of programming languages -is their ability to take small building blocks and -{\bf compose} them. For example, we know how to multiply -numbers and we know how to print; it turns out we can -combine them in a single statement: - -\begin{lstlisting} - System.out.println(17 * 3); -\end{lstlisting} -% -Any expression involving numbers, strings -and variables, can be used inside a print statement. We've -already seen one example: - -\begin{lstlisting} - System.out.println(hour*60 + minute); -\end{lstlisting} -% -But you can also put arbitrary expressions on the right-hand -side of an assignment statement: - -\begin{lstlisting} - int percentage; - percentage = (minute * 100) / 60; -\end{lstlisting} -% -This ability may not seem impressive now, but we will see -examples where composition -expresses complex computations neatly and concisely. - -WARNING: The left side of an assignment -has to be a {\em variable} name, not an expression. -That's because the left side indicates the storage location -where the result will go. Expressions -do not represent storage locations, only values. So the -following is illegal: {\tt minute+1 = hour;}. - -\section{Glossary} - -\begin{description} - -\item[variable:] A named storage location for values. All -variables have a type, which is declared when the variable -is created. - -\item[value:] A number or string (or other thing to be named later) -that can be stored in a variable. Every value belongs to a type. - -\item[type:] A set of values. The type of a variable -determines which values can be stored there. The types -we have seen are integers ({\tt int} in Java) and strings -({\tt String} in Java). - -\item[keyword:] A reserved word used by the compiler -to parse programs. You cannot use keywords, like {\tt public}, -{\tt class} and {\tt void} as variable names. - -\item[declaration:] A statement that creates a new variable and -determines its type. - -\item[assignment:] A statement that assigns a value to a variable. - -\item[expression:] A combination of variables, operators and -values that represents a single value. Expressions also -have types, as determined by their operators and operands. - -\item[operator:] A symbol that represents a -computation like addition, multiplication or string -concatenation. - -\item[operand:] One of the values on which an operator operates. - -\item[precedence:] The order in which operations are evaluated. - -\item[concatenate:] To join two operands end-to-end. - -\item[composition:] The ability to combine simple -expressions and statements into compound statements and expressions -to represent complex computations concisely. - -\index{variable} -\index{value} -\index{type} -\index{keyword} -\index{assignment} -\index{expression} -\index{operator} -\index{concatenate} -\index{operand} -\index{composition} - -\end{description} - - -\section{Exercises} - -\begin{exercise} - -If you are using this book in a class, you might enjoy this exercise: -find a partner and play "Stump the Chump'': - -Start with a program that compiles and runs correctly. One player -turns away while the other player adds an error to the program. Then -the first player tries to find and fix the error. You get two points -if you find the error without compiling the program, one point if you -find it using the compiler, and your opponent gets a point if you -don't find it. - -% Note: please don't remove the ``l'' from ``public.'' It's not as -% funny as you think. -\end{exercise} - - -\begin{exercise} -\label{ex.date} - -\begin{enumerate} - -\item Create a new program named {\tt Date.java}. Copy or -type in something like the ``Hello, World'' program and make -sure you can compile and run it. - -\item Following the example in Section~\ref{printing}, write a program -that creates variables named {\tt day}, {\tt date}, {\tt month} -and {\tt year}. {\tt day} will contain the day of the week and {\tt -date} will contain the day of the month. What type is each variable? -Assign values to those variables that represent today's date. - -\item Print the value of each variable on a line by itself. This is -an intermediate step that is useful for checking that everything is -working so far. - -\item Modify the program so that it prints the date in standard -American form: {\tt Saturday, July 16, 2011}. - -\item Modify the program again so that the total output is: - -\begin{verbatimtab} -American format: -Saturday, July 16, 2011 -European format: -Saturday 16 July, 2011 -\end{verbatimtab} - -\end{enumerate} - -The point of this exercise is to use string concatenation to display -values with different types ({\tt int} and {\tt String}), and to -practice developing programs gradually by adding a few statements -at a time. - -\end{exercise} - - -\begin{exercise} - -\begin{enumerate} - -\item Create a new program called {\tt Time.java}. From now -on, I won't remind you to start with a small, working program, -but you should. - -\item Following the example in Section 2.6, create variables -named {\tt hour}, {\tt minute} and {\tt second}, and assign -them values that are roughly the current time. Use a 24-hour -clock, so that at 2pm the value of {\tt hour} is 14. - -\item Make the program calculate and print the number of -seconds since midnight. - -\item Make the program calculate and print the number of -seconds remaining in the day. - -\item Make the program calculate and print the percentage of -the day that has passed. - -\item Change the values of {\tt hour}, {\tt minute} and {\tt second} -to reflect the current time (I assume that some time has elapsed), and -check to make sure that the program works correctly with different -values. - -\end{enumerate} - -The point of this exercise is to use some of the arithmetic -operations, and to start thinking about compound entities like the -time of day that that are represented with multiple values. Also, -you might run into problems computing percentages with {\tt ints}, -which is the motivation for floating point numbers in the next -chapter. - -HINT: you may want to use additional variables to hold values -temporarily during the computation. Variables like this, that -are used in a computation but never printed, are sometimes called -intermediate or temporary variables. - -\end{exercise} - - - -\chapter{Void methods} -\label{chap03} - -\section{Floating-point} -\index{floating-point} -\index{type!double} -\index{double(floating-point)} - -In the last chapter we had some problems dealing with numbers -that were not integers. We worked around the problem by measuring -percentages instead of fractions, but a more general solution is -to use floating-point numbers, which can represent fractions -as well as integers. In Java, the floating-point type is -called {\tt double}, which is short for ``double-precision.'' - -You can create floating-point variables and assign values to them -using the same syntax we used for the other types. For example: - -\begin{lstlisting} - double pi; - pi = 3.14159; -\end{lstlisting} -% -It is also legal to declare a variable and assign a value to it at the -same time: - -\begin{lstlisting} - int x = 1; - String empty = ""; - double pi = 3.14159; -\end{lstlisting} -% -This syntax is common; a combined declaration -and assignment is sometimes called an {\bf initialization}. -\index{initialization} - -Although floating-point numbers are useful, they are -a source of confusion because there seems to be an -overlap between integers and floating-point numbers. For -example, if you have the value {\tt 1}, is that an integer, -a floating-point number, or both? - -Java distinguishes the integer value {\tt 1} -from the floating-point value {\tt 1.0}, even though they -seem to be the same number. They belong to -different types, and strictly speaking, you are not allowed -to make assignments between types. For example, the following -is illegal: - -\begin{lstlisting} - int x = 1.1; -\end{lstlisting} -% -because the variable on the left is an {\tt int} -and the value on the right is a {\tt double}. But it is easy -to forget this rule, especially because there are places where Java -will automatically convert from one type to another. -For example: - -\begin{lstlisting} - double y = 1; -\end{lstlisting} -% -should technically not be legal, but Java allows it by converting the -{\tt int} to a {\tt double} automatically. This leniency is -convenient, but it can cause problems; for example: - -\begin{lstlisting} - double y = 1 / 3; -\end{lstlisting} -% -You might expect the variable {\tt y} to get the value -{\tt 0.333333}, which is a legal floating-point value, but in -fact it gets {\tt 0.0}. The reason is that the -expression on the right is the ratio of two integers, -so Java does {\em integer} division, which yields the integer -value {\tt 0}. Converted to floating-point, the result is -{\tt 0.0}. - -One way to solve this problem (once you figure out what -it is) is to make the right-hand side a floating-point -expression: - -\begin{lstlisting} - double y = 1.0 / 3.0; -\end{lstlisting} -% -This sets {\tt y} to {\tt 0.333333}, as expected. - -\index{arithmetic!floating-point} - -The operations we have seen so far---addition, subtraction, -multiplication, and division---also work on floating-point values, -although you might be interested to know that the underlying mechanism -is completely different. In fact, most processors have special -hardware just for performing floating-point operations. - - -\section{Converting from {\tt double} to {\tt int}} -\label{rounding} -\index{rounding} -\index{typecasting} - -As I mentioned, Java converts {\tt int}s -to {\tt double}s automatically if necessary, because no -information is lost in the translation. On the other hand, -going from a {\tt double} to an {\tt int} requires rounding -off. Java doesn't perform this operation automatically, in -order to make sure that you, as the programmer, are aware -of the loss of the fractional part of the number. - -The simplest way to convert a floating-point value to an integer is to -use a {\bf typecast}. Typecasting is so called because it allows you -to take a value that belongs to one type and ``cast'' it into another -type (in the sense of molding or reforming). - -The syntax for typecasting is to put -the name of the type in parentheses and use it as an operator. -For example, - -\begin{lstlisting} - double pi = 3.14159; - int x = (int) pi; -\end{lstlisting} -% -The {\tt(int)} operator has the effect of converting what -follows into an integer, so {\tt x} gets the value 3. - -Typecasting takes precedence over arithmetic operations, -so in the following example, the value of {\tt pi} gets -converted to an integer first, and the result -is 60.0, not 62. - -\begin{lstlisting} - double pi = 3.14159; - double x = (int) pi * 20.0; -\end{lstlisting} -% -Converting to an integer always rounds down, even if the fraction -part is 0.99999999. These behaviors (precedence and rounding) -can make typecasting error-prone. - - -\section{Math methods} -\index{Math class} -\index{class!Math} -\index{expression} -\index{argument} - -In mathematics, you have probably seen functions like $\sin$ and -$\log$, and you have learned to evaluate expressions like -$\sin(\pi/2)$ and $\log(1/x)$. First, you evaluate the -expression in parentheses, which is called the {\bf argument} of the -function. -Then you can evaluate the function itself, either by looking it up in -a table or by performing various computations. - -This process can be applied repeatedly to evaluate more complicated -expressions like $\log(1/\sin(\pi/2))$. First we evaluate the -argument of the innermost function, then evaluate the function, -and so on. - -Java provides functions that perform the most -common mathematical operations. These functions -are called {\bf methods}. -The math methods are invoked using a syntax that is similar to -the {\tt print} statements we have already seen: - -\begin{lstlisting} - double root = Math.sqrt(17.0); - double angle = 1.5; - double height = Math.sin(angle); -\end{lstlisting} -% -The first example sets {\tt root} to the square root of 17. -The second example finds the sine of the value of {\tt angle}, -which is {\tt 1.5}. Java assumes that the -values you use with {\tt sin} and the other trigonometric functions -({\tt cos}, {\tt tan}) are in {\em radians}. To -convert from degrees to radians, you can divide by 360 -and multiply by $2 \pi$. Conveniently, Java provides {\tt Math.PI}: - -\begin{lstlisting} - double degrees = 90; - double angle = degrees * 2 * Math.PI / 360.0; -\end{lstlisting} -% -Notice that {\tt PI} is in all capital letters. Java does -not recognize {\tt Pi}, {\tt pi}, or {\tt pie}. - -Another useful method in the {\tt Math} class is {\tt round}, -which rounds a floating-point value off to the nearest integer -and returns an {\tt int}. - -\begin{lstlisting} - int x = Math.round(Math.PI * 20.0); -\end{lstlisting} -% -In this case the multiplication happens first, before the -method is invoked. The result is 63 (rounded up from 62.8319). - - -\section {Composition} -\label{composition} -\index{composition} -\index{expression} - -Just as with mathematical functions, Java methods can be {\bf -composed}, meaning that you use one expression as part of another. -For example, you can use any expression as an argument to a method: - -\begin{lstlisting} - double x = Math.cos(angle + Math.PI/2); -\end{lstlisting} -% -This statement takes the value {\tt Math.PI}, divides it by two and -adds the result to the value of the variable {\tt angle}. The sum is -then passed as an argument to {\tt cos}. ({\tt -PI} is the name of a variable, not a method, so there are no -arguments, not even the empty argument {\tt()}). - -You can also take the result of one method and pass it as -an argument to another: - -\begin{lstlisting} - double x = Math.exp(Math.log(10.0)); -\end{lstlisting} -% -In Java, the {\tt log} method always uses base $e$, so this -statement finds the log base $e$ of 10 and then raises $e$ to that -power. The result gets assigned to {\tt x}; I hope you know what it -is. - -\section{Adding new methods} -\label{adding_methods} -\index{method!definition} -\index{main} -\index{method!main} - -So far we have used methods from Java libraries, -but it is also possible to add new methods. We have already -seen one method definition: {\tt main}. The method named {\tt main} -is special, but the syntax is the same for other methods: - -\begin{lstlisting} - public static void NAME( LIST OF PARAMETERS ) { - STATEMENTS - } -\end{lstlisting} -% -You can make up any name you want for your method, except -that you can't call it {\tt main} or any -Java keyword. By convention, Java methods start with a lower -case letter and use ``camel caps,'' which is a cute name for -{\tt jammingWordsTogetherLikeThis}. - -The list of parameters specifies what information, if any, you have to -provide to use (or {\bf invoke}) the new method. - -The parameter for {\tt main} is {\tt String[] args}, which -means that whoever invokes {\tt main} has to provide an array of -Strings (we'll get to arrays in Chapter~\ref{arrays}). The first -couple of methods we are going to write have no parameters, so the -syntax looks like this: - -\begin{lstlisting} - public static void newLine() { - System.out.println(""); - } -\end{lstlisting} -% -This method is named {\tt newLine}, and the empty parentheses -mean that it takes no parameters. It contains one -statement, which prints an empty {\tt String}, indicated by {\tt ""}. -Printing a {\tt String} with no letters in it may not seem all that -useful, but {\tt println} skips to the next -line after it prints, so this statement skips to the next line. - -In {\tt main} we invoke this new method the same way we invoke -Java methods: - -\begin{lstlisting} - public static void main(String[] args) { - System.out.println("First line."); - newLine(); - System.out.println("Second line."); - } -\end{lstlisting} -% -The output of this program is - -\begin{minipage}{\linewidth} -\begin{verbatimtab} -First line. - -Second line. -\end{verbatimtab} -\end{minipage} - -Notice the extra space between the lines. What if we wanted -more space between the lines? We could invoke the same -method repeatedly: - -\begin{lstlisting} - public static void main(String[] args) { - System.out.println("First line."); - newLine(); - newLine(); - newLine(); - System.out.println("Second line."); - } -\end{lstlisting} -% -Or we could write a new method, named {\tt threeLine}, that -prints three new lines: - -\begin{lstlisting} - public static void threeLine() { - newLine(); newLine(); newLine(); - } - - public static void main(String[] args) { - System.out.println("First line."); - threeLine(); - System.out.println("Second line."); - } -\end{lstlisting} -% -You should notice a few things about this program: - -\begin{itemize} - -\item You can invoke the same procedure more than once. - -\item You can have one method invoke another method. In this -case, {\tt main} invokes {\tt threeLine} and {\tt threeLine} -invokes {\tt newLine}. - -\item In {\tt threeLine} I wrote three statements all on the same - line, which is syntactically legal (remember that spaces and new - lines usually don't change the meaning of a program). It is usually - a good idea to put each statement on its own line, but I sometimes - break that rule. - -\end{itemize} - -You might wonder why it is worth the trouble to -create all these new methods. There are several -reasons; this example demonstrates two: - -\begin{enumerate} - -\item Creating a new method gives you an opportunity to -give a name to a group of statements. Methods can simplify a program -by hiding a complex computation behind a single statement, and by using -English words in place of arcane code. Which is clearer, {\tt -newLine} or {\tt System.out.println("")}? - -\item Creating a new method can make a program smaller by eliminating -repetitive code. For example, to print nine consecutive -new lines, you could invoke {\tt threeLine} three times. - -\end{enumerate} - -In Section~\ref{methods} we will come back to this question and list -some additional benefits of dividing programs into methods. - - -\section{Classes and methods} -\index{class} -\index{method} - -Pulling together the code fragments from the previous -section, the class definition looks like this: - -\begin{lstlisting} -class NewLine { - - public static void newLine() { - System.out.println(""); - } - - public static void threeLine() { - newLine(); newLine(); newLine(); - } - - public static void main(String[] args) { - System.out.println("First line."); - threeLine(); - System.out.println("Second line."); - } -} -\end{lstlisting} -% -The first line indicates that this is the class definition for a new -class called {\tt NewLine}. A {\bf class} is a collection of related -methods. In this case, the class named {\tt NewLine} contains three -methods, named {\tt newLine}, {\tt threeLine}, and {\tt main}. - -The other class we've seen is the {\tt Math} class. It contains -methods named {\tt sqrt}, {\tt sin}, and others. When -we invoke a mathematical method, we have to specify -the name of the class ({\tt Math}) and the name of the method. -That's why the syntax is slightly different for Java -methods and the methods we write: - -\begin{lstlisting} - Math.pow(2.0, 10.0); - newLine(); -\end{lstlisting} -% -The first statement invokes the {\tt pow} method in -the {\tt Math class} (which raises the first argument to the -power of the second argument). The second statement invokes -the {\tt newLine} method, which Java assumes is in the class -we are writing (i.e., {\tt NewLine}). - -If you try to invoke a method from the wrong class, the -compiler will generate an error. For example, if you -type: - -\begin{lstlisting} - pow(2.0, 10.0); -\end{lstlisting} -% -The compiler will say something like, ``Can't find a method -named {\tt pow} in class {\tt NewLine}.'' If you have -seen this message, you might have wondered why it was looking -for {\tt pow} in your class definition. Now you know. - - -\section {Programs with multiple methods} - -When you look at a class definition that contains several methods, it -is tempting to read it from top to bottom, but that is likely to be -confusing, because that is not the {\bf order of execution} of the -program. - -Execution always begins at the first statement of {\tt main}, -regardless of where it is in the program (in this example I deliberately -put it at the bottom). Statements are executed one at a time, in -order, until you reach a method invocation. Method invocations are -like a detour in the flow of execution. Instead of going to the next -statement, you go to the first line of the invoked method, execute all -the statements there, and then come back and pick up again where you -left off. - -That sounds simple enough, except that you have to remember that one -method can invoke another. Thus, while we are in the middle of {\tt -main}, we might have to go off and execute the statements in {\tt -threeLine}. But while we are executing {\tt threeLine}, we get -interrupted three times to go off and execute {\tt newLine}. - -For its part, {\tt newLine} invokes -{\tt println}, which causes yet another detour. Fortunately, -Java is adept at keeping track of where it is, so when -{\tt println} completes, it picks up where it left off in -{\tt newLine}, and then gets back to {\tt threeLine}, and then -finally gets back to {\tt main} so the program can terminate. - -Technically, the program does not terminate at the -end of {\tt main}. Instead, execution picks up where it left -off in the program that invoked {\tt main}, which is the -Java interpreter. The interpreter takes care of things -like deleting windows and general cleanup, and {\em then} -the program terminates. - -What's the moral of this sordid tale? When you -read a program, don't read from top to bottom. Instead, -follow the flow of execution. - - -\section {Parameters and arguments} -\index{parameter} -\index{argument} - -Some of the methods we have used require {\bf arguments}, -which are values that you provide when you invoke the method. -For example, to find the sine of a number, -you have to provide the number. So {\tt sin} -takes a {\tt double} as an argument. To print a string, -you have to provide the string, so {\tt println} -takes a {\tt String} as an argument. - -Some methods take more than one argument; for example, {\tt pow} -takes two {\tt doubles}, the base and the exponent. - -When you use a method, you provide arguments. When you write -a method, you specify a list of parameters. A {\bf parameter} -is a variable that stores an argument. The parameter list -indicates what arguments are required. - -For example, {\tt printTwice} specifies a single parameter, -{\tt s}, that has type {\tt String}. I called it {\tt s} to -suggest that it is a {\tt String}, but I could have given it -any legal variable name. - -\begin{lstlisting} - public static void printTwice(String s) { - System.out.println(s); - System.out.println(s); - } -\end{lstlisting} -% -When we invoke {\tt printTwice}, we have to provide -a single argument with type {\tt String}. - -\begin{lstlisting} - printTwice("Don't make me say this twice!"); -\end{lstlisting} - -When you invoke a method, the argument you provide are assigned to the -parameters. In this example, the argument {\tt "Don't make me say this - twice!"} is assigned to the parameter {\tt s}. This processing -is called {\bf parameter passing} because the value gets passed -from outside the method to the inside. - -An argument can be any kind of expression, so if you -have a {\tt String} variable, you can use it as an argument: - -\begin{lstlisting} - String argument = "Never say never."; - printTwice(argument); -\end{lstlisting} -% -The value you provide as an argument must have the same type as -the parameter. For example, if you try this: - -\begin{lstlisting} - printTwice(17); -\end{lstlisting} -% -You get an error message like ``cannot find symbol,'' which isn't very -helpful. The reason is that Java is looking for a method named -{\tt printTwice} that can take an integer argument. Since there -isn't one, it can't find such a ``symbol.'' - -{\tt System.out.println} can accept any -type as an argument. But that is an exception; most methods -are not so accommodating. - - -\section {Stack diagrams} -\label{stack} -\index{stack diagram} -\index{diagram!stack} - -Parameters and other -variables only exist inside their own methods. Within the -confines of {\tt main}, there is no such thing as {\tt s}. -If you try to use it, the compiler will complain. Similarly, -inside {\tt printTwice} there is no such thing as {\tt argument}. - -One way to keep track of where each variable is defined is -with a {\bf stack diagram}. The stack diagram for the previous -example looks like this: - -\includegraphics{figs/stack.pdf} - -For each method there is a gray box called a {\bf frame} that contains -the method's parameters and variables. The name of the method -appears outside the frame. As usual, the value of each variable -is drawn inside a box with the name of the variable beside it. - - - -\section {Methods with multiple parameters} -\label{time} -\index{parameter!multiple} -\index{method!multiple parameter} -\index{class!Time} - -The syntax for declaring and invoking methods with multiple -parameters is a common source of errors. First, remember -that you have to declare the type of every parameter. For -example - -\begin{lstlisting} - public static void printTime(int hour, int minute) { - System.out.print(hour); - System.out.print(":"); - System.out.println(minute); - } -\end{lstlisting} -% -It might be tempting to write {\tt int hour, minute}, but -that format is only legal for variable declarations, not -parameter lists. - -Another common source of confusion is that you do not have -to declare the types of arguments. The following is wrong! - -\begin{lstlisting} - int hour = 11; - int minute = 59; - printTime(int hour, int minute); // WRONG! -\end{lstlisting} -% -In this case, Java can tell the type of {\tt hour} -and {\tt minute} by looking at their declarations. It is -not necessary to include the type when you pass them -as arguments. The correct -syntax is {\tt printTime(hour, minute)}. - - -\section {Methods that return values} -\index{value method} -\index{method!value} - -Some of the methods we are using, -like the {\tt Math} methods, return values. Other methods, -like {\tt println} and {\tt newLine}, perform an action but -they don't return a value. That raises some questions: - -\begin{itemize} - -\item What happens if you invoke a method and you don't -do anything with the result (i.e. you don't assign it to -a variable or use it as part of a larger expression)? - -\item What happens if you use a {\tt print} method as part -of an expression, like {\tt System.out.println("boo!") + 7}? - -\item Can we write methods that return values, or are we -stuck with things like {\tt newLine} and {\tt printTwice}? - -\end{itemize} - -The answer to the third question is ``yes, you can write methods that -return values,'' and we'll see how in a couple of chapters. I -leave it up to you to answer the other two questions by trying them -out. In fact, any time you have a question about what is legal or -illegal in Java, a good way to find out is to ask the compiler. - - -\section{Glossary} - -\begin{description} - -\item[initialization:] A statement that declares a new variable -and assigns a value to it at the same time. -\index{initialization} - -\item[floating-point:] A type of variable (or value) that can contain -fractions as well as integers. The floating-point type we will -use is {\tt double}. - -\item[class:] A named collection of methods. So far, we have used -the {\tt Math} class and the {\tt System} class, and we have -written classes named {\tt Hello} and {\tt NewLine}. - -\item[method:] A named sequence of statements that performs a -useful function. Methods may or may not take parameters, and may -or may not return a value. - -\item[parameter:] A piece of information a method requires before -it can run. Parameters are variables: they contain values and have types. - -\item[argument:] A value that you provide when you invoke a -method. This value must have the same type as the corresponding -parameter. - -\item[frame:] A structure (represented by a gray box in stack diagrams) -that contains a method's parameters and variables. - -\item[invoke:] Cause a method to execute. - -\index{floating-point} -\index{class} -\index{method} -\index{parameter} -\index{argument} - -\end{description} - -\section{Exercises} - -\begin{exercise} - -Draw a stack frame that shows the state of the program in Section~\ref{time} -when {\tt main} invokes {\tt printTime} -with the arguments {\tt 11} and {\tt 59}. - -\end{exercise} - -\begin{exercise} - -The point of this exercise is to practice reading code and to -make sure that you understand the flow of execution through -a program with multiple methods. - -\begin{enumerate} - -\item What is the output of the following program? Be precise -about where there are spaces and where there are newlines. - -HINT: Start by describing in words what {\tt ping} and -{\tt baffle} do when they are invoked. - -\item Draw a stack diagram that shows the state of the program -the first time {\tt ping} is invoked. - -\end{enumerate} - -\begin{lstlisting} - public static void zoop() { - baffle(); - System.out.print("You wugga "); - baffle(); - } - - public static void main(String[] args) { - System.out.print("No, I "); - zoop(); - System.out.print("I "); - baffle(); - } - - public static void baffle() { - System.out.print("wug"); - ping(); - } - - public static void ping() { - System.out.println("."); - } -\end{lstlisting} - -\end{exercise} - - -\begin{exercise} - -The point of this exercise is to make sure you understand how -to write and invoke methods that take parameters. - -\begin{enumerate} - -\item Write the first line of a method named {\tt zool} that -takes three parameters: an {\tt int} and two {\tt Strings}. - -\item Write a line of code that invokes {\tt zool}, passing -as arguments the value {\tt 11}, the name of your first pet, -and the name of the street you grew up on. -\end{enumerate} - -\end{exercise} - - -\begin{exercise} - -The purpose of this exercise is to take code from a previous exercise -and encapsulate it in a method that takes parameters. You should -start with a working solution to Exercise~\ref{ex.date}. - -\begin{enumerate} - -\item Write a method called {\tt printAmerican} -that takes the day, date, month and year as parameters and that -prints them in American format. - -\item Test your method by invoking it from {\tt main} and passing -appropriate arguments. The output should look something like this -(except that the date might be different): -% -\begin{verbatimtab} -Saturday, July 16, 2011 -\end{verbatimtab} -% -\item Once you have debugged {\tt printAmerican}, write another -method called {\tt printEuropean} that prints the date in -European format. - -\end{enumerate} -\end{exercise} - - - -\chapter{Conditionals and recursion} -\label{chap04} -\label{condrecursion} - -\section{The modulus operator} -\index{modulus} -\index{operator!modulus} - -The modulus operator works on integers (and integer expressions) -and yields the {\em remainder} when the first operand is divided -by the second. In Java, the modulus operator is a percent sign, -{\tt \%}. The syntax is the same as for other operators: - -\begin{lstlisting} - int quotient = 7 / 3; - int remainder = 7 % 3; -\end{lstlisting} -% -The first operator, integer division, yields 2. The second -operator yields 1. Thus, 7 divided by 3 is 2 with 1 left over. - -The modulus operator turns out to be surprisingly useful. For -example, you can check whether one number is divisible by -another: if {\tt x \% y} is zero, then {\tt x} is divisible -by {\tt y}. - -Also, you can use the modulus operator to extract the rightmost -digit or digits from a number. For example, {\tt x \% 10} yields -the rightmost digit of {\tt x} (in base 10). Similarly -{\tt x \% 100} yields the last two digits. - - -\section{Conditional execution} -\index{conditional} -\index{statement!conditional} - -To write useful programs, we almost always need -to check conditions and change the behavior of the program -accordingly. {\bf Conditional statements} give us this ability. The -simplest form is the {\tt if} statement: - -\begin{lstlisting} - if (x > 0) { - System.out.println("x is positive"); - } -\end{lstlisting} -% -The expression in parentheses is called the condition. -If it is true, then the statements in brackets get executed. -If the condition is not true, nothing happens. - -\index{operator!comparison} -\index{operator!relational} -\index{comparison!operator} -\index{relational operator} - -The condition can contain any of the comparison operators, -sometimes called {\bf relational operators}: - -\begin{lstlisting} - x == y // x equals y - x != y // x is not equal to y - x > y // x is greater than y - x < y // x is less than y - x >= y // x is greater than or equal to y - x <= y // x is less than or equal to y -\end{lstlisting} -% -Although these operations are probably familiar to you, the -syntax Java uses is a little different from mathematical -symbols like $=$, $\neq$ and $\le$. A common error is -to use a single {\tt =} instead of a double {\tt ==}. Remember -that {\tt =} is the assignment operator, and {\tt ==} is -a comparison operator. Also, there is no such thing as -{\tt =<} or {\tt =>}. - -The two sides of a condition operator have to be the same -type. You can only compare {\tt ints} to {\tt ints} and -{\tt doubles} to {\tt doubles}. - -The operators {\tt ==} and {\tt !=} work with Strings, but they -don't do what you expect. And the other relational operators -don't do anything at all. -We will see how to compare strings Section~\ref{incomparable}. - - -\section {Alternative execution} -\label{alternative} -\index{conditional!alternative} - -A second form of conditional execution is alternative execution, -in which there are two possibilities, and the condition determines -which one gets executed. The syntax looks like: - -\begin{lstlisting} - if (x%2 == 0) { - System.out.println("x is even"); - } else { - System.out.println("x is odd"); - } -\end{lstlisting} -% -If the remainder when {\tt x} is divided by 2 is zero, then -we know that {\tt x} is even, and this code prints a message -to that effect. If the condition is false, the second -print statement is executed. Since the condition must -be true or false, exactly one of the alternatives will be -executed. - -As an aside, if you think you might want to check the parity -(evenness or oddness) of numbers often, you might want to -``wrap'' this code up in a method, as follows: - -\begin{lstlisting} - public static void printParity(int x) { - if (x%2 == 0) { - System.out.println("x is even"); - } else { - System.out.println("x is odd"); - } - } -\end{lstlisting} -% -Now you have a method named {\tt printParity} that will print -an appropriate message for any integer you care to provide. -In {\tt main} you would invoke this method like this: - -\begin{lstlisting} - printParity(17); -\end{lstlisting} -% -Always remember that when you {\em invoke} a method, you do -not have to declare the types of the arguments you provide. -Java can figure out what type they are. You should resist the -temptation to write things like: - -\begin{lstlisting} - int number = 17; - printParity(int number); // WRONG!!! -\end{lstlisting} - - -\section {Chained conditionals} -\index{conditional!chained} - -Sometimes you want to check for a number of related conditions -and choose one of several actions. One way to do this is by -{\bf chaining} a series of {\tt if}s and {\tt else}s: - -\begin{lstlisting} - if (x > 0) { - System.out.println("x is positive"); - } else if (x < 0) { - System.out.println("x is negative"); - } else { - System.out.println("x is zero"); - } -\end{lstlisting} -% -These chains can be as long as you want, although they can -be difficult to read if they get out of hand. One way to -make them easier to read is to use standard indentation, -as demonstrated in these examples. If you keep all the -statements and squiggly-brackets lined up, you are less -likely to make syntax errors and more likely to find them -if you do. - - -\section{Nested conditionals} -\index{conditional!nested} - -In addition to chaining, you can also nest one conditional -within another. We could have written the previous example -as: - -\begin{lstlisting} - if (x == 0) { - System.out.println("x is zero"); - } else { - if (x > 0) { - System.out.println("x is positive"); - } else { - System.out.println("x is negative"); - } - } -\end{lstlisting} -% -There is now an outer conditional that contains two branches. The -first branch contains a simple {\tt print} statement, but the second -branch contains another conditional statement, which has two branches -of its own. Those two branches are both {\tt print} -statements, but they could have been conditional statements as -well. - -Indentation helps make the structure -apparent, but nevertheless, nested conditionals get difficult to read -very quickly. Avoid them when you can. -\index{nested structure} - -On the other hand, this kind of {\bf nested structure} is common, and -we will see it again, so you better get used to it. - - -\section{The return statement} -\index{return} -\index{statement!return} - -The {\tt return} statement allows you to terminate the execution -of a method before you reach the end. One reason to use it -is if you detect an error condition: - -\begin{lstlisting} - public static void printLogarithm(double x) { - if (x <= 0.0) { - System.out.println("Positive numbers only, please."); - return; - } - - double result = Math.log(x); - System.out.println("The log of x is " + result); - } -\end{lstlisting} -% -This defines a method named {\tt printLogarithm} that takes a -{\tt double} named {\tt x} as a parameter. It checks whether -{\tt x} is less than or equal to zero, in which case it prints an error -message and then uses {\tt return} to exit the method. The flow of -execution immediately returns to the caller and the remaining lines of -the method are not executed. - -I used a floating-point value on the right side of the condition -because there is a floating-point variable on the left. - - -\section {Type conversion} -\index{type!conversion} -\index{typecasting} - -You might wonder how you can get away with an expression like {\tt -"The log of x is " + result}, since one of the operands is a {\tt String} -and the other is a {\tt double}. In this case Java is being -smart on our behalf, automatically converting the {\tt double} to a -{\tt String} before it does the string concatenation. - -%This kind of feature is an example of a common problem in designing a -%programming language, which is that there is a conflict between {\em -%formalism}, which is the requirement that formal languages should have -%simple rules with few exceptions, and {\em convenience}, which is the -%requirement that programming languages be easy to use in practice. - -%More often than not, convenience wins, which is usually good for -%expert programmers (who are spared from rigorous but unwieldy -%formalism), but bad for beginning programmers, who are often baffled -%by the complexity of the rules and the number of exceptions. In this -%book I have tried to simplify things by emphasizing the rules and -%omitting many of the exceptions. - -Whenever you try to ``add'' two -expressions, if one of them is a {\tt String}, Java converts the -other to a {\tt String} and then perform string concatenation. What do you -think happens if you perform an operation between an integer and a -floating-point value? - - -\section{Recursion} -\label{recursion} -\index{recursion} - -I mentioned in the last chapter that it is legal for one method to -invoke another, and we have seen several examples. I neglected to -mention that it is also legal for a method to invoke itself. It may -not be obvious why that is a good thing, but it turns out to be one of -the most magical and interesting things a program can do. - -For example, look at the following method: - -\begin{lstlisting} - public static void countdown(int n) { - if (n == 0) { - System.out.println("Blastoff!"); - } else { - System.out.println(n); - countdown(n-1); - } - } -\end{lstlisting} -% -The name of the method is {\tt countdown} and it takes a single -integer as a parameter. If the parameter is zero, it prints -the word ``Blastoff.'' Otherwise, it prints the number and -then invokes a method named {\tt countdown}---itself---passing -{\tt n-1} as an argument. - -What happens if we invoke this method, in {\tt main}, like -this: - -\begin{lstlisting} - countdown(3); -\end{lstlisting} -% -The execution of {\tt countdown} begins with {\tt n=3}, and -since {\tt n} is not zero, it prints the value 3, and then -invokes itself... - -\begin{quote} -The execution of {\tt countdown} begins with {\tt n=2}, and -since {\tt n} is not zero, it prints the value 2, and then -invokes itself... - -\begin{quote} -The execution of {\tt countdown} begins with {\tt n=1}, and -since {\tt n} is not zero, it prints the value 1, and then -invokes itself... - -\begin{quote} -The execution of {\tt countdown} begins with {\tt n=0}, and -since {\tt n} is zero, it prints the word ``Blastoff!'' -and then returns. -\end{quote} - -The {\tt countdown} that got {\tt n=1} returns. - -\end{quote} - -The {\tt countdown} that got {\tt n=2} returns. - -\end{quote} - -The {\tt countdown} that got {\tt n=3} returns. - -\noindent And then you're back in {\tt main}. So the -total output looks like: - -\begin{verbatimtab} -3 -2 -1 -Blastoff! -\end{verbatimtab} -% -As a second example, let's look again at the methods -{\tt newLine} and {\tt threeLine}. - -\begin{lstlisting} - public static void newLine() { - System.out.println(""); - } - - public static void threeLine() { - newLine(); newLine(); newLine(); - } -\end{lstlisting} -% -Although these work, they would not be much help if we wanted -to print 2 newlines, or 106. A better alternative would be - -\begin{lstlisting} - public static void nLines(int n) { - if (n > 0) { - System.out.println(""); - nLines(n-1); - } - } -\end{lstlisting} -% -This program similar to {\tt countdown}; as long as {\tt n} is greater -than zero, it prints a newline and then invokes itself to -print {\tt n-1} additional newlines. The total number -of newlines that get printed is {\tt 1 +(n-1)}, which usually -comes out to roughly {\tt n}. - -\index{recursive} -\index{newline} - -When a method invokes itself, that's called {\bf recursion}, and -such methods are {\bf recursive}. - - -\section{Stack diagrams for recursive methods} -\index{stack} -\index{diagram!state} -\index{diagram!stack} - -In the previous chapter we used a stack diagram to represent the -state of a program during a method invocation. The same kind -of diagram can make it easier to interpret a recursive method. - -Remember that every time a method gets called it creates -a new frame that contains a new version of -the method's parameters and variables. - -The following figure is a stack diagram for countdown, called -with {\tt n = 3}: - -\includegraphics{figs/stack2.pdf} - -There is one frame for {\tt main} and four frames for {\tt countdown}, -each with a different value for the parameter {\tt n}. The bottom of -the stack, {\tt countdown} with {\tt n=0} is called the {\bf base - case}. It does not make a recursive call, so there are no more -frames for {\tt countdown}. - -The frame for {\tt main} is empty because {\tt main} does not -have any parameters or variables. - - -\section{Glossary} - -\begin{description} - -\item[modulus:] An operator that works on integers and yields -the remainder when one number is divided by another. In Java -it is denoted with a percent sign({\tt \%}). - -\item[conditional:] A block of statements that may or may not -be executed depending on some condition. - -\item[chaining:] A way of joining several conditional statements -in sequence. - -\item[nesting:] Putting a conditional statement inside one or both -branches of another conditional statement. - -\item[typecast:] An operator that converts from one type to another. -In Java it appears as a type name in parentheses, like {\tt(int)}. - -\item[recursion:] The process of invoking the same method you -are currently executing. - -\item[base case:] A condition that causes a recursive method {\em not} - to make a recursive call. - - -\index{modulus} -\index{conditional} -\index{conditional!chained} -\index{conditional!nested} -\index{typecast} -\index{recursion} -\index{base case} - -\end{description} - -\section{Exercises} - -\begin{exercise} -Draw a stack diagram that shows the state of the program in Section~\ref{recursion} -after {\tt main} invokes {\tt nLines} with the parameter {\tt n=4}, -just before the last invocation of {\tt nLines} returns. -\end{exercise} - -\begin{exercise} - -This exercise reviews the flow of execution through a program -with multiple methods. Read the following code and answer the -questions below. - -\begin{lstlisting} -public class Buzz { - - public static void baffle(String blimp) { - System.out.println(blimp); - zippo("ping", -5); - } - - public static void zippo(String quince, int flag) { - if (flag < 0) { - System.out.println(quince + " zoop"); - } else { - System.out.println("ik"); - baffle(quince); - System.out.println("boo-wa-ha-ha"); - } - } - - public static void main(String[] args) { - zippo("rattle", 13); - } -} -\end{lstlisting} - -\begin{enumerate} - -\item Write the number {\tt 1} next to the first {\em statement} -of this program that will be executed. Be careful to distinguish -things that are statements from things that are not. - -\item Write the number {\tt 2} next to the second statement, and so on -until the end of the program. If a statement is executed more than -once, it might end up with more than one number next to it. - -\item What is the value of the parameter {\tt blimp} when {\tt baffle} -gets invoked? - -\item What is the output of this program? - -\end{enumerate} -\end{exercise} - - -\begin{exercise} - -The first verse of the song ``99 Bottles of Beer'' is: - -\begin{quote} -99 bottles of beer on the wall, -99 bottles of beer, -ya' take one down, ya' pass it around, -98 bottles of beer on the wall. -\end{quote} - -Subsequent verses are identical except that the number -of bottles gets smaller by one in each verse, until the -last verse: - -\begin{quote} -No bottles of beer on the wall, -no bottles of beer, -ya' can't take one down, ya' can't pass it around, -'cause there are no more bottles of beer on the wall! -\end{quote} -% -And then the song(finally) ends. - -Write a program that prints the entire lyrics of -``99 Bottles of Beer.'' Your program should include a -recursive method that does the hard part, but you -might want to write additional methods to separate the major -functions of the program. - -As you develop your code, test it with a small number of -verses, like ``3 Bottles of Beer.'' - -The purpose of this exercise is to take a problem and break it -into smaller problems, and to solve the smaller problems by writing -simple methods. -\end{exercise} - -\begin{exercise} - -What is the output of the following program? - -\begin{lstlisting} -public class Narf { - - public static void zoop(String fred, int bob) { - System.out.println(fred); - if (bob == 5) { - ping("not "); - } else { - System.out.println("!"); - } - } - - public static void main(String[] args) { - int bizz = 5; - int buzz = 2; - zoop("just for", bizz); - clink(2*buzz); - } - - public static void clink(int fork) { - System.out.print("It's "); - zoop("breakfast ", fork) ; - } - - public static void ping(String strangStrung) { - System.out.println("any " + strangStrung + "more "); - } -} -\end{lstlisting} -\end{exercise} - -\begin{exercise} -Fermat's Last Theorem says that there are no integers -$a$, $b$, and $c$ such that -% -\[ a^n + b^n = c^n \] -% -except in the case when $n=2$. - -Write a method named {\tt checkFermat} that takes four -integers as parameters---{\tt a}, {\tt b}, {\tt c} and {\tt n}---and -that checks to see if Fermat's theorem holds. If -$n$ is greater than 2 and it turns out to be true that -$a^n + b^n = c^n$, -the program should print ``Holy smokes, Fermat was wrong!'' -Otherwise the program should print ``No, that doesn't work.'' - -You should assume that there is a method named {\tt raiseToPow} -that takes two integers as arguments and that raises the -first argument to the power of the second. For example: - -\begin{lstlisting} - int x = raiseToPow(2, 3); -\end{lstlisting} -% -would assign the value {\tt 8} to {\tt x}, because $2^3 = 8$. - -\end{exercise} - - -\chapter{GridWorld: Part 1} -\label{gridworld} - -\section{Getting started} - -Now is a good time to start working with the AP Computer Science Case -Study, which is a program called GridWorld. To get started, install -GridWorld, which you can download from the College Board: -\url{http://www.collegeboard.com/student/testing/ap/compsci_a/case.html}. - -When you unpack this code, you should have a folder named {\tt - GridWorldCode} that contains {\tt projects/firstProject}, which -contains {\tt BugRunner.java}. - -Make a copy of {\tt BugRunner.java} in another folder and then import it -into your development environment. There are instructions here that -might help: \url{http://www.collegeboard.com/prod_downloads/student/testing/ap/compsci_a/ap07_gridworld_installation_guide.pdf}. - -Once you run {\tt BugRunner.java}, download the GridWorld Student -Manual from \url{http://www.collegeboard.com/prod_downloads/student/testing/ap/compsci_a/ap07_gridworld_studmanual_appends_v3.pdf}. - -The Student Manual uses vocabulary I have not presented yet, so to -get you started, here is a quick preview: - -\begin{itemize} - -\item The components of GridWorld, including Bugs, Rocks and the Grid -itself, are {\bf objects}. - -\item A {\bf constructor} is a special method that creates new objects. - -\item A {\bf class} is a set of objects; every object belongs to a -class. - -\item An object is also called an {\bf instance} because it is a member, -or instance, of a class. - -\item An {\bf attribute} is a piece of information about an object, like -its color or location. - -\item An {\bf accessor method} is a method that returns an attribute of -an object. - -\item A {\bf modifier method} changes an attribute of an object. - -\end{itemize} - -Now you should be able to read Part 1 of the Student Manual and do -the exercises. - -\section{{\tt BugRunner}} - -{\tt BugRunner.java} contains this code: - -\begin{lstlisting} -import info.gridworld.actor.ActorWorld; -import info.gridworld.actor.Bug; -import info.gridworld.actor.Rock; - -public class BugRunner -{ - public static void main(String[] args) - { - ActorWorld world = new ActorWorld(); - world.add(new Bug()); - world.add(new Rock()); - world.show(); - } -} -\end{lstlisting} - -The first three lines are {\tt import} statements; they list the -classes from GridWorld used in this program. You can find the -documentation for these classes at -\url{http://www.greenteapress.com/thinkapjava/javadoc/gridworld/}. - -Like the other programs we have seen, BugRunner defines a class -that provides a {\tt main} method. The first line of {\tt main} -creates an {\tt ActorWorld} object. {\tt new} is a Java keyword -that creates new objects. - -The next two lines create a Bug and a Rock, and add them to {\tt world}. -The last line shows the world on the screen. - -Open {\tt BugRunner.java} for editing and replace this line: - -\begin{lstlisting} - world.add(new Bug()); -\end{lstlisting} - -with these lines: - -\begin{lstlisting} - Bug redBug = new Bug(); - world.add(redBug); -\end{lstlisting} - -The first line assigns the Bug to a variable named {\tt redBug}; -we can use {\tt redBug} to invoke the Bug's methods. Try this: - -\begin{lstlisting} - System.out.println(redBug.getLocation()); -\end{lstlisting} - -Note: If you run this before adding the Bug to the {\tt world}, the result is -{\tt null}, which means that the Bug doesn't have a location yet. - -Invoke the other accessor methods and print the bug's attributes. -Invoke the methods {\tt canMove}, {\tt move} and {\tt turn} and -be sure you understand what they do. % Now try these exercises: - - -\section{Exercises} - -\begin{exercise} - -\begin{enumerate} - -\item Write a method named {\tt moveBug} that takes a bug as a parameter -and invokes {\tt move}. Test your method by calling it from {\tt main}. - -\item Modify {\tt moveBug} so that it invokes {\tt canMove} and moves -the bug only if it can. - -\item Modify {\tt moveBug} so that it takes an integer, {\tt n}, as a -parameter, and moves the bug {\tt n} times (if it can). - -\item Modify {\tt moveBug} so that if the bug can't move, it invokes -{\tt turn} instead. - -\end{enumerate} -\end{exercise} - - -\begin{exercise} - -\begin{enumerate} - -\item The {\tt Math} class provides a method named {\tt random} -that returns a double between 0.0 and 1.0 (not including 1.0). - -\item Write a method named {\tt randomBug} that takes a Bug as a - parameter and sets the Bug's direction to one of 0, 90, 180 or 270 - with equal probability, and then moves the bug if it can. - -\item Modify {\tt randomBug} to take an integer {\tt n} and repeat -{\tt n} times. - -The result is a random walk, which you can read about -at \url{http://en.wikipedia.org/wiki/Random_walk}. - -\item To see a longer random walk, you can give ActorWorld a bigger stage. -At the top of {\tt BugRunner.java}, add this {\tt import} statement: - -\begin{lstlisting} -import info.gridworld.grid.UnboundedGrid; -\end{lstlisting} - -Now replace the line that creates the ActorWorld with this: - -\begin{lstlisting} - ActorWorld world = new ActorWorld(new UnboundedGrid()); -\end{lstlisting} - -You should be able to run your random walk for a few thousand -steps (you might have to use the scrollbars to find the Bug). - -\end{enumerate} -\end{exercise} - - -\begin{exercise} - -GridWorld uses Color objects, which are defined in a Java library. -You can read the documentation at -\url{http://download.oracle.com/javase/6/docs/api/java/awt/Color.html}. - -To create Bugs with different colors, we have to import -{\tt Color}: - -\begin{lstlisting} -import java.awt.Color; -\end{lstlisting} - -Then you can access the predefined colors, like {\tt Color.blue}, or -create a new color like this: - -\begin{lstlisting} - Color purple = new Color(148, 0, 211); -\end{lstlisting} - -Make a few bugs with different colors. Then write a method named -{\tt colorBug} that takes a Bug as a parameter, reads its location, -and sets the color. - -The Location object you get from -{\tt getLocation} has methods named {\tt getRow} and {\tt getCol} that -return integers. So you can get the x-coordinate of a Bug like this: - -\begin{lstlisting} - int x = bug.getLocation().getCol(); -\end{lstlisting} - -Write a method named {\tt makeBugs} that takes an ActorWorld and an -integer {\tt n} and creates {\tt n} bugs colored according to their -location. Use the row number to control the red level and the column -to control the blue. - -\end{exercise} - - - -\chapter{Value methods} -\label{chap05} - -\section{Return values} -\index{return} -\index{statement!return} -\index{value method} -\index{method!value} -\index{return value} -\index{void} -\index{method!void} - -Some of the methods we have used, like the Math -functions, produce results. That is, the effect of -invoking the method is to generate a new value, which we -usually assign to a variable or use as part of an expression. -For example: - -\begin{lstlisting} - double e = Math.exp(1.0); - double height = radius * Math.sin(angle); -\end{lstlisting} -% -But so far all our methods have been {\bf void}; that is, methods -that return no value. When you invoke a void method, it is typically -on a line by itself, with no assignment: - -\begin{lstlisting} - countdown(3); - nLines(3); -\end{lstlisting} -% -In this chapter we write methods that return things, which I call -{\bf value} methods. The first example is {\tt area}, which takes a -{\tt double} as a parameter, and returns the area of a circle with the -given radius: - -\begin{lstlisting} - public static double area(double radius) { - double area = Math.PI * radius * radius; - return area; - } -\end{lstlisting} -% -The first thing you should notice is that the beginning of the -method definition is different. Instead of {\tt public static -void}, which indicates a void method, we see {\tt public static -double}, which means that the return value from this method -is a {\tt double}. I still haven't explained what -{\tt public static} means, but be patient. -\index{static} - -The last line is a new form of the -{\tt return} statement that includes a return value. This -statement means, ``return immediately from this method and -use the following expression as the return value.'' The -expression you provide can be arbitrarily complicated, -so we could have written this method more concisely: - -\begin{lstlisting} - public static double area(double radius) { - return Math.PI * radius * radius; - } -\end{lstlisting} -% -On the other hand, {\bf temporary} variables like {\tt area} often -make debugging easier. In either case, the type of the expression in -the {\tt return} statement must match the return type of the method. -In other words, when you declare that the return type is {\tt double}, -you are making a promise that this method will eventually -produce a {\tt double}. If you try to {\tt return} with no -expression, or an expression with the wrong type, the compiler will -take you to task. - -\index{temporary variable} -\index{variable!temporary} - -Sometimes it is useful to have multiple return -statements, one in each branch of a conditional: - -\begin{lstlisting} - public static double absoluteValue(double x) { - if (x < 0) { - return -x; - } else { - return x; - } - } -\end{lstlisting} -% -Since these return statements are in an alternative conditional, -only one will be executed. Although it is legal to have more than one -return statement in a method, you should keep in mind -that as soon as one is executed, the method -terminates without executing any subsequent statements. - -Code that appears after a {\tt return} statement, or any place else -where it can never be executed, is called {\bf dead code}. Some -compilers warn you if part of your code is dead. - -\index{dead code} - -If you put return statements inside a conditional, then -you have to guarantee that {\em every possible path} through -the program hits a return statement. For example: - -\begin{lstlisting} - public static double absoluteValue(double x) { - if (x < 0) { - return -x; - } else if (x > 0) { - return x; - } // WRONG!! - } -\end{lstlisting} -% -This program is not legal because if {\tt x} is 0, -neither condition is true and the method ends without hitting -a return statement. A typical compiler message would be ``return -statement required in absoluteValue,'' which is a confusing message -since there are already two of them. - - -\section{Program development} -\label{distance} -\index{program development} - -At this point you should be able to look at complete Java methods and -tell what they do. But it may not be clear yet how to go about -writing them. I am going to suggest a method called {\bf incremental - development}. -\index{incremental development} - -As an example, imagine you want to find the distance between -two points, given by the coordinates $(x_1, y_1)$ and -$(x_2, y_2)$. By the usual definition, -% -\begin{equation*} -distance = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2} -\end{equation*} -% -The first step is to consider what a {\tt distance} method -should look like in Java. In other words, what are the inputs -(parameters) and what is the output (return value)? - -In this case, the two points are the parameters, and it is -natural to represent them using four {\tt double}s, although -we will see later that there is a {\tt Point} object in Java -that we could use. The return value is the distance, which -will have type {\tt double}. - -Already we can write an outline of the method: - -\begin{lstlisting} - public static double distance - (double x1, double y1, double x2, double y2) { - return 0.0; - } -\end{lstlisting} -% -The statement {\tt return 0.0;} is a place-keeper that is necessary -to compile the program. Obviously, at this stage the -program doesn't do anything useful, but it is worthwhile to -try compiling it so we can identify any syntax errors before -we add more code. - -To test the new method, we have to invoke it with -sample values. Somewhere in {\tt main} I would add: - -\begin{lstlisting} - double dist = distance(1.0, 2.0, 4.0, 6.0); -\end{lstlisting} -% -I chose these values so that the horizontal -distance is 3 and the vertical distance is 4; that way, -the result will be 5 (the hypotenuse of a 3-4-5 triangle). -When you are testing a method, it is useful to know the right -answer. - -Once we have checked the syntax of the method definition, we -can start adding lines of code one at a time. After each -incremental change, we recompile and run the program. If there is -an error at any point, we have a good idea where to look: -in the last line we added. - -The next step is to find the differences -$x_2 - x_1$ and $y_2 - y_1$. I store those values in -temporary variables named {\tt dx} and {\tt dy}. - -\begin{lstlisting} - public static double distance - (double x1, double y1, double x2, double y2) { - double dx = x2 - x1; - double dy = y2 - y1; - System.out.println("dx is " + dx); - System.out.println("dy is " + dy); - return 0.0; - } -\end{lstlisting} -% -I added print statements so we can check the intermediate values -before proceeding. They should be 3.0 and 4.0. - -\index{scaffolding} - -When the method is finished I remove the print statements. Code -like that is called {\bf scaffolding}, because it is helpful for -building the program, but it is not part of the final product. - -The next step is to square {\tt dx} and {\tt dy}. We could use the -{\tt Math.pow} method, but it is simpler to multiply each term by -itself. - -\begin{lstlisting} - public static double distance - (double x1, double y1, double x2, double y2) { - double dx = x2 - x1; - double dy = y2 - y1; - double dsquared = dx*dx + dy*dy; - System.out.println("dsquared is " + dsquared); - return 0.0; - } -\end{lstlisting} -% -Again, I would compile and run the program at this stage -and check the intermediate value (which should be 25.0). - -Finally, we can use {\tt Math.sqrt} to compute and -return the result. - -\begin{lstlisting} - public static double distance - (double x1, double y1, double x2, double y2) { - double dx = x2 - x1; - double dy = y2 - y1; - double dsquared = dx*dx + dy*dy; - double result = Math.sqrt(dsquared); - return result; - } -\end{lstlisting} -% -In {\tt main}, we can print and check the value of the result. - -As you gain more experience programming, you might -write and debug more than one line at a time. Nevertheless, -incremental development can save you a lot of time. -% -The key aspects of the process are: - -\begin{itemize} - -\item Start with a working program and make small, incremental -changes. At any point, if there is an error, you will know -exactly where it is. - -\item Use temporary variables to hold intermediate values so -you can print and check them. - -\item Once the program is working, you can remove -scaffolding and consolidate multiple statements into -compound expressions, but only if it does not make the program -difficult to read. - -\end{itemize} - - -\section{Composition} -\index{composition} - -Once you define a new method, -you can use it as part of an expression, and you can build -new methods using existing methods. For example, what if someone -gave you two points, the center of the circle and a point on -the perimeter, and asked for the area of the circle? - -Let's say the center point is stored in the variables {\tt xc} -and {\tt yc}, and the perimeter point is in {\tt xp} and -{\tt yp}. The first step is to find the radius of the circle, which -is the distance between the two points. Fortunately, we have -a method, {\tt distance} that does that. - -\begin{lstlisting} - double radius = distance(xc, yc, xp, yp); -\end{lstlisting} -% -The second step is to find the area of a circle with that -radius, and return it. - -\begin{lstlisting} - double area = area(radius); - return area; -\end{lstlisting} -% -Wrapping that all up in a method, we get: - -\begin{lstlisting} - public static double circleArea - (double xc, double yc, double xp, double yp) { - double radius = distance(xc, yc, xp, yp); - double area = area(radius); - return area; - } -\end{lstlisting} -% -The temporary variables {\tt radius} and {\tt area} are -useful for development and debugging, but once the program is -working we can make it more concise by composing -the method invocations: - -\begin{lstlisting} - public static double circleArea - (double xc, double yc, double xp, double yp) { - return area(distance(xc, yc, xp, yp)); - } -\end{lstlisting} - - -\section{Overloading} -\label{overloading} -\index{overloading} - -You might have noticed that {\tt circleArea} -and {\tt area} perform similar functions---finding -the area of a circle---but take different parameters. For -{\tt area}, we have to provide the radius; for {\tt circleArea} -we provide two points. - -If two methods do the same thing, it is natural to give them -the same name. -Having more than one method with the same name, which is called {\bf -overloading}, is legal in Java {\em as long as each version takes -different parameters}. So we could rename {\tt circleArea}: - -\begin{lstlisting} - public static double area - (double x1, double y1, double x2, double y2) { - return area(distance(xc, yc, xp, yp)); - } -\end{lstlisting} -% -When you invoke an overloaded method, Java knows which version you -want by looking at the arguments that you provide. If you write: - -\begin{lstlisting} - double x = area(3.0); -\end{lstlisting} -% -Java goes looking for a method named {\tt area} that -takes one {\tt double} as an argument, and so it uses the -first version, which interprets the argument as a radius. -If you write: - -\begin{lstlisting} - double x = area(1.0, 2.0, 4.0, 6.0); -\end{lstlisting} -% -Java uses the second version of {\tt area}. And notice that the -second version of {\tt area} actually invokes the first. - -Many Java methods are overloaded, meaning that there -are different versions that accept different numbers or types of -parameters. For example, there are versions of {\tt print} and {\tt -println} that accept a single parameter of any type. In the Math -class, there is a version of {\tt abs} that works on {\tt double}s, -and there is also a version for {\tt int}s. - -Although overloading is a useful feature, it should be used -with caution. You might get yourself nicely confused if you -are trying to debug one version of a method while accidently -invoking a different one. - -And that reminds me of one of the cardinal rules of -debugging: {\bf make sure that the version of the program -you are looking at is the version of the program that is running!} - -Some day you may find yourself making one change after another -in your program, and seeing the same thing every time you run it. -This is a warning sign that you are -not running the version of the program you think you are. To -check, add a {\tt print} statement (it doesn't matter what -you print) and make sure the behavior of the program changes -accordingly. - - -\section{Boolean expressions} -\index{boolean} -\index{expression!boolean} - -Most of the operations we have seen produce results that are -the same type as their operands. For example, the {\tt +} operator -takes two {\tt int}s and produces an {\tt int}, or two {\tt double}s -and produces a {\tt double}, etc. - -\index{operator!relational} -\index{relational operator} - -The exceptions we have seen are the {\bf relational operators}, which -compare {\tt int}s and {\tt float}s and return either {\tt true} or -{\tt false}. {\tt true} and {\tt false} are special values in Java, -and together they make up a type called {\bf boolean}. You might -recall that when I defined a type, I said it was a set of values. In -the case of {\tt int}s, {\tt double}s and {\tt String}s, those sets -are pretty big. For {\tt boolean}s, there are only two values. - -Boolean expressions and variables work just like other types of -expressions and variables: - -\begin{lstlisting} - boolean flag; - flag = true; - boolean testResult = false; -\end{lstlisting} -% -The first example is a simple variable declaration; -the second example is an assignment, and the third example is an -initialization. - -The values {\tt true} and {\tt false} -are keywords in Java, so they may appear in a different color, -depending on your development environment. - -\index{initialization} -\index{statement!initialization} - -The result of a conditional operator is a boolean, -so you can store the result of a comparison in a variable: - -\begin{lstlisting} - boolean evenFlag = (n%2 == 0); // true if n is even - boolean positiveFlag = (x > 0); // true if x is positive -\end{lstlisting} -% -and then use it as part of a conditional statement later: - -\begin{lstlisting} - if (evenFlag) { - System.out.println("n was even when I checked it"); - } -\end{lstlisting} -% -A variable used in this way is called a {\bf flag} -because it flags the presence or absence of some condition. - - -\section{Logical operators} -\index{logical operator} -\index{operator!logical} - -There are three {\bf logical operators} in Java: AND, OR and NOT, -which are denoted by the symbols {\tt \&\&}, {\tt ||} and -{\tt !}. The semantics of these operators is similar -to their meaning in English. For example {\tt x > 0 \&\& x < 10} -is true only if {\tt x} is greater than zero AND less than 10. -\index{semantics} - -{\tt evenFlag || n\%3 == 0} is true if {\em either} of -the conditions is true, that is, if {\tt evenFlag} is true OR the -number is divisible by 3. - -Finally, the NOT operator inverts a boolean expression, so {\tt - !evenFlag} is true if {\tt evenFlag} is false---if the number is -odd. - -\index{nested structure} - -Logical operators can simplify nested -conditional statements. For example, can you re-write -this code using a single conditional? - -\begin{lstlisting} - if (x > 0) { - if (x < 10) { - System.out.println("x is a positive single digit."); - } - } -\end{lstlisting} - - -\section{Boolean methods} -\label{boolean} -\index{boolean} -\index{method!boolean} - -Methods can return boolean values just like any other type, -which is often convenient for hiding tests inside -methods. For example: - -\begin{lstlisting} - public static boolean isSingleDigit(int x) { - if (x >= 0 && x < 10) { - return true; - } else { - return false; - } - } -\end{lstlisting} -% -The name of this method is {\tt isSingleDigit}. It is common -to give boolean methods names that sound like yes/no questions. -The return type is {\tt boolean}, which means that every return -statement has to provide a boolean expression. - -The code itself is straightforward, although it is longer than -it needs to be. Remember that the expression {\tt x >= 0 \&\& x < 10} -has type boolean, so there is nothing wrong with returning it -directly and avoiding the {\tt if} statement altogether: - -\begin{lstlisting} - public static boolean isSingleDigit(int x) { - return (x >= 0 && x < 10); - } -\end{lstlisting} -% -In {\tt main} you can invoke this method in the usual ways: - -\begin{lstlisting} - boolean bigFlag = !isSingleDigit(17); - System.out.println(isSingleDigit(2)); -\end{lstlisting} -% -The first line sets {\tt bigFlag} to {\tt true} -only if 17 is {\em not} a single-digit number. The second -line prints {\tt true} because 2 is a single-digit number. - -The most common use of boolean methods is inside conditional -statements - -\begin{lstlisting} - if (isSingleDigit(x)) { - System.out.println("x is little"); - } else { - System.out.println("x is big"); - } -\end{lstlisting} - - -\section {More recursion} -\index{recursion} -\index{language!complete} -\index{factorial} -\label{factorial} - -Now that we have methods that return values, we have a {\bf Turing - complete} programming language, which means that we can compute -anything computable, for any reasonable definition of ``computable.'' -\index{Turing, Alan} -\index{Church, Alonzo} -% -This idea was developed by Alonzo Church and Alan Turing, so it is -known as the Church-Turing thesis. You can read more about it at -\url{http://en.wikipedia.org/wiki/Turing_thesis}. - -To give you an idea of what you can do with the tools we have learned, -let's look at some methods for evaluating recursively-defined -mathematical functions. A recursive definition is similar to a -circular definition, in the sense that the definition contains a -reference to the thing being defined. A truly circular definition is -not very useful: - -\begin{description} - -\item[recursive:] an adjective used to describe a method that is recursive. - -\end{description} - -If you saw that definition in the dictionary, you might be -annoyed. On the other hand, if you looked up the definition -of the mathematical function {\bf factorial}, you might -get something like: -% -\begin{eqnarray*} -&& 0! = 1 \\ -&& n! = n \cdot(n-1)! -\end{eqnarray*} -% -(Factorial is usually denoted with the symbol $!$, which is -not to be confused with the logical operator {\tt !} which -means NOT.) This definition says that the factorial of 0 is 1, -and the factorial of any other value, $n$, is $n$ multiplied -by the factorial of $n-1$. So $3!$ is 3 times $2!$, which is 2 times -$1!$, which is 1 times $0!$. Putting it all together, we get -$3!$ equal to 3 times 2 times 1 times 1, which is 6. - -If you can write a recursive definition of something, you can usually -write a Java method to evaluate it. The first step is to decide what -the parameters are and what the return type is. Since factorial is -defined for integers, the method takes an -integer as a parameter and returns an integer: - -\begin{lstlisting} - public static int factorial(int n) { - } -\end{lstlisting} - -\noindent If the argument happens to be zero, return 1: - -\begin{lstlisting} - public static int factorial(int n) { - if (n == 0) { - return 1; - } - } -\end{lstlisting} -% -That's the base case. - -Otherwise, and this is the interesting part, we have to make -a recursive call to find the factorial of $n-1$, and then -multiply it by $n$. - -\begin{lstlisting} - public static int factorial(int n) { - if (n == 0) { - return 1; - } else { - int recurse = factorial(n-1); - int result = n * recurse; - return result; - } - } -\end{lstlisting} -% -The flow of execution for this program is similar to {\tt countdown} -from Section~\ref{recursion}. -If we invoke {\tt factorial} with the value 3: - -Since 3 is not zero, we take the second branch and calculate -the factorial of $n-1$... - -\begin{quote} -Since 2 is not zero, we take the second branch and calculate -the factorial of $n-1$... - -\begin{quote} -Since 1 is not zero, we take the second branch and calculate -the factorial of $n-1$... - -\begin{quote} -Since 0 {\em is} zero, we take the first branch and return -the value 1 immediately without making any more recursive -invocations. - -\end{quote} - -The return value (1) gets multiplied by {\tt n}, which is 1, -and the result is returned. - -\end{quote} - -The return value (1) gets multiplied by {\tt n}, which is 2, -and the result is returned. - -\end{quote} - -\noindent The return value (2) gets multiplied by {\tt n}, which is 3, -and the result, 6, is returned to {\tt main}, or whoever -invoked {\tt factorial(3)}. - -\index{stack} -\index{diagram!state} -\index{diagram!stack} - -Here is what the stack diagram looks like for this sequence of -method invocations: - -\includegraphics{figs/stack3.pdf} - -The return values are shown being passed back up the stack. - -Notice that in the last frame {\tt recurse} and {\tt result} do not -exist because when {\tt n=0} the branch that creates them does not -execute. - - -\section{Leap of faith} -\label{leap of faith} -\index{leap of faith} - -Following the flow of execution is one way to read programs, but it can -quickly become disorienting. An alternative is what I call the ``leap -of faith.'' When you come to a method invocation, instead of -following the flow of execution, you {\em assume} that the method -works correctly and returns the appropriate value. - -In fact, you are already practicing this leap of faith -when you use Java methods. When you invoke {\tt Math.cos} -or {\tt System.out.println}, you don't examine the implementations of -those methods. You just assume that they work. - -You can apply the same logic to your own methods. -For example, in Section~\ref{boolean} we wrote a method called -{\tt isSingleDigit} that determines whether a number is between -0 and 9. Once we convince ourselves that this method -is correct---by testing and examination of the code---we can -use the method without ever looking at the code again. - -The same is true of recursive programs. When you get to -the recursive invocation, instead of following the flow of -execution, you should {\em assume} that the recursive invocation -works, and then ask yourself, -``Assuming that I can find the factorial of $n-1$, can I -compute the factorial of $n$?'' Yes, you can, by multiplying by $n$. - -Of course, it is strange to assume that the method -works correctly when you have not even finished writing it, -but that's why it's called a leap of faith! - - -\section{One more example} -\index{fibonacci} -\label{fibonacci} - -The second most common example of a recursively-defined -mathematical function is {\tt fibonacci}, which has the -following definition: -% -\begin{eqnarray*} -&& fibonacci(0) = 1 \\ -&& fibonacci(1) = 1 \\ -&& fibonacci(n) = fibonacci(n-1) + fibonacci(n-2); -\end{eqnarray*} -% -Translated into Java, this is - -\begin{lstlisting} - public static int fibonacci(int n) { - if (n == 0 || n == 1) { - return 1; - } else { - return fibonacci(n-1) + fibonacci(n-2); - } - } -\end{lstlisting} -% -If you try to follow the flow of execution here, even for small -values of {\tt n}, your head explodes. But according to the leap of -faith, if we assume that the two recursive invocations work correctly, then -it is clear that we get the right result by adding them together. - - -\section{Glossary} - -\begin{description} - -\item[return type:] The part of a method declaration that indicates -what type of value the method returns. - -\item[return value:] The value provided as the result of a method -invocation. - -\item[dead code:] Part of a program that can never be executed, -often because it appears after a {\tt return} statement. - -\item[scaffolding:] Code that is used during program development -but is not part of the final version. - -\item[void:] A special return type that indicates a void method; -that is, one that does not return a value. - -\item[overloading:] Having more than one method with the same name -but different parameters. When you invoke an overloaded method, -Java knows which version to use by looking at the arguments you -provide. - -\item[boolean:] A type of variable that can contain only the two -values {\tt true} and {\tt false}. - -\item[flag:] A variable (usually {\tt boolean}) that records -a condition or status information. - -\item[conditional operator:] An operator that compares two values -and produces a boolean that indicates the relationship between the -operands. - -\item[logical operator:] An operator that combines boolean values -and produces boolean values. - -\index{return type} -\index{return value} -\index{dead code} -\index{scaffolding} -\index{void} -\index{overloading} -\index{boolean} -\index{operator!conditional} -\index{operator!logical} - - -\end{description} - - -\section{Exercises} - -\begin{exercise} -\label{ex.isdiv} - -Write a method named {\tt isDivisible} that takes -two integers, {\tt n} and {\tt m} and that returns {\tt true} -if {\tt n} is divisible by {\tt m} and {\tt false} otherwise. - -\end{exercise} - - -\begin{exercise} -\label{ex.multadd} - -Many computations can be expressed concisely using the ``multadd'' -operation, which takes three operands and computes {\tt a*b + c}. Some -processors even provide a hardware implementation of this operation for -floating-point numbers. - -\begin{enumerate} - -\item Create a new program called {\tt Multadd.java}. - -\item Write a method called {\tt multadd} that takes three {\tt doubles} -as parameters and that returns their multadditionization. - -\item Write a {\tt main} method that tests {\tt multadd} by invoking it with a -few simple parameters, like {\tt 1.0, 2.0, 3.0}. - -\item Also in {\tt main}, use {\tt multadd} to compute the -following values: -% -\begin{eqnarray*} -& \sin \frac{\pi}{4} + \frac{\cos \frac{\pi}{4}}{2} & \\ -& \log 10 + \log 20 & -\end{eqnarray*} -% -\item Write a method called {\tt yikes} that takes a -double as a parameter and that uses {\tt multadd} to calculate -% -\begin{eqnarray*} -x e^{-x} + \sqrt{1 - e^{-x}} -\end{eqnarray*} -% -HINT: the Math method for raising $e$ to a power is {\tt Math.exp}. - -\end{enumerate} - -In the last part, you get a chance to write a method that invokes -a method you wrote. Whenever you do that, it is a good idea to -test the first method carefully before you start working on the -second. Otherwise, you might find yourself debugging two methods -at the same time, which can be difficult. - -One of the purposes of this exercise is to practice pattern-matching: -the ability to recognize a specific problem as an instance of a -general category of problems. - -\end{exercise} - - -\begin{exercise} -If you are given three sticks, you may or may not be able to arrange -them in a triangle. For example, if one of the sticks is 12 inches -long and the other two are one inch long, you will -not be able to get the short sticks to meet in the middle. For any -three lengths, there is a simple test to see if it is possible to form -a triangle: - -\begin{quotation} -``If any of the three lengths is greater than the sum of the other two, -then you cannot form a triangle. Otherwise, you can.'' -\end{quotation} - -Write a method named {\tt isTriangle} that it takes three integers as -arguments, and that returns either {\tt true} or {\tt false}, -depending on whether you can or cannot form a triangle from sticks -with the given lengths. - -The point of this exercise is to use conditional statements to -write a value method. - -\end{exercise} - - -\begin{exercise} -What is the output of the following program? The purpose of -this exercise is to make sure you understand logical operators -and the flow of execution through value methods. - -\begin{lstlisting} - public static void main(String[] args) { - boolean flag1 = isHoopy(202); - boolean flag2 = isFrabjuous(202); - System.out.println(flag1); - System.out.println(flag2); - if (flag1 && flag2) { - System.out.println("ping!"); - } - if (flag1 || flag2) { - System.out.println("pong!"); - } - } - - public static boolean isHoopy(int x) { - boolean hoopyFlag; - if (x%2 == 0) { - hoopyFlag = true; - } else { - hoopyFlag = false; - } - return hoopyFlag; - } - - public static boolean isFrabjuous(int x) { - boolean frabjuousFlag; - if (x > 0) { - frabjuousFlag = true; - } else { - frabjuousFlag = false; - } - return frabjuousFlag; - } -\end{lstlisting} -\end{exercise} - - - -\begin{exercise} -The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is -% -\[ Distance = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2} \] -% -Write a method named {\tt distance} that takes four -doubles as parameters---{\tt x1}, {\tt y1}, {\tt x2} and {\tt -y2}---and that prints the distance between the points. - -You should assume that there is a method named {\tt sumSquares} -that calculates and returns the sum of the squares of its arguments. -For example: - -\begin{lstlisting} - double x = sumSquares(3.0, 4.0); -\end{lstlisting} -% -would assign the value {\tt 25.0} to {\tt x}. - -The point of this exercise is to write a new method that uses an -existing one. You should write only one method: {\tt distance}. You -should not write {\tt sumSquares} or {\tt main} and you should not -invoke {\tt distance}. -\end{exercise} - - -\begin{exercise} -The point of this exercise is to use a stack diagram to understand -the execution of a recursive program. - -\begin{lstlisting} -public class Prod { - - public static void main(String[] args) { - System.out.println(prod(1, 4)); - } - - public static int prod(int m, int n) { - if (m == n) { - return n; - } else { - int recurse = prod(m, n-1); - int result = n * recurse; - return result; - } - } -} -\end{lstlisting} -% -\begin{enumerate} - -\item Draw a stack diagram showing the state of the program just -before the last instance of {\tt prod} completes. -What is the output of this program? - -\item Explain in a few words what {\tt prod} does. - -\item Rewrite {\tt prod} without using the temporary variables -{\tt recurse} and {\tt result}. - -\end{enumerate} -\end{exercise} - - -\begin{exercise} -The purpose of this exercise is to translate a recursive definition -into a Java method. The Ackerman function is defined for non-negative -integers as follows: -% -\begin{eqnarray} -A(m, n) = \begin{cases} - n+1 & \mbox{if } m = 0 \\ - A(m-1, 1) & \mbox{if } m > 0 \mbox{ and } n = 0 \\ -A(m-1, A(m, n-1)) & \mbox{if } m > 0 \mbox{ and } n > 0. -\end{cases} -\end{eqnarray} -% -Write a method called {\tt ack} that takes two {\tt int}s as -parameters and that computes and returns the value -of the Ackerman function. - -Test your implementation of Ackerman by invoking it -from {\tt main} and printing the return value. - -WARNING: the return value gets very big very quickly. You should try it -only for small values of $m$ and $n$ (not bigger than 2). - -\end{exercise} - - -\begin{exercise} -\begin{enumerate} - -\item Create a program called {\tt Recurse.java} and -type in the following methods: - -\begin{lstlisting} - // first: returns the first character of the given String - public static char first(String s) { - return s.charAt(0); - } - - // last: returns a new String that contains all but the - // first letter of the given String - public static String rest(String s) { - return s.substring(1, s.length()); - } - - // length: returns the length of the given String - public static int length(String s) { - return s.length(); - } -\end{lstlisting} - -\item Write some code in {\tt main} that tests each of these -methods. Make sure they work, and make sure you understand -what they do. - -\item Write a method called {\tt printString} that takes a -String as a parameter and that prints the letters of the -String, one on each line. It should be a {\tt void} method. - -\item Write a method called {\tt printBackward} that does -the same thing as {\tt printString} but that prints the String -backward (one character per line). - -\item Write a method called {\tt reverseString} that takes -a String as a parameter and that returns a new String as a -return value. The new String should contain the same letters -as the parameter, but in reverse order. For example, the -output of the following code - -\begin{lstlisting} - String backwards = reverseString("Allen Downey"); - System.out.println(backwards); -\end{lstlisting} -% -should be - -\begin{verbatimtab} -yenwoD nellA -\end{verbatimtab} - -\end{enumerate} -\end{exercise} - - -\begin{exercise} -\label{ex.power} -Write a recursive method called {\tt power} that -takes a double {\tt x} and an integer {\tt n} and that -returns $x^n$. - -Hint: a recursive definition of this -operation is $x^n = x \cdot x^{n-1}$. -Also, remember that anything raised to the zeroeth power -is 1. - -Optional challenge: you can make this method more efficient, when {\tt - n} is even, using $x^n = \left( x^{n/2} \right)^2$. - -\end{exercise} - - -\begin{exercise} -\label{gcd} -(This exercise is based on page 44 of Ableson and Sussman's -{\em Structure and Interpretation of Computer Programs}.) - -The following technique is known as Euclid's Algorithm because -it appears in Euclid's {\em Elements} (Book 7, ca.~300 BC). -It may be the oldest nontrivial algorithm\footnote{For a definition -of ``algorithm'', jump ahead to Section~\ref{algorithm}.}. - -The process is based on the observation that, if $r$ is the -remainder when $a$ is divided by $b$, then the common divisors -of $a$ and $b$ are the same as the common divisors of $b$ and $r$. -Thus we can use the equation -% -\[ gcd(a, b) = gcd(b, r) \] -% -to successively reduce the problem of computing a GCD to the -problem of computing the GCD of smaller and smaller pairs of integers. -For example, -% -\[ gcd(36, 20) = gcd(20, 16) = gcd(16, 4) = gcd(4, 0) = 4 \] -% -implies that the GCD of 36 and 20 is 4. It can be shown -that for any two starting numbers, this repeated reduction eventually -produces a pair where the second number is 0. Then the GCD is the -other number in the pair. - -Write a method called {\tt gcd} that takes two integer parameters and -that uses Euclid's algorithm to compute and return the greatest -common divisor of the two numbers. -\end{exercise} - - -\chapter{Iteration and loops} -\label{chap06} - -\section{Multiple assignment} -\index{assignment} -\index{statement!assignment} -\index{multiple assignment} - -You can make more than one assignment to the same variable; -the effect is to replace the old value with the new. - -\begin{lstlisting} - int liz = 5; - System.out.print(liz); - liz = 7; - System.out.println(liz); -\end{lstlisting} -% -The output of this program is {\tt 57}, because the first -time we print {\tt liz} her value is 5, and the second time -her value is 7. - -This kind of {\bf multiple assignment} is the reason I -described variables as a {\em container} for values. When -you assign a value to a variable, you change the contents of -the container, as shown in the figure: - - -\includegraphics{figs/assign2.pdf} - - -When there are multiple assignments to a variable, it is especially -important to distinguish between an assignment statement and a -statement of equality. Because Java uses the {\tt =} symbol for -assignment, it is tempting to interpret a statement like {\tt a = b} -as a statement of equality. It is not! - -First of all, equality is commutative, and assignment is not. -For example, in mathematics if $a = 7$ then $7 = a$. But in -Java {\tt a = 7;} is a legal assignment statement, and {\tt 7 = a;} -is not. - -Furthermore, in mathematics, a statement of equality is true -for all time. If $a = b$ now, then $a$ will always equal $b$. -In Java, an assignment statement can make two variables equal, -but they don't have to stay that way! - -\begin{lstlisting} - int a = 5; - int b = a; // a and b are now equal - a = 3; // a and b are no longer equal -\end{lstlisting} -% -The third line changes the value of {\tt a} but it does not -change the value of {\tt b}, so they are no longer equal. -In some programming languages a different symbol is used -for assignment, such as {\tt <-} or {\tt :=}, to -avoid this confusion. - -Although multiple assignment is frequently useful, you should use it -with caution. If the values of variables change often, it can make -the code difficult to read and debug. - - -\section{The {\tt while} statement} -\index{statement!while} -\index{while statement} -\index{iteration} - -Computers are often used to automate repetitive tasks. Repeating -tasks without making errors is something that -computers do well and people do poorly. - -We have already seen methods like {\tt countdown} and {\tt factorial} -that use recursion to perform repetition. This process is also called -{\bf iteration}. Java provides language features that make -it easier to write these methods. -In this chapter we are going to look at the {\tt while} statement. -Later on (in Section~\ref{for}) will check out the {\tt for} statement. - -Using a {\tt while} statement, we can rewrite {\tt countdown}: - -\begin{lstlisting} - public static void countdown(int n) { - while (n > 0) { - System.out.println(n); - n = n-1; - } - System.out.println("Blastoff!"); - } -\end{lstlisting} -% -You can almost read a {\tt while} statement like -English. What this means is, ``While {\tt n} is greater than -zero, print the value of {\tt n} and then reduce -the value of {\tt n} by 1. When you get to zero, print the -word `Blastoff!''' - -More formally, the flow of execution for a {\tt while} statement -is as follows: - -\begin{enumerate} - -\item Evaluate the condition in parentheses, yielding {\tt true} -or {\tt false}. - -\item If the condition is false, exit the {\tt while} statement -and continue execution at the next statement. - -\item If the condition is true, execute the statements -between the squiggly-brackets, and then go back to step 1. - -\end{enumerate} - -This type of flow is called a {\bf loop} because the third step loops -back around to the top. The statements inside the loop are called -the {\bf body} of the loop. -% -If the condition is false the -first time through the loop, the statements inside the loop are -never executed. - -\index{loop} -\index{loop!body} -\index{loop!infinite} -\index{body!loop} -\index{infinite loop} - -The body of the loop should change the value of -one or more variables so that, eventually, the condition becomes -false and the loop terminates. Otherwise the loop will repeat -forever, which is called an {\bf infinite} loop. An endless -source of amusement for computer scientists is the observation -that the directions on shampoo, ``Lather, rinse, repeat,'' are -an infinite loop. - -In the case of {\tt countdown}, we can prove that the loop -terminates if {\tt n} is positive. -% -In other cases it is not so easy to tell: - -\begin{lstlisting} - public static void sequence(int n) { - while (n != 1) { - System.out.println(n); - if (n%2 == 0) { // n is even - n = n / 2; - } else { // n is odd - n = n*3 + 1; - } - } - } -\end{lstlisting} -% -The condition for this loop is {\tt n != 1}, so the loop -will continue until {\tt n} is 1, which will make the condition -false. - -At each iteration, the program prints the value of {\tt n} and then -checks whether it is even or odd. If it is even, the value of -{\tt n} is divided by two. If it is odd, the value is replaced -by $3n+1$. For example, if the starting value (the argument passed -to {\tt sequence}) is 3, the resulting sequence is -3, 10, 5, 16, 8, 4, 2, 1. - -Since {\tt n} sometimes increases and sometimes decreases, there is no -obvious proof that {\tt n} will ever reach 1, or that the program will -terminate. For some particular values of {\tt n}, we can prove -termination. For example, if the starting value is a power of two, then -the value of {\tt n} will be even every time through the loop, until -we get to 1. The previous example ends with such a sequence, -starting with 16. - -Particular values aside, the interesting question is whether -we can prove that this program terminates for {\em all} values of n. -So far, no one has been able to prove it {\em or} disprove it! -For more information, see \url{http://en.wikipedia.org/wiki/Collatz_conjecture}. - - -\section{Tables} -\index{table} -\index{logarithm} - -One of the things loops are good for is generating and printing -tabular data. For example, before computers were readily -available, people had to calculate logarithms, -sines and cosines, and other common mathematical functions -by hand. - -To make that easier, there were books containing long tables -where you could find the values of various functions. -Creating these tables was slow and boring, and the results -were full of errors. - -When computers appeared on the scene, one of the initial reactions -was, ``This is great! We can use the computers to generate the -tables, so there will be no errors.'' That turned out to be true -(mostly), but shortsighted. Soon thereafter computers were so -pervasive that the tables became obsolete. - -Well, almost. For some operations, computers use tables of values to -get an approximate answer, and then perform computations to improve -the approximation. In some cases, there have been errors in the -underlying tables, most famously in the table the original Intel -Pentium used to perform floating-point division\footnote{See - \url{http://en.wikipedia.org/wiki/Pentium_FDIV_bug}.}. - -\index{division!floating-point} - -Although a ``log table'' is not as useful as it once was, it still -makes a good example of iteration. The following program prints a -sequence of values in the left column and their logarithms in the -right column: - -\begin{lstlisting} - double x = 1.0; - while (x < 10.0) { - System.out.println(x + " " + Math.log(x)); - x = x + 1.0; - } -\end{lstlisting} -% -The output of this program is - -\begin{verbatimtab} -1.0 0.0 -2.0 0.6931471805599453 -3.0 1.0986122886681098 -4.0 1.3862943611198906 -5.0 1.6094379124341003 -6.0 1.791759469228055 -7.0 1.9459101490553132 -8.0 2.0794415416798357 -9.0 2.1972245773362196 -\end{verbatimtab} -% -Looking at these values, can you tell what base the {\tt log} -method uses? - -Since powers of two are important -in computer science, we often want logarithms with -respect to base 2. To compute them, we can use the formula: -% -\begin{equation*} -\log_2 x = log_e x / log_e 2 -\end{equation*} -% -Changing the {\tt print} statement to - -\begin{lstlisting} - System.out.println(x + " " + Math.log(x) / Math.log(2.0)); -\end{lstlisting} -% -yields - -\begin{verbatimtab} -1.0 0.0 -2.0 1.0 -3.0 1.5849625007211563 -4.0 2.0 -5.0 2.321928094887362 -6.0 2.584962500721156 -7.0 2.807354922057604 -8.0 3.0 -9.0 3.1699250014423126 -\end{verbatimtab} -% -We can see that 1, 2, 4 and 8 are powers of two, because -their logarithms base 2 are round numbers. If we wanted to find -the logarithms of other powers of two, we could modify the -program like this: - -\begin{lstlisting} - double x = 1.0; - while (x < 100.0) { - System.out.println(x + " " + Math.log(x) / Math.log(2.0)); - x = x * 2.0; - } -\end{lstlisting} -% -Now instead of adding something to {\tt x} each time through -the loop, which yields an arithmetic sequence, we multiply -{\tt x} by something, yielding a {\bf geometric} sequence. -The result is: - -\begin{verbatimtab} -1.0 0.0 -2.0 1.0 -4.0 2.0 -8.0 3.0 -16.0 4.0 -32.0 5.0 -64.0 6.0 -\end{verbatimtab} -% -Log tables may not be useful any more, but for computer scientists, -knowing the powers of two is! When you have an idle -moment, you should memorize the powers of two up to 65536 -(that's $2^{16}$). - - -\section{Two-dimensional tables} -\index{table!two-dimensional} - -A two-dimensional table consists of rows and columns that make -it easy to find values at the intersections. A multiplication -table is a good example. Let's say you want to print a -multiplication table for the values from 1 to 6. - -A good way to start is to write a simple loop that prints -the multiples of 2, all on one line. - -\begin{lstlisting} - int i = 1; - while (i <= 6) { - System.out.print(2*i + " "); - i = i + 1; - } - System.out.println(""); -\end{lstlisting} -% -The first line initializes a variable named {\tt i}, which is going -to act as a counter, or {\bf loop variable}. As the loop executes, -the value of {\tt i} increases from 1 to 6; when {\tt i} is 7, the -loop terminates. Each time through the loop, we print the value {\tt - 2*i} and three spaces. Since we use {\tt System.out.print}, -the output appears on a single line. - -\index{loop variable} -\index{variable!loop} - -In some environments the -output from {\tt print} gets stored without being displayed until {\tt -println} is invoked. If the program terminates, and you forget to -invoke {\tt println}, you may never see the stored output. - -The output of this program is: - -\begin{verbatimtab} -2 4 6 8 10 12 -\end{verbatimtab} -% -So far, so good. The next step is to {\bf encapsulate} and {\bf -generalize}. - - -\section {Encapsulation and generalization} -\label{encapsulation} - -Encapsulation means taking a piece of code and wrapping it up -in a method, allowing you to take advantage of all the things methods -are good for. We have seen two examples of encapsulation, when we -wrote {\tt printParity} in Section~\ref{alternative} and {\tt -isSingleDigit} in Section~\ref{boolean}. - -Generalization means taking something specific, like printing -multiples of 2, and making it more general, like printing the -multiples of any integer. -\index{encapsulation} -\index{generalization} - -Here's a method that encapsulates the loop from the previous -section and generalizes it to print multiples of {\tt n}. - -\begin{lstlisting} - public static void printMultiples(int n) { - int i = 1; - while (i <= 6) { - System.out.print(n*i + " "); - i = i + 1; - } - System.out.println(""); - } -\end{lstlisting} -% -To encapsulate, all I had to do was add the first line, -which declares the name, parameter, -and return type. To generalize, all I had to do was replace -the value 2 with the parameter {\tt n}. - -If I invoke this method with the argument 2, I get the same -output as before. With argument 3, the output is: - -\begin{verbatimtab} -3 6 9 12 15 18 -\end{verbatimtab} -% -and with argument 4, the output is - -\begin{verbatimtab} -4 8 12 16 20 24 -\end{verbatimtab} -% -By now you can probably guess how we are going to print a -multiplication table: we'll invoke {\tt printMultiples} repeatedly with -different arguments. In fact, we are going to use another loop to -iterate through the rows. - -\begin{lstlisting} - int i = 1; - while (i <= 6) { - printMultiples(i); - i = i + 1; - } -\end{lstlisting} -% -First of all, notice how similar this loop is to the one inside {\tt -printMultiples}. All I did was replace the print statement with a -method invocation. - -The output of this program is - -\begin{verbatimtab} -1 2 3 4 5 6 -2 4 6 8 10 12 -3 6 9 12 15 18 -4 8 12 16 20 24 -5 10 15 20 25 30 -6 12 18 24 30 36 -\end{verbatimtab} -% -which is a (slightly sloppy) multiplication table. If the -sloppiness bothers you, Java provides methods that give you -more control over the format of the output, but I'm not -going to get into that here. - - -\section{Methods and encapsulation} -\label{methods} -\index{method} -\index{encapsulation} - -In Section~\ref{adding_methods} I listed some of the -reasons methods are useful. Here are several more: - -\begin{itemize} - -\item By giving a name to a sequence of statements, you make -your program easier to read and debug. - -\item Dividing a long program into methods allows you to -separate parts of the program, debug them in isolation, and -then compose them into a whole. - -\item Methods facilitate both recursion and iteration. - -\item Well-designed methods are often useful for many programs. -Once you write and debug one, you can reuse it. - -\end{itemize} - -To demonstrate encapsulation again, I'll take the code -from the previous section and wrap it up in a method: - -\begin{lstlisting} - public static void printMultTable() { - int i = 1; - while (i <= 6) { - printMultiples(i); - i = i + 1; - } - } -\end{lstlisting} -% -The development process I am demonstrating is called -{\bf encapsulation and generalization}. -You start by adding -code to {\tt main} or another method. When you get -it working, you extract it and wrap it up in a method. -Then you generalize the method by adding parameters. -\index{program development} -\index{encapsulation} -\index{generalization} - -Sometimes you don't know -when you start writing exactly how to divide the program into -methods. This process lets you design as you go along. - - -\section{Local variables} -\index{local variable} -\index{variable!local} - -You might wonder how we can use the same -variable {\tt i} in both {\tt printMultiples} and {\tt -printMultTable}. Didn't I say that you can only declare a variable -once? And doesn't it cause problems when one of the methods changes -the value of the variable? - -The answer to both questions is ``no,'' because the {\tt i} in {\tt -printMultiples} and the {\tt i} in {\tt printMultTable} are -{\em not the same variable}. They have the same name, but -they do not refer to the same storage location, and changing -the value of one has no effect on the other. - -Variables declared inside a method definition are -called {\bf local variables} because they only exist inside -the method. You cannot access a local variable from outside -its ``home'' method, and you are free to have multiple -variables with the same name, as long as they are not in -the same method. - -Although it can be confusing, there are good -reasons to reuse names. For example, it is common to -use the names {\tt i}, {\tt j} and {\tt k} as loop variables. -If you avoid using them in one method just because you -used them somewhere else, you make the program -harder to read. - -\index{loop variable} -\index{variable!loop} - -\section{More generalization} -\index{generalization} - -As another example of generalization, imagine you wanted -a program that would print a multiplication table of any -size, not just the 6x6 table. You could add a parameter to -{\tt printMultTable}: - -\begin{lstlisting} - public static void printMultTable(int high) { - int i = 1; - while (i <= high) { - printMultiples(i); - i = i + 1; - } - } -\end{lstlisting} -% -I replaced the value 6 with the parameter {\tt high}. If I -invoke {\tt printMultTable} with the argument 7, I get - -\begin{verbatimtab} -1 2 3 4 5 6 -2 4 6 8 10 12 -3 6 9 12 15 18 -4 8 12 16 20 24 -5 10 15 20 25 30 -6 12 18 24 30 36 -7 14 21 28 35 42 -\end{verbatimtab} -% -which is fine, except that I probably want the table to -be square (same number of rows and columns), which means -I have to add another parameter to {\tt printMultiples}, -to specify how many columns the table should have. - -I also call this parameter {\tt high}, -demonstrating that different methods can have parameters -with the same name (just like local variables): - -\begin{lstlisting} - public static void printMultiples(int n, int high) { - int i = 1; - while (i <= high) { - System.out.print(n*i + " "); - i = i + 1; - } - System.out.println(""); - } - - public static void printMultTable(int high) { - int i = 1; - while (i <= high) { - printMultiples(i, high); - i = i + 1; - } - } -\end{lstlisting} -% -Notice that when I added a new parameter, I had to change the first -line, and I also had to -change the place where the method is invoked in {\tt printMultTable}. -As expected, this program generates a square 7x7 table: - -\begin{verbatimtab} -1 2 3 4 5 6 7 -2 4 6 8 10 12 14 -3 6 9 12 15 18 21 -4 8 12 16 20 24 28 -5 10 15 20 25 30 35 -6 12 18 24 30 36 42 -7 14 21 28 35 42 49 -\end{verbatimtab} -% -When you generalize a method appropriately, you often find -that it has capabilities you did not plan. -For example, you might notice that the multiplication table -is symmetric, because $ab = ba$, so all the entries in the -table appear twice. You could save ink by printing only -half the table. To do that, you only have to change one -line of {\tt printMultTable}. Change - -\begin{lstlisting} - printMultiples(i, high); -\end{lstlisting} -% -to - -\begin{lstlisting} - printMultiples(i, i); -\end{lstlisting} -% -and you get - -\begin{verbatimtab} -1 -2 4 -3 6 9 -4 8 12 16 -5 10 15 20 25 -6 12 18 24 30 36 -7 14 21 28 35 42 49 -\end{verbatimtab} -% -I'll leave it up to you to figure out how it works. - - -\section{Glossary} - -\begin{description} - -\item[loop:] A statement that executes repeatedly while -some condition is satisfied. - -\item[infinite loop:] A loop whose condition is always true. - -\item[body:] The statements inside the loop. - -\item[iteration:] One pass through (execution of) the body -of the loop, including the evaluation of the condition. - -\item[encapsulate:] To divide a large complex program into -components (like methods) and isolate the components from -each other (for example, by using local variables). - -\item[local variable:] A variable that is declared inside -a method and that exists only within that method. Local variables -cannot be accessed from outside their home method, and do not -interfere with any other methods. - -\item[generalize:] To replace something unnecessarily specific -(like a constant value) with something appropriately general -(like a variable or parameter). Generalization makes code more -versatile, more likely to be reused, and sometimes even easier -to write. - -\item[program development:] A process for writing programs. - So far we have seen ``incremental development'' and ``encapsulation - and generalization''. - -\index{loop} -\index{infinite loop} -\index{loop!infinite} -\index{iteration} -\index{encapsulation} -\index{generalization} -\index{local variable} -\index{variable!local} -\index{program development} - -\end{description} - - -\section{Exercises} - -\begin{exercise} -\label{infloop} - -Consider the following code: - -\begin{lstlisting} -public static void main(String[] args) { - loop(10); -} - -public static void loop(int n) { - int i = n; - while (i > 0) { - System.out.println(i); - if (i%2 == 0) { - i = i/2; - } else { - i = i+1; - } - } -} -\end{lstlisting} -% -\begin{enumerate} - -\item Draw a table that shows the value of the variables {\tt i} -and {\tt n} during the execution of {\tt loop}. The table should -contain one column for each variable and one line for each -iteration. - -\item What is the output of this program? - -\end{enumerate} -\end{exercise} - - -\begin{exercise} -Let's say you are given a number, $a$, and you want to find -its square root. One way to do that is to start with a very -rough guess about the answer, $x_0$, and then improve -the guess using the following formula: -% -\begin{equation*} -x_1 =(x_0 + a/x_0) / 2 -\end{equation*} -% -For example, if we want to find the square root of 9, and -we start with $x_0 = 6$, then $x_1 =(6 + 9/6) /2 = 15/4 = 3.75$, -which is closer. - -We can repeat the procedure, using $x_1$ to calculate $x_2$, -and so on. In this case, $x_2 = 3.075$ and $x_3 = 3.00091$. -So that is converging very quickly on the right answer(which -is 3). - -Write a method called {\tt squareRoot} that takes a {\tt double} -as a parameter and that returns an approximation of the square -root of the parameter, using this technique. You may not use -{\tt Math.sqrt}. - -As your initial guess, you should use $a/2$. Your method should -iterate until it gets two consecutive estimates that differ by less -than 0.0001; in other words, until the absolute value of $x_n - -x_{n-1}$ is less than 0.0001. You can use {\tt Math.abs} to calculate -the absolute value. -\end{exercise} - - -\begin{exercise} -In Exercise~\ref{ex.power} we wrote a recursive version of {\tt -power}, which takes a double {\tt x} and an integer {\tt n} and -returns $x^n$. Now write an iterative method to perform the same -calculation. -\end{exercise} - -\begin{exercise} -Section~\ref{factorial} presents a recursive method -that computes the factorial function. -Write an iterative version of {\tt factorial}. -\end{exercise} - -\begin{exercise} -One way to calculate $e^x$ is to use the infinite series expansion -% -\begin{equation*} -e^x = 1 + x + x^2 / 2! + x^3 / 3! + x^4 / 4! + ... -\end{equation*} -% -If the loop variable is named {\tt i}, then the $i$th term is -$x^i / i!$. - -\begin{enumerate} - -\item Write a method called {\tt myexp} that adds up the first {\tt n} -terms of this series. You can use the {\tt factorial} -method from Section~\ref{factorial} or your iterative version from the -previous exercise. - -\item You can make this method much more efficient if you realize that -in each iteration the numerator of the term is the same as its -predecessor multiplied by {\tt x} and the denominator is the same as -its predecessor multiplied by {\tt i}. Use this observation to -eliminate the use of {\tt Math.pow} and {\tt factorial}, and check -that you still get the same result. - -\item Write a method called {\tt check} that takes a single parameter, -{\tt x}, and that prints the values of {\tt x}, {\tt Math.exp(x)} and -{\tt myexp(x)} for various values of {\tt x}. The output should look -something like: - -\begin{verbatimtab} -1.0 2.708333333333333 2.718281828459045 -\end{verbatimtab} - -%the next line used to use \\ in an attempt to escape the backslash character -%but this doesn't work: \\ produces a newline -%according to the LaTeX symbol list -%http://www.tex.ac.uk/tex-archive/info/symbols/comprehensive/symbols-letter.pdf -%\textbackslash is the actual way to escape a backslash -%(but it seems not to respect the \tt font) -HINT: you can use the String {\tt "\textbackslash t"} to print a tab character -between columns of a table. - -\item Vary the number of terms in the series (the second argument -that {\tt check} sends to {\tt myexp}) and see the effect on -the accuracy of the result. Adjust this value until the estimated -value agrees with the ``correct'' answer when {\tt x} is 1. - -\item Write a loop in {\tt main} that invokes {\tt check} with the -values 0.1, 1.0, 10.0, and 100.0. How does the accuracy of the -result vary as {\tt x} varies? Compare the number of digits of -agreement rather than the difference between the actual and -estimated values. - -\item Add a loop in {\tt main} that checks {\tt myexp} with the values --0.1, -1.0, -10.0, and -100.0. Comment on the accuracy. - -\end{enumerate} -\end{exercise} - - -\begin{exercise} -One way to evaluate $\exp(-x^2)$ is to use the infinite series expansion -% -\begin{equation*} -\exp(-x^2) = 1 - x^2 + x^4/2 - x^6/6 + \ldots -\end{equation*} -% -In other words, we need to add up a series of terms where the $i$th -term is equal to $(-1)^i x^{2i} / i!$. Write a method named {\tt gauss} -that takes {\tt x} and {\tt n} as arguments and that returns the sum -of the first {\tt n} terms of the series. You should not use {\tt -factorial} or {\tt pow}. -\end{exercise} - - -\chapter{Strings and things} -\label{chap07} -\label{strings} - -\section{Characters} -\index{method!string} -\index{String method} -\index{method!object} -\index{object method} -\index{class!String} - -In Java and other object-oriented languages, {\bf objects} are collections -of related data that come with a set of methods. These methods -operate on the objects, performing computations and sometimes -modifying the object's data. - -{\tt Strings} are objects, -so you might ask ``What is the data -contained in a {\tt String} object?''~and~``What are the methods we -can invoke on {\tt String} objects?'' -\index{documentation} -% -The components of a {\tt String} object are letters or, more generally, -characters. Not all characters are letters; some are numbers, -symbols, and other things. For simplicity I -call them all letters. -% -There are many methods, but I use only a few in this -book. The rest are documented at -\url{http://download.oracle.com/javase/6/docs/api/java/lang/String.html}. - -The first method we will look at is {\tt charAt}, which allows you to -extract letters from a {\tt String}. -% To store the result, we need a new type: -{\tt char} is the variable type that can store -individual characters (as opposed to strings of them). - -\index{char} -\index{type!char} -\index{charAt} - -{\tt char}s work just like the other types we have seen: - -\begin{lstlisting} - char ltr = 'c'; - if (ltr == 'c') { - System.out.println(ltr); - } -\end{lstlisting} -% -Character values appear in single quotes, like {\tt 'c'}. Unlike -string values (which appear in double quotes), character values -can contain only a single letter or symbol. - -\index{quote} -\index{double-quote} -\index{value!char} - -Here's how the {\tt charAt} method is used: - -\begin{lstlisting} - String fruit = "banana"; - char letter = fruit.charAt(1); - System.out.println(letter); -\end{lstlisting} -% -{\tt fruit.charAt()} means that I am -invoking the {\tt charAt} method on the object named -{\tt fruit}. -I am passing the argument {\tt 1} to this method, -which means that I want to know the first letter of -the string. The result is a character, which is stored in a -{\tt char} named {\tt letter}. When I print the value of -{\tt letter}, I get a surprise: - -\begin{verbatimtab} -a -\end{verbatimtab} -% -{\tt a} is not the first letter of {\tt "banana"}. Unless you are a -computer scientist. For technical reasons, computer scientists -start counting from zero. The 0th letter (``zeroeth'') of {\tt -"banana"} is {\tt b}. The 1th letter (``oneth'') is {\tt a} and the -2th (``twooth'') letter is {\tt n}. - -If you want the zereoth letter of a string, you have to pass -0 as an argument: - -\begin{lstlisting} - char letter = fruit.charAt(0); -\end{lstlisting} - - -\section{Length} -\index{String!length} -\index{length!String} - -The next {\tt String} method we'll look at is {\tt length}, which -returns the number of characters in the string. For example: - -\begin{lstlisting} - int length = fruit.length(); -\end{lstlisting} -% -{\tt length} takes no arguments -and returns an integer, in this case 6. Notice that it is -legal to have a variable with the same name as a method (although -it can be confusing for human readers). - -To find the last letter of a string, you might be tempted to -try something like - -\begin{lstlisting} - int length = fruit.length(); - char last = fruit.charAt(length); // WRONG!! -\end{lstlisting} -% -That won't work. The reason is that there is no 6th letter -in {\tt "banana"}. Since we started counting at 0, the 6 -letters are numbered from 0 to 5. To get the last character, -you have to subtract 1 from {\tt length}. - -\begin{lstlisting} - int length = fruit.length(); - char last = fruit.charAt(length-1); -\end{lstlisting} - - -\section{Traversal} -\label{traverse} -\index{traverse} - -A common thing to do with a string is -start at the beginning, select each character in turn, do -some computation with it, and continue until the end. This pattern -of processing is called a {\bf traversal}. A natural -way to encode a traversal is with a {\tt while} statement: - -\begin{lstlisting} - int index = 0; - while (index < fruit.length()) { - char letter = fruit.charAt(index); - System.out.println(letter); - index = index + 1; - } -\end{lstlisting} -% -This loop traverses the string and prints each letter on -a line by itself. Notice that the condition is -{\tt index < fruit.length()}, which means that when -{\tt index} is equal to the length of the string, the -condition is false and the body of the loop is not executed. -The last character we access is the one with the -index {\tt fruit.length()-1}. - -\index{loop variable} -\index{variable!loop} -\index{index} - -The name of the loop variable is {\tt index}. An {\bf -index} is a variable or value used to specify a member of an ordered -set, in this case the string of characters. The index -indicates (hence the name) which one you want. - -\section{Run-time errors} -\label{StringIndexOutOfBounds} -\index{error!run-time} -\index{run-time error} -\index{exception!StringIndexOutOfBounds} - -Way back in Section~\ref{run-time} I talked about run-time errors, -which are errors that don't appear until a program has started -running. In Java run-time errors are called {\bf exceptions}. - -You probably haven't seen many run-time errors, because we -haven't been doing many things that can cause one. Well, now we are. -If you use the {\tt charAt} method and provide an index that is -negative or greater than {\tt length-1}, it {\bf throws} an exception. -You can think of ``throwing'' an exception like throwing -a tantrum. - -When that happens, Java prints an error message with -the type of exception and a {\bf stack trace}, which shows the methods -that were running when the exception occurred. Here is an example: - -\begin{lstlisting} -public class BadString { - - public static void main(String[] args) { - processWord("banana"); - } - - public static void processWord(String s) { - char c = getLastLetter(s); - System.out.println(c); - } - - public static char getLastLetter(String s) { - int index = s.length(); // WRONG! - char c = s.charAt(index); - return c; - } -} -\end{lstlisting} - -Notice the error in {\tt getLastLetter}: the index of the last -character should be {\tt s.length()-1}. Here's what you get: - -\begin{verbatimtab} -Exception in thread "main" java.lang.StringIndexOutOfBoundsException: -String index out of range: 6 - at java.lang.String.charAt(String.java:694) - at BadString.getLastLetter(BadString.java:24) - at BadString.processWord(BadString.java:18) - at BadString.main(BadString.java:14) -\end{verbatimtab} - -Then the program ends. -The stack trace can be hard to read, but it contains a lot of information. - - -\section{Reading documentation} -\label{documentation} -\index{documentation} - -If you go to -\url{http://download.oracle.com/javase/6/docs/api/java/lang/String.html}. -and click on {\tt charAt}, you get the following documentation -(or something like it): - -\begin{verbatimtab} -public char charAt(int index) - -Returns the char value at the specified index. An index ranges -from 0 to length() - 1. The first char value of the sequence is -at index 0, the next at index 1, and so on, as for array indexing. - -Parameters: index - the index of the char value. - -Returns: the char value at the specified index of this string. - The first char value is at index 0. - -Throws: IndexOutOfBoundsException - if the index argument is - negative or not less than the length of this string. -\end{verbatimtab} - -The first line is the method's {\bf prototype}, which specifies the -name of the method, the type of the parameters, and the return type. - -The next line describes what the method does. The following -lines explain the parameters and return values. In this case -the explanations are redundant, but the documentation is -supposed to fit a standard format. The last line describes -the exceptions this method might throw. - -It might take some time to get -comfortable with this kind of documentation, but it is worth the effort. - - -\section{The {\tt indexOf} method} -\index{indexOf} - -{\tt indexOf} is the inverse of {\tt charAt}: -{\tt charAt} takes an index and returns the character at that -index; {\tt indexOf} takes a character and finds the index -where that character appears. - -{\tt charAt} fails if the index is out of range, and throws an -exception. {\tt indexOf} fails if the character does not appear in -the string, and returns the value {\tt -1}. - -\begin{lstlisting} - String fruit = "banana"; - int index = fruit.indexOf('a'); -\end{lstlisting} -% -This finds the index of the letter {\tt 'a'} in the string. -In this case, the letter appears three times, so it is not -obvious what {\tt indexOf} should do. According to the -documentation, it returns the index of the {\em first} appearance. - -To find subsequent appearances, there is another -version of {\tt indexOf}. It takes a -second argument that indicates where in the string to start -looking. For an explanation of this kind -of overloading, see Section~\ref{overloading}. - -If we invoke: - -\begin{lstlisting} - int index = fruit.indexOf('a', 2); -\end{lstlisting} -% -it starts at the twoeth letter (the first {\tt n}) and finds -the second {\tt a}, which is at index 3. If the letter happens -to appear at the starting index, the starting index is the -answer. So - -\begin{lstlisting} - int index = fruit.indexOf('a', 5); -\end{lstlisting} -% -returns 5. - - -\section{Looping and counting} -\label{loopcount} -\index{traverse!counting} -\index{loop!counting} - -The following program counts the -number of times the letter {\tt 'a'} appears in a string: - -\begin{lstlisting} - String fruit = "banana"; - int length = fruit.length(); - int count = 0; - - int index = 0; - while (index < length) { - if (fruit.charAt(index) == 'a') { - count = count + 1; - } - index = index + 1; - } - System.out.println(count); -\end{lstlisting} -% -This program demonstrates a common idiom, called a {\bf counter}. The -variable {\tt count} is initialized to zero and then incremented each -time we find an {\tt 'a'}. To {\bf increment} is to increase by one; -it is the opposite of {\bf decrement}. -%, and unrelated to {\bf excrement}, which is a noun -When we exit the loop, {\tt count} -contains the result: the total number of a's. -\index{counter} -\index{increment} -\index{decrement} - - -\section{Increment and decrement operators} -\index{operator!increment} -\index{operator!decrement} - -Incrementing and decrementing are such common operations that -Java provides special operators for them. The {\tt ++} -operator adds one to the current value of an {\tt int} or -{\tt char}. {\tt --} subtracts one. Neither operator works -on {\tt double}s, {\tt boolean}s or {\tt String}s. - -Technically, it is legal to increment a variable and use it -in an expression at the same time. For example, you might see -something like: - -\begin{lstlisting} - System.out.println(i++); -\end{lstlisting} -% -Looking at this, it is not clear whether the increment will -take effect before or after the value is printed. Because -expressions like this tend to be confusing, I discourage -you from using them. In fact, to discourage you even more, -I'm not going to tell you what the result is. If you really -want to know, you can try it. - -Using the increment operators, we can rewrite the letter-counter: - -\begin{lstlisting} - int index = 0; - while (index < length) { - if (fruit.charAt(index) == 'a') { - count++; - } - index++; - } -\end{lstlisting} -% -It is a common error to write something like - -\begin{lstlisting} - index = index++; // WRONG!! -\end{lstlisting} -% -Unfortunately, this is syntactically legal, so the compiler -will not warn you. The effect of this statement is to leave -the value of {\tt index} unchanged. This is often a difficult -bug to track down. - -Remember, you can write {\tt index = index+1}, or you -can write {\tt index++}, but you shouldn't mix them. - -% \section{Character arithmetic} -% \index{char} -% \index{type!char} -% \index{operator!char} -% \index{arithmetic!char} - -% It may seem odd, but you can do arithmetic with characters. -% If you have a variable named {\tt letter} that contains a character, -% then {\tt letter - 'a'} will tell you where in the alphabet it appears -%(keeping in mind that 'a' is the zeroeth letter of the alphabet and -% 'z' is the 25th). - -% This sort of thing is useful for converting between the characters -% that contain numbers, like '0', '1' and '2', and the corresponding -% integers. They are not the same thing. For example, if you try this - -% \begin{lstlisting} -% char letter = '3'; -% int x =(int) letter; -% System.out.println(x); -% \end{lstlisting} -% % -% you might expect the value 3, but depending on your environment, -% you might get 51, which is the ASCII code that is used to -% represent the character '3', or you might get something else -% altogether. To convert '3' to the corresponding integer value -% you can subtract '0': - -% \begin{lstlisting} -% int x =(int)(letter - '0'); -% \end{lstlisting} -% % -% Technically, in both of these examples the typecast({\tt(int)}) is -% unnecessary, since Java will convert type {\tt char} to type {\tt int} -% automatically. I included the typecasts to emphasize the difference -% between the types, and because I'm a stickler about that sort of -% thing. - -% Since this conversion can be a little ugly, it is preferable to use -% the {\tt digit} method in the {\tt Character} class. For example: - -% \begin{lstlisting} -% int x = Character.digit(letter, 10); -% \end{lstlisting} -% % -% converts {\tt letter} to the corresponding digit, interpreting -% it as a base 10 number. - -% Another use for character arithmetic is to loop through the letters of -% the alphabet in order. For example, in Robert McCloskey's book {\em -% Make Way for Ducklings}, the names of the ducklings form an -% abecedarian series: Jack, Kack, Lack, Mack, Nack, Ouack, Pack and -% Quack. Here is a loop that prints these names in order: - -% \begin{lstlisting} -% char letter = 'J'; -% while (letter <= 'Q') { - % System.out.println(letter + "ack"); - % letter++; -% } -% \end{lstlisting} -% -% Notice that in addition to the arithmetic operators, we can also -% use the conditional operators on characters. The output of this -% program is: - -% \begin{verbatimtab} -% Jack -% Kack -% Lack -% Mack -% Nack -% Oack -% Pack -% Qack -% \end{verbatimtab} -% % -% Of course, that's not quite right because I've misspelled ``Ouack'' -% and ``Quack.'' As an exercise, modify the program to correct -% this error. - - -\section{{\tt String}s are immutable} -\label{immutable} -\index{class!String} -\index{immutable} -\index{String} -\index{toUpperCase} -\index{toLowerCase} - -As you read the documentation of the {\tt String} methods, you -might notice {\tt toUpperCase} and {\tt toLowerCase}. These -methods are often a source of confusion, because it sounds -like they have the effect of changing (or mutating) an -existing string. Actually, neither these methods nor any -others can change a string, because strings are {\bf immutable}. - -When you invoke {\tt toUpperCase} on a {\tt String}, you get a -{\em new} {\tt String} as a return value. For example: - -\begin{lstlisting} - String name = "Alan Turing"; - String upperName = name.toUpperCase(); -\end{lstlisting} -% -After the second line is executed, {\tt upperName} contains -the value {\tt "ALAN TURING"}, but {\tt name} still contains -{\tt "Alan Turing"}. -\index{Turing, Alan} - - -\section{{\tt String}s are incomparable} -\label{incomparable} -\index{class!String} -\index{comparison!String} -\index{String} -\index{equals} -\index{compareTo} - -It is often necessary to compare strings to see if they are the same, -or to see which comes first in alphabetical order. It would be -nice if we could use the comparison operators, like {\tt ==} and -{\tt >}, but we can't. - -To compare {\tt String}s, we have to use the {\tt equals} -and {\tt compareTo} methods. For example: - -\begin{lstlisting} - String name1 = "Alan Turing"; - String name2 = "Ada Lovelace"; - - if (name1.equals (name2)) { - System.out.println("The names are the same."); - } - - int flag = name1.compareTo (name2); - if (flag == 0) { - System.out.println("The names are the same."); - } else if (flag < 0) { - System.out.println("name1 comes before name2."); - } else if (flag > 0) { - System.out.println("name2 comes before name1."); - } -\end{lstlisting} -% -The syntax here is a little weird. To compare two {\tt String}s, -you have to invoke a method on one of them and pass the other as an -argument. - -The return value from {\tt equals} is straightforward enough; -{\tt true} if the strings contain the same characters, and -{\tt false} otherwise. - -The return value from {\tt compareTo} is a weird, too. It is -the difference between the first characters in the strings -that differ. If the strings are equal, it is 0. If the -first string (the one on which the method is invoked) comes -first in the alphabet, the difference is negative. Otherwise, -the difference is positive. In this case the return value -is positive 8, because the second letter of ``Ada'' comes -before the second letter of ``Alan'' by 8 letters. - -Just for completeness, I should admit that it is {\em legal}, but very -seldom {\em correct}, to use the {\tt ==} operator with {\tt String}s. -I explain why in Section~\ref{equivalence}; for now, don't do it. - - -\section{Glossary} - -\begin{description} - -\item[object:] A collection of related data that comes with a set of -methods that operate on it. The objects we have used so far are -{\tt String}s, Bugs, Rocks, and the other GridWorld objects. - -\item[index:] A variable or value used to select one of the -members of an ordered set, like a character from a string. - -\item[exception:] A run-time error. -\index{exception} -\index{run-time error} - -\item[throw:] Cause an exception. - -\item[stack trace:] A report that shows the state of a program -when an exception occurs. - -\item[prototype:] The first line of a method, which specifies -the name, parameters and return type. - -\item[traverse:] To iterate through all the elements of a set -performing a similar operation on each. - -\item[counter:] A variable used to count something, usually -initialized to zero and then incremented. - -\item[increment:] Increase the value of a variable by one. -The increment operator in Java is {\tt ++}. - -\item[decrement:] Decrease the value of a variable by one. -The decrement operator in Java is {\tt --}. - - -\index{object} -\index{index} -\index{traverse} -\index{counter} -\index{increment} -\index{decrement} - -\end{description} - - -\section{Exercises} - -\begin{exercise} -Write a method that takes a {\tt String} -as an argument and that prints the letters backwards all on -one line. -\end{exercise} - -\begin{exercise} -Read the stack trace in Section~\ref{StringIndexOutOfBounds} -and answer these questions: - -\begin{itemize} - -\item What kind of Exception occurred, and what package is it defined -in? - -\item What is the value of the index that caused the exception? - -\item What method threw the exception, and where is -that method defined? - -\item What method invoked {\tt charAt}? - -\item In {\tt BadString.java}, what is the line number where {\tt charAt} -was invoked? - -\end{itemize} - -\end{exercise} - -\begin{exercise} - -Encapsulate the code in Section~\ref{loopcount} in a method named -{\tt countLetters}, and generalize it so that it accepts the -string and the letter as arguments. -\index{encapsulation} -\index{generalization} - -Then rewrite the method so that it uses -{\tt indexOf} to locate the a's, rather than checking -the characters one by one. - -\end{exercise} - -\begin{exercise} -The purpose of this exercise is to review encapsulation -and generalization. - -\begin{enumerate} - -\item Encapsulate the following code fragment, transforming it -into a method that takes a String as an argument and that -returns the final value of {\tt count}. - -\item In a sentence or two, describe what the resulting method does -(without getting into the details of how). - -\item Now that you have generalized the code -so that it works on any String, what could you do to -generalize it more? - -\end{enumerate} - -\begin{lstlisting} - String s = "((3 + 7) * 2)"; - int len = s.length(); - - int i = 0; - int count = 0; - - while (i < len) { - char c = s.charAt(i); - - if (c == '(') { - count = count + 1; - } else if (c == ')') { - count = count - 1; - } - i = i + 1; - } - - System.out.println(count); -\end{lstlisting} -\end{exercise} - - -\begin{exercise} - -The point of this exercise is to explore Java types -and fill in some of the details that aren't covered -in the chapter. - -\begin{enumerate} - -\item Create a new program named {\tt Test.java} and write -a {\tt main} method that contains -expressions that combine -various types using the {\tt +} operator. For example, what -happens when you ``add'' a {\tt String} and a {\tt char}? -Does it perform addition or concatenation? What is the type -of the result? (How can you determine the type of the result?) - -\item Make a bigger copy of the following table and fill it in. At the -intersection of each pair of types, you should indicate whether it is -legal to use the {\tt +} operator with these types, what operation is -performed (addition or concatenation), and what the type of the result -is. - -\begin{tabular}{|l|l|l|l|l|} \hline - & boolean & char & int & String \\ \hline -boolean & & & & \\ \hline -char & & & & \\ \hline -int & & & & \\ \hline -String & & & & \\ \hline -\end{tabular} - -\item Think about some of the choices the designers of Java -made when they filled in this table. How many of the entries -seem unavoidable, as if there were no other choice? -How many seem like arbitrary choices from several equally -reasonable possibilities? How many seem problematic? - -\item Here's a puzzler: normally, the statement {\tt x++} is exactly - equivalent to {\tt x = x + 1}. But if {\tt x} is a {\tt char}, it's - not! In that case, {\tt x++} is legal, but {\tt x = x + 1} causes - an error. Try it out and see what the error message is, then see if - you can figure out what is going on. - -\end{enumerate} -\end{exercise} - - -\begin{exercise} - -What is the output of this program? Describe in a sentence -what {\tt mystery} does (not how it works). - -\begin{lstlisting} -public class Mystery { - - public static String mystery(String s) { - int i = s.length() - 1; - String total = ""; - - while (i >= 0 ) { - char ch = s.charAt(i); - System.out.println(i + " " + ch); - - total = total + ch; - i--; - } - return total; - } - - public static void main(String[] args) { - System.out.println(mystery("Allen")); - } -} -\end{lstlisting} - -\end{exercise} - - -\begin{exercise} -A friend of yours shows you the following method and -explains that if {\tt number} is any two-digit number, the program -will output the number backwards. He claims that if {\tt number} is -17, the method will output {\tt 71}. - -Is he right? If not, explain what the program actually does and -modify it so that it does the right thing. - -\begin{lstlisting} - int number = 17; - int lastDigit = number%10; - int firstDigit = number/10; - System.out.println(lastDigit + firstDigit); -\end{lstlisting} - -\end{exercise} - -\begin{exercise} -What is the output of the following program? - -\begin{lstlisting} -public class Enigma { - - public static void enigma(int x) { - if (x == 0) { - return; - } else { - enigma(x/2); - } - - System.out.print(x%2); - } - - public static void main(String[] args) { - enigma(5); - System.out.println(""); - } -} -\end{lstlisting} - -Explain in 4-5 words what the method {\tt enigma} really does. -\end{exercise} - - -\begin{exercise} -\label{palindrome} - -\begin{enumerate} - -\item Create a new program named {\tt Palindrome.java}. - -\item Write a method named {\tt first} -that takes a String and returns the first letter, and one named -{\tt last} that returns the last letter. - -\item Write a method named {\tt middle} that takes a String and -returns a substring that contains everything {\em except} the -first and last characters. - -Hint: read the documentation of the {\tt substring} method in -the {\tt String} class. -Run a few tests to make sure you understand how {\tt substring} works -before you try to write {\tt middle}. - -What happens if you invoke {\tt middle} on a string that has only -two letters? One letter? No letters? - -\item The usual definition of a palindrome is a word that reads the -same both forward and backward, like ``otto'' and -``palindromeemordnilap.'' An alternative way to define a property -like this is to specify a way of testing for the property. For -example, we might say, ``a single letter is a palindrome, and a -two-letter word is a palindrome if the letters are the same, and -any other word is a palindrome if -the first letter is the same as the -last and the middle is a palindrome.'' - -Write a recursive method named {\tt isPalindrome} that takes -a {\tt String} and that returns a boolean indicating whether the -word is a palindrome or not. - -\item Once you have a working palindrome checker, look for ways -to simplify it by reducing the number of conditions you check. -Hint: it might be useful to adopt the definition that the empty -string is a palindrome. - -\item On a piece of paper, figure out a strategy for checking -palindromes iteratively. There are several possible approaches, -so make sure you have a solid plan before you start writing code. - -\item Implement your strategy in a method called {\tt isPalindromeIter}. - -\item Optional: Appendix~\ref{javaio} provides code for reading a list -of words from a file. Read a list of words and print the palindromes. - -\end{enumerate} -\end{exercise} - - -\begin{exercise} -\label{abecedarian} - -A word is said to be ``abecedarian'' if the letters in the -word appear in alphabetical order. For example, the following -are all 6-letter English abecedarian words. - -\begin {quote} -abdest, acknow, acorsy, adempt, adipsy, agnosy, befist, behint, -beknow, bijoux, biopsy, cestuy, chintz, deflux, dehors, dehort, -deinos, diluvy, dimpsy -\end{quote} - -\begin{enumerate} - -\item Describe a process for checking whether a given word (String) -is abecedarian, assuming that the word contains only lower-case -letters. Your process can be iterative or recursive. - -\item Implement your process in a method called {\tt isAbecedarian}. - -\end{enumerate} -\end{exercise} - - -\begin{exercise} -\label{dupledrome} -A dupledrome is a word that contains only double letters, -like ``llaammaa'' or ``ssaabb''. I conjecture that there -are no dupledromes in common English use. To test that -conjecture, I would like a program that reads -words from the dictionary one at a time and checks them for -dupledromity. - -Write a method called {\tt isDupledrome} that takes a String -and returns a boolean indicating whether the word is a dupledrome. -\end{exercise} - - - -\begin{exercise} -\begin{enumerate} - -\item The Captain Crunch decoder ring works by taking each letter in a -string and adding 13 to it. For example, 'a' becomes 'n' and 'b' -becomes 'o'. The letters ``wrap around'' at the end, so 'z' becomes -'m'. - -Write a method that takes a String and that returns a new String -containing the encoded version. You should assume that the String -contains upper and lower case letters, and spaces, but no other -punctuation. Lower case letters should be tranformed into other lower -case letters; upper into upper. You should not encode the spaces. - -\item Generalize the Captain Crunch method so that instead of adding -13 to the letters, it adds any given amount. Now you should be able -to encode things by adding 13 and decode them by adding -13. Try it. - -\end{enumerate} -\end{exercise} - - -\begin{exercise} - -If you did the GridWorld exercises in Chapter~\ref{gridworld}, you -might enjoy this exercise. The goal is to use trigonometry to get the -Bugs to chase each other. - -Make a copy of {\tt BugRunner.java} named {\tt ChaseRunner.java} and -import it into your development environment. Before you change -anything, check that you can compile and run it. - -\begin{itemize} - -\item Create two Bugs, one red and one blue. - -\item Write a method called {\tt distance} that takes two Bugs -and computes the distance between them. Remember that you can -get the x-coordinate of a Bug like this: - -\begin{lstlisting} - int x = bug.getLocation().getCol(); -\end{lstlisting} - -\item Write a method called {\tt turnToward} that takes two -Bugs and turns one to face the other. HINT: use {\tt Math.atan2}, -but remember that the result is in radians, so you have to -convert to degrees. Also, for Bugs, 0 degress is North, not East. - -\item Write a method called {\tt moveToward} that takes two -Bugs, turns the first to face the second, and then moves the -first one, if it can. - -\item Write a method called {\tt moveBugs} that takes two Bugs -and an integer {\tt n}, and moves each Bug toward the other {\tt n} -times. You can write this method recursively, or use a while loop. - -\item Test each of your methods as you develop them. When they are - all working, look for opportunities to improve them. For example, - if you have redundant code in {\tt distance} and {\tt turnToward}, - you could encapsulate the repeated code in a method. - -\end{itemize} - -\end{exercise} - - - - -\chapter{Mutable objects} -\label{chap08} -\label{objects} -\index{object} - - -%\section{{\tt Point}s and {\tt Rectangle}s} -\index{String} -\index{type!String} - -{\tt String}s are objects, but they are atypical objects -because - -\begin{itemize} - -\item They are immutable. - -\item They have no attributes. - -\item You don't have to use {\tt new} to create one. - -\end{itemize} - -In this chapter, we use two objects from Java libraries, - {\tt Point} and {\tt Rectangle}. -But first, I want to make it clear that these points -and rectangles are not graphical objects that appear on the -screen. They are values that contain data, just like {\tt int}s -and {\tt double}s. Like other values, they are used internally -to perform computations. - - -\section{Packages} -\index{package} -\index{AWT} -\index{Abstract Window Toolkit|see {AWT}} -\index{import} -\index{statement!import} - -The Java libraries are divided into {\bf -packages}, including {\tt java.lang}, which contains most of the -classes we have used so far, and {\tt java.awt}, -the {\bf Abstract Window Toolkit} (AWT), -which contains classes for windows, buttons, graphics, etc. - -To use a class defined in another package, you have to {\bf - import} it. {\tt Point} and {\tt Rectangle} are in the -{\tt java.awt} package, so to import them like this: - -\begin{lstlisting} - import java.awt.Point; - import java.awt.Rectangle; -\end{lstlisting} - -All {\tt import} statements appear at the beginning of the program, -outside the class definition. - -The classes in {\tt java.lang}, like {\tt Math} and {\tt String}, are -imported automatically, which is why we haven't needed the -{\tt import} statement yet. - - -\section{{\tt Point} objects} -\index{Point} -\index{class!Point} - -A point is two numbers (coordinates) -that we treat collectively as a single object. In mathematical -notation, points are often written in parentheses, with a comma -separating the coordinates. For example, $(0, 0)$ indicates -the origin, and $(x, y)$ indicates the point $x$ units to the -right and $y$ units up from the origin. - -\index{new} -\index{statement!new} - -In Java, a point is represented by a {\tt Point} object. To -create a new point, you have to use {\tt new}: - -\begin{lstlisting} - Point blank; - blank = new Point(3, 4); -\end{lstlisting} -% -The first line is a conventional variable declaration: {\tt blank} -has type {\tt Point}. The second line invokes {\tt new}, specifies -the type of the new object, and provides arguments. The arguments are -the coordinates of the new point, $(3, 4)$. - -\index{declaration} -\index{statement!declaration} -\index{reference} -\index{state diagram} -\index{state} - -The result of {\tt new} is a {\bf reference} to the new -point, so {\tt blank} contains a reference to the -newly-created object. There is a standard way to diagram this -assignment, shown in the figure. - - -\includegraphics{figs/reference.pdf} - - -As usual, the name of the variable {\tt blank} appears outside the box -and its value appears inside the box. In this case, that value is a -reference, which is shown graphically with an arrow. The -arrow points to the object we're referring to. - -The big box shows the newly-created object with the two values -in it. The names {\tt x} and {\tt y} are the names of the {\bf -instance variables}. - -Taken together, all the variables, values, and objects in a -program are called the {\bf state}. Diagrams like this that -show the state of the program are called {\bf state diagrams}. -As the program runs, the state changes, so you should think -of a state diagram as a snapshot of a particular point in the -execution. - - -\section{Instance variables} -\index{variable!instance} -\index{instance variable} - -The pieces of data that make up an object are called instance -variables because each object, which is an {\bf instance} of its -type, has its own copy of the instance variables. - -It's like the glove compartment of a car. Each car is an instance -of the type ``car,'' and each car has its own glove compartment. If -you ask me to get something from the glove compartment of your car, -you have to tell me which car is yours. - -\index{dot notation} - -Similarly, if you want to read a value from an instance variable, you -have to specify the object you want to get it from. In Java this is -done using ``dot notation.'' - -\begin{lstlisting} - int x = blank.x; -\end{lstlisting} -% -The expression {\tt blank.x} means ``go to the object {\tt blank} -refers to, and get the value of {\tt x}.'' In this case we assign -that value to a local variable named {\tt x}. There is no -conflict between the local variable named {\tt x} and the instance -variable named {\tt x}. The purpose of dot notation is to identify -{\em which} variable you are referring to unambiguously. - -You can use dot notation as part of any Java expression, so the -following are legal. - -\begin{lstlisting} - System.out.println(blank.x + ", " + blank.y); - int distance = blank.x * blank.x + blank.y * blank.y; -\end{lstlisting} -% -The first line prints {\tt 3, 4}; the second line calculates -the value 25. - -\section{Objects as parameters} -\index{parameter} -\index{object!as parameter} - -You can pass objects as parameters in the usual way. For -example: - -\begin{lstlisting} - public static void printPoint(Point p) { - System.out.println("(" + p.x + ", " + p.y + ")"); - } -\end{lstlisting} -% -This method takes a point as an argument and prints it in -the standard format. If you invoke {\tt printPoint(blank)}, -it prints {\tt(3, 4)}. Actually, Java already has a -method for printing {\tt Points}. If you invoke -{\tt System.out.println(blank)}, you get - -\begin{lstlisting} -java.awt.Point[x=3,y=4] -\end{lstlisting} -% -This is a standard format Java uses for printing objects. It prints -the name of the type, followed by the names and values of the instance -variables. - -As a second example, we can rewrite the {\tt distance} method from -Section~\ref{distance} so that it takes two {\tt Point}s as parameters -instead of four {\tt double}s. - -\begin{lstlisting} - public static double distance(Point p1, Point p2) { - double dx = (double)(p2.x - p1.x); - double dy = (double)(p2.y - p1.y); - return Math.sqrt(dx*dx + dy*dy); - } -\end{lstlisting} -% -The typecasts are not really necessary; I added them as a -reminder that the instance variables in a {\tt Point} are integers. - - -\section{Rectangles} -\index{Rectangle} -\index{class!Rectangle} - -{\tt Rectangle}s are similar to points, except that they have four -instance variables: {\tt x}, {\tt y}, {\tt width} and {\tt -height}. Other than that, everything is pretty much the same. - -This example -creates a {\tt Rectangle} object and makes {\tt box} refer to it. - -\begin{lstlisting} - Rectangle box = new Rectangle(0, 0, 100, 200); -\end{lstlisting} -% -This figure shows the effect of this assignment. - - -\includegraphics{figs/rectangle.pdf} - -If you print {\tt box}, you get - -\begin{lstlisting} -java.awt.Rectangle[x=0,y=0,width=100,height=200] -\end{lstlisting} -% -Again, this is the result of a Java method that knows how -to print {\tt Rectangle} objects. - - -\section{Objects as return types} -\index{object!as return type} -\index{return} -\index{statement!return} - -You can write methods that return objects. For example, -{\tt findCenter} takes a {\tt Rectangle} as an argument and -returns a {\tt Point} that contains the coordinates of the -center of the {\tt Rectangle}: - -\begin{lstlisting} - public static Point findCenter(Rectangle box) { - int x = box.x + box.width/2; - int y = box.y + box.height/2; - return new Point(x, y); - } -\end{lstlisting} -% -Notice that you can use {\tt new} to create a new object, -and then immediately use the result as the return value. - - -\section{Objects are mutable} -\index{object!mutable} -\index{mutable} - -You can change the contents of an object by making an assignment -to one of its instance variables. For example, to ``move'' -a rectangle without changing its size, you can modify the -{\tt x} and {\tt y} values: - -\begin{lstlisting} - box.x = box.x + 50; - box.y = box.y + 100; -\end{lstlisting} -% -The result is shown in the figure: - - -\includegraphics{figs/rectangle2.pdf} - - -\index{encapsulation} -\index{generalization} - -We can encapsulate this code in a method and -generalize it to move the rectangle by any amount: - -\begin{lstlisting} - public static void moveRect(Rectangle box, int dx, int dy) { - box.x = box.x + dx; - box.y = box.y + dy; - } -\end{lstlisting} -% -The variables {\tt dx} and {\tt dy} indicate how far to move the -rectangle in each direction. Invoking this method has the effect of -modifying the {\tt Rectangle} that is passed as an argument. - -\begin{lstlisting} - Rectangle box = new Rectangle(0, 0, 100, 200); - moveRect(box, 50, 100); - System.out.println(box); -\end{lstlisting} -% -prints {\tt java.awt.Rectangle[x=50,y=100,width=100,height=200]}. - -Modifying objects by passing them as arguments to methods can be -useful, but it can also make debugging more difficult because it is -not always clear which method invocations do or do not modify their -arguments. Later, I discuss some pros and cons of this -programming style. - -Java provides methods that operate on Points and Rectangles. You can -read the documentation at -\url{http://download.oracle.com/javase/6/docs/api/java/awt/Point.html} -and -\url{http://download.oracle.com/javase/6/docs/api/java/awt/Rectangle.html}. - -For example, {\tt translate} has the same effect as {\tt moveRect}, -but instead of passing the Rectangle as an argument, you use dot -notation: - -\begin{lstlisting} - box.translate(50, 100); -\end{lstlisting} -% -%The effect is the same. - - -\section{Aliasing} -\label{aliasing} -\index{aliasing} -\index{reference} - -Remember that when you assign an object to a variable, you -are assigning a {\em reference} to an object. It is possible to have -multiple variables that refer to the same object. For example, -this code: - -\begin{lstlisting} - Rectangle box1 = new Rectangle(0, 0, 100, 200); - Rectangle box2 = box1; -\end{lstlisting} -% -generates a state diagram that looks like this: - - -\includegraphics{figs/aliasing.pdf} - - -{\tt box1} and {\tt box2} refer to the same object. -In other words, this object has two names, {\tt box1} and {\tt box2}. -When a person uses two names, it's called {\bf aliasing}. Same thing -with objects. - -When two variables are aliased, any changes that affect one -variable also affect the other. For example: - -\begin{lstlisting} - System.out.println(box2.width); - box1.grow(50, 50); - System.out.println(box2.width); -\end{lstlisting} -% -The first line prints {\tt 100}, which is the width of the -{\tt Rectangle} referred to by {\tt box2}. The second -line invokes the {\tt grow} method on {\tt box1}, which -expands the {\tt Rectangle} by 50 pixels in every direction -(see the documentation for more details). The effect -is shown in the figure: - - -\includegraphics{figs/aliasing2.pdf} - - -Whatever changes are -made to {\tt box1} also apply to {\tt box2}. Thus, the -value printed by the third line is {\tt 200}, the width of -the expanded rectangle. (As an aside, it is perfectly legal -for the coordinates of a {\tt Rectangle} to be negative.) - -As you can tell even from this simple example, code that -involves aliasing can get confusing fast, and can be -difficult to debug. In general, aliasing should be avoided -or used with care. - - -\section {{\tt null}} -\index{null} - -When you create an object variable, remember that you are -creating a {\em reference} to an object. Until you make -the variable point to an object, the value of the variable -is {\tt null}. {\tt null} is a special value (and -a Java keyword) that means ``no object.'' - -The declaration {\tt Point blank;} is equivalent to this -initialization - -\begin{lstlisting} - Point blank = null; -\end{lstlisting} -% -and is shown in the following state diagram: - - -\includegraphics{figs/reference2.pdf} - - -The value {\tt null} is represented by a small square with no arrow. - -\index{exception!NullPointer} -\index{run-time error} - -If you try to use a null object, either by accessing an instance -variable or invoking a method, Java throws a {\tt -NullPointerException}, prints an error message -and terminates the program. - -\begin{lstlisting} - Point blank = null; - int x = blank.x; // NullPointerException - blank.translate(50, 50); // NullPointerException -\end{lstlisting} -% -On the other hand, it is legal to pass a null object as an argument or -receive one as a return value. In fact, it is common to do so, for -example to represent an empty set or indicate an error condition. - - -\section {Garbage collection} -\index{garbage collection} - -In Section~\ref{aliasing} we talked about what happens when -more than one variable refers to the same object. What happens -when {\em no} variable refers to an object? For example: - -\begin{lstlisting} - Point blank = new Point(3, 4); - blank = null; -\end{lstlisting} -% -The first line creates a new {\tt Point} object and makes -{\tt blank} refer to it. The second line changes {\tt blank} -so that instead of referring to the object, it refers to -nothing (the null object). - - -\includegraphics{figs/reference3.pdf} - - -If no one refers to an object, then no one can read or write any of -its values, or invoke a method on it. In effect, it ceases to exist. -We could keep the object in memory, but it would only waste space, so -periodically as your program runs, the system looks for stranded -objects and reclaims them, in a process called {\bf garbage -collection}. Later, the memory space occupied by the object will -be available to be used as part of a new object. - -You don't have to do anything to make garbage collection happen, -and in general you will not be aware of it. But you -should know that it periodically runs in the background. - - -\section {Objects and primitives} -\index{type!object} -\index{type!primitive} -\index{object type} -\index{primitive type} - -There are two kinds of types in Java, primitive types and -object types. Primitives, like {\tt int} and {\tt boolean} -begin with lower-case letters; object types begin with -upper-case letters. This distinction is useful because it -reminds us of some of the differences between them: - -\begin{itemize} - -\item When you declare a primitive variable, you get storage -space for a primitive value. When you declare an object variable, you -get a space for a reference to an object. To get space for -the object itself, you have to use {\tt new}. - -\item If you don't initialize a primitive type, it is given -a default value that depends on the type. For example, -{\tt 0} for {\tt int}s and {\tt false} for {\tt boolean}s. -The default value for object types is {\tt null}, which indicates -no object. - -\item Primitive variables are well isolated in the sense that there is -nothing you can do in one method that will affect a variable in -another method. Object variables can be tricky to work with because -they are not as well isolated. If you pass a reference to an object -as an argument, the method you invoke might modify the object, in which -case you will see the effect. Of course, that can be a good thing, but you -have to be aware of it. - -\end{itemize} - -There is one other difference between primitives and object -types. You cannot add new primitives to Java -(unless you get yourself on the standards committee), but -you can create new object types! We'll see how in the next -chapter. - -\section{Glossary} - -\begin{description} - -\item[package:] A collection of classes. Java -classes are organized in packages. - -\item[AWT:] The Abstract Window Toolkit, one of the biggest -and commonly-used Java packages. - -\item[instance:] An example from a category. My cat is an -instance of the category ``feline things.'' Every object is -an instance of some class. - -\item[instance variable:] One of the named data items that make -up an object. Each object (instance) has its own copy of -the instance variables for its class. - -\item[reference:] A value that indicates an object. In a -state diagram, a reference appears as an arrow. - -\item[aliasing:] The condition when two or more variables refer -to the same object. - -\item[garbage collection:] The process of finding objects that -have no references and reclaiming their storage space. - -\item[state:] A complete description of all the variables and -objects and their values, at a given point during the execution -of a program. - -\item[state diagram:] A snapshot of the state of a program, shown -graphically. - -\index{package} -\index{AWT} -\index{instance} -\index{instance variable} -\index{reference} -\index{aliasing} -\index{garbage collection} -\index{state} -\index{state diagram} - -\end{description} - - -\section{Exercises} - -\begin{exercise} -\begin{enumerate} - -\item For the following program, draw a stack diagram showing the -local variables and parameters of {\tt main} and {\tt riddle}, and show -any objects those variables refer to. - -\item What is the output of this program? - -\end{enumerate} - -\begin{lstlisting} -public static void main(String[] args) -{ - int x = 5; - Point blank = new Point(1, 2); - - System.out.println(riddle(x, blank)); - System.out.println(x); - System.out.println(blank.x); - System.out.println(blank.y); -} - -public static int riddle(int x, Point p) -{ - x = x + 7; - return x + p.x + p.y; -} -\end{lstlisting} - -The point of this exercise is to make sure you understand the -mechanism for passing Objects as parameters. -\end{exercise} - - -\begin{exercise} -\begin{enumerate} - -\item For the following program, draw a stack diagram showing the -state of the program just before {\tt distance} returns. Include all -variables and parameters and the objects those variables refer to. - -\item What is the output of this program? - -\end{enumerate} - -\begin{lstlisting} -public static double distance(Point p1, Point p2) { - int dx = p1.x - p2.x; - int dy = p1.y - p2.y; - return Math.sqrt(dx*dx + dy*dy); -} - -public static Point findCenter(Rectangle box) { - int x = box.x + box.width/2; - int y = box.y + box.height/2; - return new Point(x, y); -} - -public static void main(String[] args) { - Point blank = new Point(5, 8); - - Rectangle rect = new Rectangle(0, 2, 4, 4); - Point center = findCenter(rect); - - double dist = distance(center, blank); - - System.out.println(dist); -} -\end{lstlisting} -% -\end{exercise} - - - -\begin{exercise} -The method {\tt grow} is part of the {\tt Rectangle} class. Read the -documentation at -\url{http://download.oracle.com/javase/6/docs/api/java/awt/Rectangle.html#grow(int, int)}. - -\begin{enumerate} - -\item What is the output of the following program? - -\item Draw a state diagram that shows the state of the -program just before the end of {\tt main}. -Include all local variables and the objects -they refer to. - -\item At the end of {\tt main}, are {\tt p1} and -{\tt p2} aliased? Why or why not? - -\end{enumerate} - -\begin{lstlisting} -public static void printPoint(Point p) { - System.out.println("(" + p.x + ", " + p.y + ")"); -} - -public static Point findCenter(Rectangle box) { - int x = box.x + box.width/2; - int y = box.y + box.height/2; - return new Point(x, y); -} - -public static void main(String[] args) { - - Rectangle box1 = new Rectangle(2, 4, 7, 9); - Point p1 = findCenter(box1); - printPoint(p1); - - box1.grow(1, 1); - Point p2 = findCenter(box1); - printPoint(p2); -} -\end{lstlisting} - -\end{exercise} - - -\begin{exercise} -\label{ex.biginteger} -You might be sick of the factorial -method by now, but we're going to do one more version. - -\begin{enumerate} - -\item Create a new program called {\tt Big.java} and -write an iterative version of {\tt factorial}. - -\item Print a table of the integers from 0 to 30 along with their -factorials. At some point around 15, you will probably see -that the answers are not right any more. Why not? - -\item BigIntegers are Java objects that can represent arbitrarily big - integers. There is no upper bound except the limitations of memory - size and processing speed. Read the documentation of BigIntegers at - \url{http://download.oracle.com/javase/6/docs/api/java/math/BigInteger.html}. - -\item To use BigIntegers, you have to add {\tt import -java.math.BigInteger} to the beginning of your program. - -\item There are several ways to create a -BigInteger, but the one I recommend uses {\tt valueOf}. -The following code converts an integer to a {\tt BigInteger}: - -\begin{lstlisting} - int x = 17; - BigInteger big = BigInteger.valueOf(x); -\end{lstlisting} - -Type in this code and try it out. Try printing a BigInteger. - -\item Because BigIntegers are not primitive types, -the usual math operators don't work. Instead we -have to use methods like {\tt add}. To -add two BigIntegers, invoke {\tt add} on one -and pass the other as an argument. For example: - -\begin{lstlisting} - BigInteger small = BigInteger.valueOf(17); - BigInteger big = BigInteger.valueOf(1700000000); - BigInteger total = small.add(big); -\end{lstlisting} - -Try out some of the other methods, like {\tt multiply} and -{\tt pow}. - -\item Convert {\tt factorial} so that it performs its calculation -using BigIntegers and returns a BigInteger as a result. -You can leave the parameter alone---it will still be an integer. - -\item Try printing the table again with your modified factorial -method. Is it correct up to 30? How high can you make it go? I -calculated the factorial of all the numbers from 0 to 999, but my -machine is pretty slow, so it took a while. The last number, 999!, -has 2565 digits. - -\end{enumerate} -\end{exercise} - -\begin{exercise} -Many encryption techniques depend on the -ability to raise large integers to an integer power. Here is a -method that implements a (reasonably) fast technique for integer -exponentiation: - -\begin{lstlisting} -public static int pow(int x, int n) { - if (n == 0) return 1; - - // find x to the n/2 recursively - int t = pow(x, n/2); - - // if n is even, the result is t squared - // if n is odd, the result is t squared times x - - if (n%2 == 0) { - return t*t; - } else { - return t*t*x; - } -} -\end{lstlisting} - -The problem with this method is that it only works if the result -is smaller than 2 billion. Rewrite it so that the result is -a {\tt BigInteger}. The parameters should still be integers, though. - -You can use the BigInteger methods {\tt add} and {\tt multiply}, but -don't use {\tt pow}, which would spoil the fun. -\end{exercise} - - -\begin{exercise} -If you are interested in graphics, now is a good time to read -Appendix~\ref{graphics} and do the exercises there. -\end{exercise} - - -\chapter{GridWorld: Part 2} -\label{gridworld2} - -Part 2 of the GridWorld case study uses some features we haven't -seen yet, so you will get a preview now and more details later. -As a reminder, you can find the -documentation for the GridWorld classes at -\url{http://www.greenteapress.com/thinkapjava/javadoc/gridworld/}. - -When you install GridWorld, you should have a folder named {\tt - projects/boxBug}, which contains {\tt BoxBug.java}, {\tt - BoxBugRunner.java} and {\tt BoxBug.gif}. - -Copy these files into your working folder and import them into -your development environment. -There are instructions here that -might help: \url{http://www.collegeboard.com/prod_downloads/student/testing/ap/compsci_a/ap07_gridworld_installation_guide.pdf}. - -Here is the code from {\tt BoxBugRunner.java}: - -\begin{lstlisting} -import info.gridworld.actor.ActorWorld; -import info.gridworld.grid.Location; - -import java.awt.Color; - -public class BoxBugRunner { - public static void main(String[] args) { - ActorWorld world = new ActorWorld(); - BoxBug alice = new BoxBug(6); - alice.setColor(Color.ORANGE); - BoxBug bob = new BoxBug(3); - world.add(new Location(7, 8), alice); - world.add(new Location(5, 5), bob); - world.show(); - } -} -\end{lstlisting} - -Everything here should be familiar, with the possible exception of -{\tt Location}, which is part of GridWorld, and similar to {\tt - java.awt.Point}. - -{\tt BoxBug.java} contains the class definition for BoxBug. - -\begin{lstlisting} -public class BoxBug extends Bug { - private int steps; - private int sideLength; - - public BoxBug(int length) { - steps = 0; - sideLength = length; - } -} -\end{lstlisting} - -The first line says that this class extends {\tt Bug}, which means -that a {\tt BoxBug} is a kind of {\tt Bug}. - -The next two lines are instance variables. Every {\tt Bug} -has variables named {\tt sideLength}, which determines the size of the -box it draws, and {\tt steps}, which keeps track of how many steps -the {\tt Bug} has taken. - -The next line defines a {\bf constructor}, which is a special -method that initializes the instance variables. When you create -a {\tt Bug} by invoking {\tt new}, Java invokes this constructor. - -The parameter of the constructor is the side length. - -{\tt Bug} behavior is controlled by the {\tt act} method. Here -is the {\tt act} method for {\tt BoxBug}: - -\begin{lstlisting} - public void act() { - if (steps < sideLength && canMove()) { - move(); - steps++; - } - else { - turn(); - turn(); - steps = 0; - } - } -\end{lstlisting} - -If the {\tt BoxBug} can move, and has not taken the required number -of steps, it moves and increments {\tt steps}. - -If it hits a wall or completes one side of the box, it turns 90 degrees -to the right and resets {\tt steps} to 0. - -Run the program and see what it does. Did you get the behavior you -expected? - - -\section{Termites} - -I wrote a class called {\tt Termite} that extends {\tt Bug} and adds -the ability to interact with flowers. To run it, download these files -and import them into your development environment: - -\url{http://thinkapjava.com/code/Termite.java} \\ -\url{http://thinkapjava.com/code/Termite.gif} \\ -\url{http://thinkapjava.com/code/TermiteRunner.java} \\ -\url{http://thinkapjava.com/code/EternalFlower.java} - -Because {\tt Termite} extends {\tt Bug}, all {\tt Bug} methods -also work on {\tt Termite}s. But {\tt Termite}s have additional -methods that {\tt Bug}s don't have. - -\begin{lstlisting} - /** - * Returns true if the termite has a flower. - */ - public boolean hasFlower(); - - /** - * Returns true if the termite is facing a flower. - */ - public boolean seeFlower(); - - /** - * Creates a flower unless the termite already has one. - */ - public void createFlower(); - - /** - * Drops the flower in the termites current location. - * - * Note: only one Actor can occupy a grid cell, so the effect - * of dropping a flower is delayed until the termite moves. - */ - public void dropFlower(); - - /** - * Throws the flower into the location the termite is facing. - */ - public void throwFlower(); - - /** - * Picks up the flower the termite is facing, if there is - * one, and if the termite doesn't already have a flower. - */ - public void pickUpFlower(); -\end{lstlisting} - -For some methods {\tt Bug} provides one definition and {\tt Termite} -provides another. In that case, the {\tt Termite} method -{\bf overrides} the {\tt Bug} method. - -For example, {\tt Bug.canMove} -returns {\tt true} if there is a flower in the next location, so -{\tt Bug}s can trample {\tt Flower}s. {\tt Termite.canMove} returns -{\tt false} if there is any object in the next location, so -{\tt Termite} behavior is different. - -As another example, Termites have a version of {\tt turn} that takes -an integer number of degrees as a parameter. Finally, Termites -have {\tt randomTurn}, which turns left or right 45 degrees at random. - -% TODO: move for loops into the string chapter. - -Here is the code from {\tt TermiteRunner.java}: - -\begin{lstlisting} -public class TermiteRunner -{ - public static void main(String[] args) - { - ActorWorld world = new ActorWorld(); - makeFlowers(world, 20); - - Termite alice = new Termite(); - world.add(alice); - - Termite bob = new Termite(); - bob.setColor(Color.blue); - world.add(bob); - - world.show(); - } - - public static void makeFlowers(ActorWorld world, int n) { - for (int i = 0; i time2.hour) return true; - if (time1.hour < time2.hour) return false; - - if (time1.minute > time2.minute) return true; - if (time1.minute < time2.minute) return false; - - if (time1.second > time2.second) return true; - return false; - } -\end{lstlisting} -% -What is the result of this method if the two times are equal? Does -that seem like the appropriate result for this method? If you were -writing the documentation for this method, would you mention that case -specifically? - -A second example is {\tt addTime}, which calculates the sum of two -times. For example, if it is {\tt 9:14:30}, and your breadmaker takes -3 hours and 35 minutes, you could use {\tt addTime} to figure out when -the bread will be done. - -Here is a rough draft of this method that is not quite right: - -\begin{lstlisting} - public static Time addTime(Time t1, Time t2) { - Time sum = new Time(); - sum.hour = t1.hour + t2.hour; - sum.minute = t1.minute + t2.minute; - sum.second = t1.second + t2.second; - return sum; - } -\end{lstlisting} -% -Although this method returns a {\tt Time} object, it is not -a constructor. You should go back and compare the syntax of -a method like this with the syntax of a constructor, because -it is easy to get confused. - -Here is an example of how to use this method. If {\tt currentTime} -contains the current time and {\tt breadTime} contains the amount -of time it takes for your breadmaker to make bread, then you -could use {\tt addTime} to figure out when the bread will be -done. - -\begin{lstlisting} - Time currentTime = new Time(9, 14, 30.0); - Time breadTime = new Time(3, 35, 0.0); - Time doneTime = addTime(currentTime, breadTime); - printTime(doneTime); -\end{lstlisting} -% -The output of this program is {\tt 12:49:30.0}, which is -correct. On the other hand, there are cases where the result -is not correct. Can you think of one? - -The problem is that this method does not deal with cases -where the number of seconds or minutes adds up to more than -60. In that case, we have to ``carry'' the extra seconds -into the minutes column, or extra minutes into the hours -column. - -Here's a corrected version of the method. - -\begin{lstlisting} - public static Time addTime(Time t1, Time t2) { - Time sum = new Time(); - sum.hour = t1.hour + t2.hour; - sum.minute = t1.minute + t2.minute; - sum.second = t1.second + t2.second; - - if (sum.second >= 60.0) { - sum.second -= 60.0; - sum.minute += 1; - } - if (sum.minute >= 60) { - sum.minute -= 60; - sum.hour += 1; - } - return sum; - } -\end{lstlisting} -% -Although it's correct, it's starting to get big. Later -I suggest much shorter alternative. - -\index{increment} -\index{decrement} -\index{operator!increment} -\index{operator!decrement} - -This code demonstrates two operators we have not seen before, -{\tt +=} and {\tt -=}. These operators provide a concise -way to increment and decrement variables. They are similar -to {\tt ++} and {\tt --}, except (1) they work on {\tt double}s -as well as {\tt int}s, and (2) the amount of the increment -does not have to be 1. The statement {\tt sum.second -= 60.0;} -is equivalent to {\tt sum.second = sum.second - 60;} - - -\section{Modifiers} -\index{modifier} -\index{method!modifier} - -As an example of a modifier, consider {\tt increment}, -which adds a given number of seconds to a {\tt Time} object. -Again, a rough draft of this method looks like: - -\begin{lstlisting} - public static void increment(Time time, double secs) { - time.second += secs; - - if (time.second >= 60.0) { - time.second -= 60.0; - time.minute += 1; - } - if (time.minute >= 60) { - time.minute -= 60; - time.hour += 1; - } - } -\end{lstlisting} -% -The first line performs the basic operation; the remainder -deals with the same cases we saw before. - -Is this method correct? What happens if the argument {\tt secs} -is much greater than 60? In that case, it is not enough to -subtract 60 once; we have to keep doing it until {\tt second} -is below 60. We can do that by replacing the {\tt if} -statements with {\tt while} statements: - -\begin{lstlisting} - public static void increment(Time time, double secs) { - time.second += secs; - - while (time.second >= 60.0) { - time.second -= 60.0; - time.minute += 1; - } - while (time.minute >= 60) { - time.minute -= 60; - time.hour += 1; - } - } -\end{lstlisting} -% -This solution is correct, but not very efficient. -Can you think of a solution that does not require iteration? - - -\section{Fill-in methods} -\index{fill-in method} -\index{method!fill-in} - -Instead of creating a new object every time {\tt addTime} is -invoked, we could require the caller to provide an -object where {\tt addTime} stores the result. Compare -this to the previous version: - -\begin{lstlisting} - public static void addTimeFill(Time t1, Time t2, Time sum) { - sum.hour = t1.hour + t2.hour; - sum.minute = t1.minute + t2.minute; - sum.second = t1.second + t2.second; - - if (sum.second >= 60.0) { - sum.second -= 60.0; - sum.minute += 1; - } - if (sum.minute >= 60) { - sum.minute -= 60; - sum.hour += 1; - } - } -\end{lstlisting} -% -The result is stored in {\tt sum}, so the return type is {\tt void}. - -Modifiers and fill-in methods are efficient because they -don't have to create new objects. But they make it more -difficult to isolate parts of a program; in large projects they can -cause errors that are hard to find. - -Pure functions help manage the complexity of large projects, -in part by making certain kinds of errors impossible. Also, they -lend themselves to certain kids of composition and nesting. -And because the result of a pure function depends only on the parameters, -it is possible to speed them up by storing previously-computed -results. -\index{pure function} - -I recommend that you write pure functions whenever -it is reasonable, and resort to modifiers only if there -is a compelling advantage. - - -\section{Incremental development and planning} -\index{incremental development} -\index{prototyping} -\index{program development!incremental} -\index{program development!planning} - -In this chapter I demonstrated a program development process called -{\bf rapid prototyping}\footnote{What I am calling rapid prototyping - is similar to test-driven development (TDD); the difference is that - TDD is usually based on automated testing. See - \url{http://en.wikipedia.org/wiki/Test-driven_development}.}. For -each method, I wrote a rough draft that performed the -basic calculation, then tested it on a few cases, correcting flaws -as I found them. - -This approach can be effective, but it can lead to code -that is unnecessarily complicated---since it deals with many -special cases---and unreliable---since it is hard to convince -yourself that you have found {\em all} the errors. - -An alternative is to look for insight -into the problem that can make the programming easier. In -this case the insight is that a {\tt Time} is really a three-digit -number in base 60! The {\tt second} is the ``ones column,'' -the {\tt minute} is the ``60's column'', and the {\tt hour} -is the ``3600's column.'' - -When we wrote {\tt addTime} and {\tt increment}, we were effectively -doing addition in base 60, which is why we had to ``carry'' from one -column to the next. - -\index{arithmetic!floating-point} - -Another approach to the whole problem is to convert -{\tt Time}s into {\tt double}s and take advantage of the fact that -the computer already knows how to do arithmetic with {\tt double}s. -Here is a method that converts a {\tt Time} into a {\tt double}: - -\begin{lstlisting} - public static double convertToSeconds(Time t) { - int minutes = t.hour * 60 + t.minute; - double seconds = minutes * 60 + t.second; - return seconds; - } -\end{lstlisting} -% -Now all we need is a way to convert from a {\tt double} -to a {\tt Time} object. We could write a method to -do it, but it might make more sense to write it as a third -constructor: - -\begin{lstlisting} - public Time(double secs) { - this.hour =(int)(secs / 3600.0); - secs -= this.hour * 3600.0; - this.minute =(int)(secs / 60.0); - secs -= this.minute * 60; - this.second = secs; - } -\end{lstlisting} -% -This constructor is a little different from the others; -it involves some calculation along with assignments to the -instance variables. - -You might have to think to convince yourself that the technique -I am using to convert from one base to another is correct. But once -you're convinced, we can use these methods to rewrite {\tt addTime}: - -\begin{lstlisting} - public static Time addTime(Time t1, Time t2) { - double seconds = convertToSeconds(t1) + convertToSeconds(t2); - return new Time(seconds); - } -\end{lstlisting} -% -This is shorter than the original version, and it is much easier -to demonstrate that it is correct (assuming, as usual, that the -methods it invokes are correct). As an exercise, rewrite {\tt -increment} the same way. - - -\section{Generalization} -\index{generalization} - -In some ways converting from base 60 to base 10 and back is -harder than just dealing with times. Base conversion is more -abstract; our intuition for dealing with times is better. - -But if we have the insight to treat times as base 60 numbers, -and make the investment of writing the conversion methods -({\tt convertToSeconds} and the third constructor), we get -a program that is shorter, easier to read and debug, and more -reliable. - -It is also easier to add features later. Imagine -subtracting two {\tt Time}s to find the duration between them. The -naive approach would be to implement subtraction complete with -``borrowing.'' Using the conversion methods would be much easier. - -Ironically, sometimes making a problem harder (more general) -makes it easier (fewer special cases, fewer opportunities for error). - - -\section{Algorithms} -\label{algorithm} -\index{algorithm} - -When you write a general solution for a class of problems, as -opposed to a specific solution to a single problem, you have -written an {\bf algorithm}. This word is -not easy to define, so I will try a couple of approaches. - -First, consider some things that are not algorithms. When you learned -to multiply single-digit numbers, you probably memorized the -multiplication table. In effect, you memorized 100 specific -solutions, so that knowledge is not really algorithmic. - -But if you were ``lazy,'' you probably learned a few -tricks. For example, to find the product of $n$ and 9, you can -write $n-1$ as the first digit and $10-n$ as the second digit. This -trick is a general solution for multiplying any single-digit number by 9. -That's an algorithm! - -Similarly, the techniques you learned for addition with carrying, -subtraction with borrowing, and long division are all algorithms. One -of the characteristics of algorithms is that they do not require any -intelligence to carry out. They are mechanical processes in which -each step follows from the last according to a simple set of rules. - -In my opinion, it is embarrassing that humans spend so much -time in school learning to execute algorithms that, -quite literally, require no intelligence. -% -On the other hand, the process of designing algorithms is -interesting, intellectually challenging, and a central part -of what we call programming. - -Some of the things that people do naturally, without difficulty -or conscious thought, are the most difficult to express -algorithmically. Understanding natural language is a good -example. We all do it, but so far no one has been able to -explain {\em how} we do it, at least not in the form of an -algorithm. - -Soon you will have the opportunity to design -simple algorithms for a variety of problems. - - -\section{Glossary} - -\begin{description} - -\item[class:] Previously, I defined a class as a collection -of related methods. In this chapter we learned that a class -definition is also a template for a new type of object. - -\item[instance:] A member of a class. Every object is an -instance of some class. - -\item[constructor:] A special method that initializes the instance -variables of a newly-constructed object. - -\item[startup class:] The class that contains the {\tt main} -method where execution of the program begins. - -\item[pure function:] A method whose result depends only on its -parameters, and that has no side-effects other than returning -a value. - -\item[modifier:] A method that changes one or more of the objects -it receives as parameters, and usually returns {\tt void}. - -\item[fill-in method:] A type of method that takes an ``empty'' -object as a parameter and fills in its instance variables instead -of generating a return value. - -\item[algorithm:] A set of instructions for solving a class of -problems by a mechanical process. - -\index{class} -\index{instance} -\index{constructor} -\index{startup class} -\index{pure function} -\index{modifier} -\index{algorithm} - -\end{description} - - -\section{Exercises} - -\begin{exercise} -In the board game Scrabble\footnote{Scrabble is a registered trademark -owned in the U.S.A and Canada by Hasbro Inc., and in the rest of the world -by J.W. Spear \& Sons Limited of Maidenhead, Berkshire, England, a subsidiary -of Mattel Inc.}, each tile contains a letter, which is used to spell -words, and a score, which is used to determine the value of words. - -\begin{enumerate} - -\item Write a definition for a class named {\tt Tile} -that represents Scrabble tiles. The instance variables should -be a character named {\tt letter} and an integer named {\tt value}. - -\item Write a constructor that takes parameters named {\tt letter} -and {\tt value} and initializes the instance variables. - -\item Write a method named {\tt printTile} that takes a {\tt Tile} -object as a parameter and prints the instance variables in -a reader-friendly format. - -\item Write a method named {\tt testTile} that creates a -Tile object with the letter {\tt Z} and the value 10, and -then uses {\tt printTile} to print the state of the object. - -\end{enumerate} - -The point of this exercise is to practice the mechanical part -of creating a new class definition and code that tests it. -\end{exercise} - - -\begin{exercise} -Write a class definition for {\tt Date}, an object type that -contains three integers, {\tt year}, {\tt month} and {\tt day}. -This class should provide two constructors. The first should -take no parameters. The second should take parameters named -{\tt year}, {\tt month} and {\tt day}, and use them to initialize -the instance variables. - -Write a {\tt main} method that creates a new {\tt Date} object -named {\tt birthday}. The new object should contain your birthdate. -You can use either constructor. -\end{exercise} - - -\begin{exercise} -\label{ex.rational} - -A rational number is a number that can be represented as the ratio of -two integers. For example, $2/3$ is a rational number, and you can -think of 7 as a rational number with an implicit 1 in the denominator. -For this assignment, you are going to write a class definition for -rational numbers. - -\begin{enumerate} - -\item Create a new program called {\tt Rational.java} that defines a -class named {\tt Rational}. A {\tt Rational} object should have two -integer instance variables to store the numerator and denominator. - -\item Write a constructor that takes no arguments and that sets the -numerator to 0 and denominator to 1. - -\item Write a method called {\tt printRational} that takes -a Rational object as an argument and prints it in some -reasonable format. - -\item Write a {\tt main} method that creates a new object with -type Rational, sets its instance variables to some values, and prints -the object. - -\item At this stage, you have a minimal testable -program. Test it and, if necessary, debug it. - -\item Write a second constructor for your class that takes two -arguments and that uses them to initalize the instance -variables. - -\item Write a method called {\tt negate} that reverses the sign of -a rational number. This method should be a modifier, so it should -return {\tt void}. Add lines to {\tt main} to test the new method. - -\item Write a method called {\tt invert} that inverts the number by - swapping the numerator and denominator. Add lines to {\tt main} to - test the new method. - -\item Write a method called {\tt toDouble} that converts the rational -number to a double (floating-point number) and returns the result. -This method is a pure function; it does not modify the object. -As always, test the new method. - -\item Write a modifier named {\tt reduce} that reduces a rational - number to its lowest terms by finding the greatest common divisor - (GCD) of the numerator and denominator and dividing through. - This method should be a pure function; it should - not modify the instance variables of the object on which it is - invoked. To find the GCD, see Exercise~\ref{gcd}). - -\item Write a method called {\tt add} that takes two Rational -numbers as arguments and returns a new Rational object. The return -object should contain the sum of the arguments. - -There are several ways to add fractions. You can use any one you -want, but you should make sure that the result of the operation is -reduced so that the numerator and denominator have no common divisor -(other than 1). -\end{enumerate} - -The purpose of this exercise is to write a class definition that -includes a variety of methods, including constructors, modifiers and -pure functions. -\end{exercise} - - - - -\chapter{Arrays} -\label{chap10} -\label{arrays} -\index{array} -\index{type!array} - -An {\bf array} is a set of values where each value is identified by an -index. You can make an array of {\tt int}s, {\tt double}s, or any -other type, but all the values in an array have to have the same type. - -Syntactically, array types look like other Java types except they are -followed by {\tt []}. For example, {\tt int[]} is the type ``array of -integers'' and {\tt double[]} is the type ``array of doubles.'' - -You can declare variables with these types in the usual ways: - -\begin{lstlisting} - int[] count; - double[] values; -\end{lstlisting} -% -Until you initialize these variables, they are set to {\tt null}. -To create the array itself, use {\tt new}. - -\begin{lstlisting} - count = new int[4]; - values = new double[size]; -\end{lstlisting} -% -The first assignment makes {\tt count} refer to an array of 4 -integers; the second makes {\tt values} refer to an array of {\tt -double}s. The number of elements in {\tt values} depends on {\tt -size}. You can use any integer expression as an array -size. - -\index{null} -\index{state diagram} - -The following figure shows how arrays are represented in state -diagrams: - - -\includegraphics{figs/array.pdf} - - -The large numbers inside the boxes are the {\bf elements} of -the array. The small numbers outside the boxes are the -indices used to identify each box. When you allocate an -array if {\tt int}s, the elements are initialized to zero. - - -\section{Accessing elements} -\index{element} -\index{array!element} - -To store values in the array, use the -{\tt []} operator. For example {\tt count[0]} refers to the -``zeroeth'' element of the array, and {\tt count[1]} refers to the -``oneth'' element. You can use the {\tt []} operator anywhere in an -expression: - -\begin{lstlisting} - count[0] = 7; - count[1] = count[0] * 2; - count[2]++; - count[3] -= 60; -\end{lstlisting} -% -These are all legal assignment statements. Here is the -result of this code fragment: - - -\includegraphics{figs/array2.pdf} - - -The elements of the array -are numbered from 0 to 3, which means that there is no element with -the index 4. This should sound familiar, since we saw the same thing -with {\tt String} indices. Nevertheless, it is a common error to go -beyond the bounds of an array, which throws an {\tt -ArrayOutOfBoundsException}. -\index{exception!ArrayOutOfBounds} -\index{run-time error} -\index{index} - -You can use any expression as an index, as long as it has type {\tt -int}. One of the most common ways to index an array is with a loop -variable. For example: -\index{expression} - -\begin{lstlisting} - int i = 0; - while (i < 4) { - System.out.println(count[i]); - i++; - } -\end{lstlisting} -% -This is a standard {\tt while} loop that counts from 0 -up to 4, and when the loop variable {\tt i} is 4, the -condition fails and the loop terminates. Thus, the body -of the loop is only executed when {\tt i} is 0, 1, 2 and 3. - -\index{loop} -\index{loop variable} -\index{variable!loop} - -Each time through the loop we use {\tt i} as an index into -the array, printing the {\tt i}th element. This type of -array traversal is very common. - - -\section{Copying arrays} -\index{array!copying} - -When you copy an array variable, remember that you are -copying a reference to the array. For example: - -\begin{lstlisting} - double[] a = new double [3]; - double[] b = a; -\end{lstlisting} -% -This code creates one array of three {\tt double}s, and -sets two different variables to refer to it. -This situation is a form of aliasing. - - -\includegraphics{figs/array3.pdf} - - -Any changes in either array -will be reflected in the other. This is not usually the -behavior you want; more often you want to -allocate a new array and copy elements from -one to the other. - -\begin{lstlisting} - double[] b = new double [3]; - - int i = 0; - while (i < 4) { - b[i] = a[i]; - i++; - } -\end{lstlisting} - - -\section{Arrays and objects} -\index{object!compared to array} -\index{array!compared to object} - -In many ways, arrays behave like objects: - -\begin{itemize} - -\item When you declare an array variable, you get a reference -to an array. - -\item You have to use {\tt new} to create the array itself. - -\item When you pass an array as an argument, you pass a reference, -which means that the invoked method can change the contents -of the array. - -\end{itemize} - -Some of the objects we looked at, like {\tt Rectangles}, are -similar to arrays in the sense that they are collections of -values. This raises the question, ``How is an array of 4 integers -different from a Rectangle object?'' -\index{collection} - -If you go back to the definition of ``array'' at the beginning -of the chapter, you see one difference: the -elements of an array are identified by indices, and the -elements of an object have names. - -Another difference is that the -elements of an array have to be the same type. Objects can -have instance variables with different types. - - -\section{{\tt for} loops} -\label{for} - -The loops we have written have a number of elements -in common. All of them start by initializing a variable; -they have a test, or condition, that depends on that variable; -and inside the loop they do something to that variable, -like increment it. - -\index{loop!for} -\index{for} -\index{statement!for} - -This type of loop is so common that there is another -loop statement, called {\tt for}, that expresses it more -concisely. The general syntax looks like this: - -\begin{lstlisting} - for (INITIALIZER; CONDITION; INCREMENTOR) { - BODY - } -\end{lstlisting} -% -This statement is equivalent to - -\begin{lstlisting} - INITIALIZER; - while (CONDITION) { - BODY - INCREMENTOR - } -\end{lstlisting} -% -except that it is more concise and, since it puts all the -loop-related statements in one place, it is easier to read. -For example: - -\begin{lstlisting} - for (int i = 0; i < 4; i++) { - System.out.println(count[i]); - } -\end{lstlisting} -% -is equivalent to - -\begin{lstlisting} - int i = 0; - while (i < 4) { - System.out.println(count[i]); - i++; - } -\end{lstlisting} - - -\section{Array length} -\index{length!array} -\index{array!length} - -All arrays have one named instance variable: {\tt length}. -Not surprisingly, it contains the length of the array (number -of elements). It is a good idea to use this value as the upper -bound of a loop, rather than a constant value. That way, if -the size of the array changes, you won't have to go through the -program changing all the loops; they will work correctly for any -size array. - -\begin{lstlisting} - for (int i = 0; i < a.length; i++) { - b[i] = a[i]; - } -\end{lstlisting} -% -The last time the body of the loop gets executed, {\tt i} -is {\tt a.length - 1}, which is the index of the last element. When -{\tt i} is equal to {\tt a.length}, the condition fails and the body -is not executed, which is a good thing, since it would throw an -exception. This code assumes that the array {\tt b} contains at least -as many elements as {\tt a}. - - -\section{Random numbers} -\label{random} -\label{pseudorandom} -\index{random number} -\index{deterministic} -\index{nondeterministic} - -Most computer programs do the same thing every time they are executed, -so they are said to be {\bf deterministic}. Usually, determinism is a -good thing, since we expect the same calculation to yield the same -result. But for some applications we want the -computer to be unpredictable. Games are an obvious example, but -there are more. - -Making a program truly {\bf nondeterministic} turns out to be not so -easy, but there are ways to make it at least seem nondeterministic. -One of them is to generate random numbers and use them to determine -the outcome of the program. Java provides a method that generates -{\bf pseudorandom} numbers, which may not be truly random, but for our -purposes, they will do. - -Check out the documentation of the {\tt random} method in the {\tt -Math} class. The return value is a {\tt double} between 0.0 and 1.0. -To be precise, it is greater than or equal to 0.0 and strictly less -than 1.0. Each time you invoke {\tt random} you get the next -number in a pseudorandom sequence. -To see a sample, run this loop: - -\begin{lstlisting} - for (int i = 0; i < 10; i++) { - double x = Math.random(); - System.out.println(x); - } -\end{lstlisting} -% -To generate a random {\tt double} between 0.0 and an upper bound like -{\tt high}, you can multiply {\tt x} by {\tt high}. - - -\section{Array of random numbers} -\label{randarray} - -How would you generate a random integer between {\tt low} and {\tt high}? -If your implementation of {\tt randomInt} is correct, then -every value in the range from {\tt low} to {\tt high-1} should -have the same probability. If you generate a long series -of numbers, every value should appear, at least approximately, -the same number of times. - -One way to test your method is to -generate a large number of random values, -store them in an array, and count the number of times each -value occurs. - -The following method takes a single argument, the size of -the array. It allocates a new array of integers, fills -it with random values, and returns a reference to the new -array. - -\begin{lstlisting} - public static int[] randomArray(int n) { - int[] a = new int[n]; - for (int i = 0; i= low && a[i] < high) count++; - } - return count; -} -\end{lstlisting} -% -I wasn't specific about whether something equal -to {\tt low} or {\tt high} falls in the range, but you can -see from the code that {\tt low} is in and {\tt high} is out. -That keeps us from counting any elements twice. - -Now we can count the number of scores in the ranges we are -interested in: - -\begin{lstlisting} -int[] scores = randomArray(30); -int a = inRange(scores, 90, 100); -int b = inRange(scores, 80, 90); -int c = inRange(scores, 70, 80); -int d = inRange(scores, 60, 70); -int f = inRange(scores, 0, 60); -\end{lstlisting} - - -\section{The histogram} -\index{range} -\index{histogram} - -This code is repetitious, but it is acceptable as -long as the number of ranges is small. But imagine that -we want to keep track of the number of times each score appears, -all 100 possible values. Would you want to write this? - -\begin{lstlisting} -int count0 = inRange(scores, 0, 1); -int count1 = inRange(scores, 1, 2); -int count2 = inRange(scores, 2, 3); -... -int count3 = inRange(scores, 99, 100); -\end{lstlisting} - -I don't think so. What we really want is a way to store 100 integers, -preferably so we can use an index to access each one. Hint: array. - -The counting pattern is the same whether we use a single counter or an -array of counters. In this case, we initialize the array outside the -loop; then, inside the loop, we invoke {\tt inRange} and store the -result: - -\begin{lstlisting} - int[] counts = new int[100]; - - for (int i = 0; i < counts.length; i++) { - counts[i] = inRange(scores, i, i+1); - } -\end{lstlisting} -% -The only tricky thing here is that we are using the loop variable -in two roles: as in index into the array, and as the parameter to -{\tt inRange}. - - -\section{A single-pass solution} -\label{singlepass} - -This code works, but it is not as efficient as it could -be. Every time it invokes {\tt inRange}, it traverses the -entire array. As the number of ranges increases, that gets -to be a lot of traversals. - -It would be better to make a single pass through the array, -and for each value, compute which range it falls in. Then -we could increment the appropriate counter. -In this example, that computation is trivial, because we -can use the value itself as an index into the array of counters. - -Here is code that traverses an array of scores once and generates -a histogram. - -\begin{lstlisting} - int[] counts = new int[100]; - - for (int i = 0; i < scores.length; i++) { - int index = scores[i]; - counts[index]++; - } -\end{lstlisting} - - -\section{Glossary} - -\begin{description} - -\item[array:] A collection of values, where all the -values have the same type, and each value is identified by -an index. - -\item[element:] One of the values in an array. The {\tt []} -operator selects elements. - -\item[index:] An integer variable or value used to indicate -an element of an array. - -\item[deterministic:] A program that does the same thing every -time it is invoked. - -\item[pseudorandom:] A sequence of numbers that appear to be -random, but which are actually the product of a deterministic -computation. - -\item[histogram:] An array of integers where each integer -counts the number of values that fall into a certain range. - -\index{array} -\index{element} -\index{index} -\index{deterministic} -\index{pseudorandom} - -\end{description} - - -\section{Exercises} - -\begin{exercise} -Write a method called {\tt cloneArray} that takes an -array of integers as a parameter, creates a new array that is the same -size, copies the elements from the first array into the new one, and -then returns a reference to the new array. -\end{exercise} - - -\begin{exercise} -Write a method called {\tt randomDouble} that takes two doubles, -{\tt low} and {\tt high}, and that returns a random double $x$ -so that $low \le x < high$. -\end{exercise} - - -\begin{exercise} -\label{ex.randint} -Write a method called {\tt randomInt} that takes two arguments, -{\tt low} and {\tt high}, and that returns a random integer between -{\tt low} and {\tt high}, not including {\tt high}. -\end{exercise} - - -\begin{exercise} -Encapsulate the code in Section~\ref{singlepass} in a method called -{\tt makeHist} that takes an array of scores and returns a histogram -of the values in the array. -\end{exercise} - - -\begin{exercise} -Write a method named {\tt areFactors} that takes -an integer {\tt n} and an array of integers, and that returns -{\tt true} if the numbers in the array are all factors of {\tt n} -(which is to say that {\tt n} is divisible by all of them). -HINT: See Exercise~\ref{ex.isdiv}. -\end{exercise} - - -\begin{exercise} -Write a method that takes an array of integers and an integer named -{\tt target} as arguments, and that returns the first index where -{\tt target} appears in the array, if it does, and -1 otherwise. -\end{exercise} - - -\begin{exercise} -Some programmers disagree with the general rule that variables -and methods should be given meaningful names. Instead, they -think variables and methods should be named after fruit. - -For each of the following methods, write one sentence that -describes abstractly what the method does. For each variable, -identify the role it plays. - -\begin{lstlisting} -public static int banana(int[] a) { - int grape = 0; - int i = 0; - while (i < a.length) { - grape = grape + a[i]; - i++; - } - return grape; -} - -public static int apple(int[] a, int p) { - int i = 0; - int pear = 0; - while (i < a.length) { - if (a[i] == p) pear++; - i++; - } - return pear; -} - -public static int grapefruit(int[] a, int p) { - for (int i = 0; i} and the others) -don't work for object types. For {\tt String}s Java provides -a {\tt compareTo} method. For {\tt Card}s we have -to write our own, which we will call {\tt compareCard}. -Later, we will use this method to sort a deck of cards. - -\index{ordering} -\index{complete ordering} -\index{partial ordering} - -Some sets are completely ordered, which means that you can compare any -two elements and tell which is bigger. Integers and floating-point -numbers are totally ordered. Some sets are unordered, which means -that there is no meaningful way to say that one element is bigger than -another. Fruits are unordered, which is why we cannot compare apples -and oranges. In Java, the {\tt boolean} type is unordered; we cannot -say that {\tt true} is greater than {\tt false}. - -The set of playing cards is partially ordered, which means that -sometimes we can compare cards and sometimes not. For example, I know -that the 3 of Clubs is higher than the 2 of Clubs, and the 3 of -Diamonds is higher than the 3 of Clubs. But which is better, the 3 of -Clubs or the 2 of Diamonds? One has a higher rank, but the other has -a higher suit. -\index{comparable} - -To make cards comparable, we have to decide which is more -important, rank or suit. The choice is -arbitrary, but when you buy a new deck of cards, it comes sorted -with all the Clubs together, followed by all the Diamonds, and so on. -So let's say that suit is more important. - -With that decided, we can write {\tt compareCard}. It -takes two {\tt Card}s as parameters and returns 1 if -the first card wins, -1 if the second card wins, and 0 if -they are equivalent. - -First we compare suits: - -\begin{lstlisting} - if (c1.suit > c2.suit) return 1; - if (c1.suit < c2.suit) return -1; -\end{lstlisting} -% -If neither statement is true, the suits must be equal, -and we have to compare ranks: - -\begin{lstlisting} - if (c1.rank > c2.rank) return 1; - if (c1.rank < c2.rank) return -1; -\end{lstlisting} -% -If neither of these is true, the ranks must be equal, -so we return {\tt 0}. - - -\section{Arrays of cards} -\label{cardarray} -\index{array!of object} -\index{object!array of} -\index{deck} - -By now we have seen several examples of composition (the ability to -combine language features in a variety of arrangements). One of the -first examples we saw was using a method invocation as part of an -expression. Another example is the nested structure of statements: -you can put an {\tt if} statement within a {\tt while} loop, or within -another {\tt if} statement, etc. -\index{composition} - -Having seen this pattern, and having learned about arrays and objects, -you should not be surprised to learn that you can make arrays of -objects. And you can define objects with arrays as -instance variables; you can make arrays that contain arrays; you can -define objects that contain objects, and so on. -In the next two chapters we will see examples of these -combinations using {\tt Card} objects. - -This example creates an array of 52 cards: - -\begin{lstlisting} - Card[] cards = new Card[52]; -\end{lstlisting} - -Here is the state diagram for this object: - -\index{state diagram} - -\includegraphics{figs/cardarray.pdf} - -The array contains -{\em references} to objects; it does not contain the -{\tt Card} objects themselves. The elements are -initialized to {\tt null}. You can access the elements of -the array in the usual way: - -\begin{lstlisting} - if (cards[0] == null) { - System.out.println("No cards yet!"); - } -\end{lstlisting} -% -But if you try to access the instance variables of the -non-existent {\tt Card}s, you get a {\tt NullPointerException}. -\index{exception!NullPointer} -\index{run-time error} -\index{null} - -\begin{lstlisting} - cards[0].rank; // NullPointerException -\end{lstlisting} -% -But that is the correct syntax for accessing the {\tt -rank} of the ``zeroeth'' card in the deck. This is another example of - composition, combining the syntax for accessing an element - of an array and an instance variable of an object. - -\index{composition} -\index{loop!nested} - -The easiest way to populate the deck with {\tt Card} objects -is to write nested for loops (i.e., one loop inside the body of another): - -\begin{lstlisting} - int index = 0; - for (int suit = 0; suit <= 3; suit++) { - for (int rank = 1; rank <= 13; rank++) { - cards[index] = new Card(suit, rank); - index++; - } - } -\end{lstlisting} -% -The outer loop enumerates the suits from 0 to 3. For -each suit, the inner loop enumerates the ranks from 1 -to 13. Since the outer loop runs 4 times, and -the inner loop runs 13 times, -the body is executed is 52 times. - -\index{index} - -I used {\tt index} to keep track of where in the -deck the next card should go. The following state diagram -shows what the deck looks like after the first two cards -have been allocated: - -\includegraphics{figs/cardarray2.pdf} - - -\section{The {\tt printDeck} method} -\label{printdeck} -\index{printDeck} -\index{print!array of Cards} - -When you work with arrays, it is convenient to have -a method that prints the contents. We have -seen the pattern for traversing an array several times, so the -following method should be familiar: - -\begin{lstlisting} - public static void printDeck(Card[] cards) { - for (int i = 0; i < cards.length; i++) { - printCard(cards[i]); - } - } -\end{lstlisting} - -Since {\tt cards} has type {\tt Card[]}, an element of {\tt cards} -has type {\tt Card}. So {\tt cards[i]} is a legal argument -for {\tt printCard}. - - -\section{Searching} -\label{findcard} -\index{searching} -\index{findCard} - -The next method I'll write is {\tt findCard}, which searches -an array of {\tt Card}s to see whether it contains a certain -card. This method -gives me a chance to demonstrate two algorithms: -{\bf linear search} and {\bf bisection search}. -\index{linear search} -\index{bisection search} -\index{traverse} -\index{loop!search} - -Linear search is pretty obvious; we traverse -the deck and compare each card to the one we are looking for. If we -find it we return the index where the card appears. If it is not in -the deck, we return -1. - -\begin{lstlisting} -public static int findCard(Card[] cards, Card card) { - for (int i = 0; i< cards.length; i++) { - if (sameCard(cards[i], card)) { - return i; - } - } - return -1; -} -\end{lstlisting} -% -The arguments of {\tt findCard} are {\tt card} and {\tt cards}. -It might seem odd to have a variable with the same name as a type (the -{\tt card} variable has type {\tt Card}). We can tell the difference -because the variable begins with a lower-case letter. - -\index{statement!return} -\index{return!inside loop} - -The method returns as soon as it discovers -the card, which means that we do not have to traverse the entire -deck if we find the card we are looking for. If we get to the end -of the loop, we know the card is not in the deck. - -If the cards in the deck are not in order, there is no way to search -faster than this. We have to look at every card because -otherwise we can't be certain the card we want is not -there. - -\index{bisection search} - -But when you look for a word in a dictionary, you don't search -linearly through every word, because the words are in -alphabetical order. As a result, you probably use an algorithm -similar to a bisection search: - -\begin {enumerate} - -\item Start in the middle somewhere. - -\item Choose a word on the page and compare it to the word you -are looking for. - -\item If you find the word you are looking for, stop. - -\item If the word you are looking for comes after the word on -the page, flip to somewhere later in the dictionary and go to -step 2. - -\item If the word you are looking for comes before the word on -the page, flip to somewhere earlier in the dictionary and go to -step 2. - -\end {enumerate} - -If you ever get to the point where there are two adjacent words on the -page and your word comes between them, you can conclude that your word -is not in the dictionary. - -Getting back to the deck of cards, if we know the cards are in order, -we can write a faster version of {\tt findCard}. The best way to -write a bisection search is with a recursive method, because bisection -is naturally recursive. \index{findBisect} - -The trick is to write a method called {\tt findBisect} that takes -two indices as parameters, {\tt low} and {\tt high}, indicating the -segment of the array that should be searched (including both -{\tt low} and {\tt high}). - -\begin{enumerate} - -\item To search the array, choose an index between {\tt low} and {\tt -high} (call it {\tt mid}) and compare it to the card you are looking -for. - -\item If you found it, stop. - -\item If the card at {\tt mid} is higher than your card, search -the range from {\tt low} to {\tt mid-1}. - -\item If the card at {\tt mid} is lower than your card, search -the range from {\tt mid+1} to {\tt high}. - -\end{enumerate} - -Steps 3 and 4 look suspiciously like recursive invocations. Here's -what this looks like translated into Java code: - -\begin{lstlisting} -public static int findBisect(Card[] cards, Card card, int low, int high) { - // TODO: need a base case - int mid = (high + low) / 2; - int comp = compareCard(cards[mid], card); - - if (comp == 0) { - return mid; - } else if (comp > 0) { - return findBisect(cards, card, low, mid-1); - } else { - return findBisect(cards, card, mid+1, high); - } -} -\end{lstlisting} -% -This code contains the kernel of a bisection search, but it -is still missing an important piece, which is why I added a TODO comment. -% -As written, the method recurses forever -if the card is not in the deck. We -need a base case to handle this condition. -\index{recursion} - -If {\tt high} is less than {\tt low}, -there are no cards between them, -see we conclude that the card is not in the deck. -If we handle that case, the method works correctly: - -\begin{lstlisting} -public static int findBisect(Card[] cards, Card card, int low, int high) { - System.out.println(low + ", " + high); - - if (high < low) return -1; - - int mid = (high + low) / 2; - int comp = compareCard(cards[mid], card); - - if (comp == 0) { - return mid; - } else if (comp > 0) { - return findBisect(cards, card, low, mid-1); - } else { - return findBisect(cards, card, mid+1, high); - } -} -\end{lstlisting} - -I added a print statement so I can follow -the sequence of recursive invocations. I tried out the -following code: - -\begin{lstlisting} - Card card1 = new Card(1, 11); - System.out.println(findBisect(cards, card1, 0, 51)); -\end{lstlisting} -% -And got the following output: - -\begin{verbatimtab} -0, 51 -0, 24 -13, 24 -19, 24 -22, 24 -23 -\end{verbatimtab} -% -Then I made up a card that is not in the deck (the 15 of Diamonds), -and tried to find it. I got the following: - -\begin{verbatimtab} -0, 51 -0, 24 -13, 24 -13, 17 -13, 14 -13, 12 --1 -\end{verbatimtab} -% -These tests don't prove that this program is correct. In fact, no -amount of testing can prove that a program is correct. On the other -hand, by looking at a few cases and examining the code, you might be -able to convince yourself. -\index{testing} -\index{correctness} - -The number of recursive invocations is typically 6 or 7, -so we only invoke {\tt compareCard} 6 or 7 times, -compared to up to 52 times if we did a linear search. In general, -bisection is much faster than a linear search, and even more so for -large arrays. - -Two common errors in recursive programs are forgetting to include a -base case and writing the recursive call so that the base case is never -reached. Either error causes infinite recursion, -which throws a {\tt StackOverflowException}. -(Think of a stack diagram for a recursive method that never ends.) -\index{recursion!infinite} -\index{infinite recursion} -\index{exception!StackOverflow} - - -\section{Decks and subdecks} -\index{deck} -\index{subdeck} - -\index{prototype} -Here is the prototype (see Section~\ref{documentation}) of {\tt findBisect}: - -\begin{lstlisting} -public static int findBisect(Card[] deck, Card card, int low, int high) -\end{lstlisting} - -\index{parameter!abstract} -\index{abstract parameter} - -We can think of {\tt cards}, {\tt low}, and {\tt high} -as a single parameter that specifies a {\bf subdeck}. -This way of thinking is common, and is sometimes referred -to as an {\bf abstract parameter}. What I mean by ``abstract'' is -something that is not literally part of the program text, but which -describes the function of the program at a higher level. - -For example, when you invoke a method and pass an array and the bounds -{\tt low} and {\tt high}, there is nothing that prevents the invoked -method from accessing parts of the array that are out of bounds. So -you are not literally sending a subset of the deck; you are really -sending the whole deck. But as long as the recipient plays by the -rules, it makes sense to think of it abstractly as a subdeck. - -This kind of thinking, in which a program takes on meaning beyond what -is literally encoded, is an important part of thinking like a computer -scientist. The word ``abstract'' gets used so often and in so many -contexts that it comes to lose its meaning. Nevertheless, {\bf abstraction} -is a central idea in computer science (and many other fields). -\index{abstraction} - -A more general definition of ``abstraction'' is ``The process of -modeling a complex system with a simplified description to -suppress unnecessary details while capturing relevant behavior.'' - - -\section{Glossary} - -\begin{description} - -\item[encode:] To represent one set of values using another -set of values, by constructing a mapping between them. - -\item[identity:] Equality of references. Two -references that point to the same object in memory. - -\item[equivalence:] Equality of values. Two references -that point to objects that contain the same data. - -\item[abstract parameter:] A set of parameters that act together -as a single parameter. - -\item[abstraction:] The process of interpreting a program -(or anything else) at a higher level than what is literally -represented by the code. - -\index{encode} -\index{identity} -\index{equivalence} -\index{abstract parameter} -\index{abstraction} - -\end{description} - - - -\section{Exercises} - -\begin{exercise} -Encapsulate the code in Section~\ref{compare} in a method. -Then modify it so that aces are ranked higher than Kings. -\end{exercise} - - -\begin{exercise} -Encapsulate the deck-building code of Section~\ref{cardarray} in a method called -{\tt makeDeck} that takes no parameters and returns a -fully-populated array of {\tt Card}s. -\end{exercise} - - -\begin{exercise} -In Blackjack the object of the game is to get a collection of cards -with a score of 21. The score for a hand is the sum of scores for all -cards. The score for an aces is 1, for all face cards is ten, and -for all other cards the score is the same as the rank. Example: the -hand (Ace, 10, Jack, 3) has a total score of 1 + 10 + 10 + 3 = 24. - -Write a method called {\tt handScore} that takes an array of cards as -an argument and that returns the total score. -\end{exercise} - - -\begin{exercise} -In Poker a ``flush'' is a hand that contains five -or more cards of the same suit. A hand can contain any number of cards. - -\begin{enumerate} - -\item Write a method called {\tt suitHist} that takes an array of Cards as a -parameter and that returns a histogram of the suits in the hand. -Your solution should only traverse the array once. - -\item Write a method called {\tt hasFlush} that takes an array of Cards as a -parameter and that returns {\tt true} if the hand contains a flush, -and {\tt false} otherwise. - -\end{enumerate} - -\end{exercise} - - -\begin{exercise} -Working with cards is more interesting if you can display them on -the screen. If you haven't played with the graphics examples in -Appendix~\ref{graphics}, you might want to do that now. - -First download -\url{http://thinkapjava.com/code/CardTable.java} -and -\url{http://thinkapjava.com/code/cardset.zip} into the same folder. -Then unzip {\tt cardset.zip}, which contains a {\tt cardset-oxymoron} -subfolder with all the card images. (Note the variable {\tt cardset} -in {\tt CardTable.main} is the name of this folder.) -Run {\tt CardTable.java} and you -should see images of a pack of cards laid out on a green table. - -You can use this class as a starting place to implement your own -card games. -\end{exercise} - - - -\chapter{Objects of Arrays} -\label{chap12} -\index{deck} -\index{array!of Cards} - -WARNING: In this chapter, we take another step toward object-oriented -programming, but we are not there yet. So many of the examples are -non-idiomatic; that is, they are not good Java. This transitional -form will help you learn (I hope), but don't write code like this. - -You can download the code in this chapter from -\url{http://thinkapjava.com/code/Card2.java}. - - -\section{The {\tt Deck} class} -\label{deck} - -In the previous chapter, we worked with an array of objects, -but I also mentioned that it is possible to have an object -that contains an array as an instance variable. In this -chapter we create a {\tt Deck} object -that contains an array of {\tt Card}s. - -\index{instance variable} -\index{variable!instance} - -The class definition looks like this: - -\begin{lstlisting} -class Deck { - Card[] cards; - - public Deck(int n) { - this.cards = new Card[n]; - } -} -\end{lstlisting} -% -The constructor initializes the instance variable with -an array of cards, but it doesn't create any cards. -Here is a state diagram showing what a -{\tt Deck} looks like with no cards: - -\index{state diagram} -\index{constructor} - -\includegraphics{figs/deckobject.pdf} - -Here is a no-argument constructor that makes a -52-card deck and populates it with {\tt Card}s: - -\begin{lstlisting} - public Deck() { - this.cards = new Card[52]; - int index = 0; - for (int suit = 0; suit <= 3; suit++) { - for (int rank = 1; rank <= 13; rank++) { - cards[index] = new Card(suit, rank); - index++; - } - } - } -\end{lstlisting} - -This method is similar to {\tt makeDeck}; -we just changed the syntax to make it a constructor. -To invoke it, we use {\tt new}: - -\index{new} -\index{statement!new} - -\begin{lstlisting} - Deck deck = new Deck(); -\end{lstlisting} -% -Now it makes sense to put -the methods that pertain to {\tt Deck}s in the {\tt Deck} -class definition. Looking at the methods we have written so -far, one obvious candidate is {\tt printDeck} (Section~\ref{printdeck}). -Here's how it looks, rewritten to work with a {\tt Deck}: -\index{printDeck} - -\begin{lstlisting} - public static void printDeck(Deck deck) { - for (int i = 0; i < deck.cards.length; i++) { - Card.printCard(deck.cards[i]); - } - } -\end{lstlisting} -% -One change is the type of the parameter, -from {\tt Card[]} to {\tt Deck}. - -The second change is that we can no -longer use {\tt deck.length} to get the length of the array, because -{\tt deck} is a {\tt Deck} object now, not an array. It contains an -array, but it is not an array. So we have to write -{\tt deck.cards.length} to extract the array from the {\tt Deck} -object and get the length of the array. - -For the same reason, we have to use {\tt deck.cards[i]} to access an -element of the array, rather than just {\tt deck[i]}. - -The last change -is that the invocation of {\tt printCard} has to say explicitly that -{\tt printCard} is defined in the {\tt Card} class. - - -\section{Shuffling} -\label{shuffle} -\index{shuffling} - -For most card games you need to be able to shuffle the deck; -that is, put the cards in a random order. In Section~\ref{random} -we saw how to generate random numbers, but it is not obvious how -to use them to shuffle a deck. - -One possibility is to model the way humans shuffle, which is usually -by dividing the deck in two and then choosing -alternately from each deck. Since humans usually don't shuffle -perfectly, after about 7 iterations the order of the deck is pretty -well randomized. But a computer program would have the annoying -property of doing a perfect shuffle every time, which is not really -very random. In fact, after 8 perfect shuffles, you would find the -deck back in the order you started in. For more information, see -\url{http://en.wikipedia.org/wiki/Faro_shuffle}. - -A better shuffling algorithm is to traverse the deck one card at a -time, and at each iteration choose two cards and swap them. - -Here is an outline of how this algorithm works. To sketch the -program, I am using a combination of Java statements and English -words that is sometimes called {\bf pseudocode}: \index{pseudocode} - -\begin{lstlisting} - for (int i = 0; i < deck.cards.length; i++) { - // choose a number between i and deck.cards.length-1 - // swap the ith card and the randomly-chosen card - } -\end{lstlisting} -% -The nice thing about pseudocode is that it often makes it -clear what methods you are going to need. In this case, we -need something like {\tt randomInt}, which chooses a random -integer between {\tt low} and {\tt high}, -and {\tt swapCards} which takes two indices and switches the -cards at the indicated positions. -\index{random number} -\index{swapCards} -\index{reference} - -This process---writing pseudocode first and then writing -methods to make it work---is called {\bf top-down development} -(see \url{http://en.wikipedia.org/wiki/Top-down_and_bottom-up_design}). -\index{program development} - - -\section{Sorting} -\label{sorting} -\index{sorting} - -Now that we have messed up the deck, we need a way to put it back in -order. There is an algorithm for sorting that is ironically similar -to the algorithm for shuffling. It's called {\bf selection sort} -because it works by traversing the array repeatedly and selecting the -lowest remaining card each time. -\index{selection sort} - -During the first iteration we find the lowest card and swap -it with the card in the 0th position. During the {\tt i}th, we find the -lowest card to the right of {\tt i} and swap it with the {\tt i}th -card. - -Here is pseudocode for selection sort: - -\begin{lstlisting} - for (int i = 0; i < deck.cards.length; i++) { - // find the lowest card at or to the right of i - // swap the ith card and the lowest card - } -\end{lstlisting} -% -Again, the pseudocode helps with the design of the {\bf helper -methods}. In this case we can use {\tt swapCards} again, -so we only need one new one, called {\tt indexLowestCard}, -that takes an array of cards and an index where it should -start looking. -\index{helper method} -\index{method!helper} - - - -\section {Subdecks} -\index{subdeck} - -How should we represent a hand or some other subset of a full deck? -One possibility is to create a new class called {\tt Hand}, which -might extend {\tt Deck}. Another possibility, the one I will -demonstrate, is to represent a hand with a {\tt Deck} object with -fewer than 52 cards. - -We might want a method, {\tt subdeck}, that takes a Deck -and a range of indices, and that returns a new Deck that -contains the specified subset of the cards: - -\begin{lstlisting} -public static Deck subdeck(Deck deck, int low, int high) { - Deck sub = new Deck(high-low+1); - - for (int i = 0; i grid = getGrid(); -\end{lstlisting} - -The type in angle-brackets (\verb"<>") is a {\bf type parameter} -that specifies the contents of {\tt grid}. In other words, {\tt grid} -is not just a {\tt Grid}, it's a {\tt Grid} that contains {\tt Actor}s. - -The next step is to get the neighbors of the current location. -{\tt Grid} provides a method that does just that: - -\begin{lstlisting} - ArrayList neighbors = grid.getNeighbors(loc); -\end{lstlisting} - -The return value from {\tt getNeighbors} is an {\tt ArrayList} -of {\tt Actors}. The {\tt size} method returns the length of -the {\tt ArrayList}, and {\tt get} selects an element. So -we can print the neighbors like this. - -\begin{lstlisting} - for (int i = 0; i < neighbors.size(); i++) { - Actor actor = neighbors.get(i); - System.out.println(actor); - } -\end{lstlisting} - -Traversing an {\tt ArrayList} is such a common operation there's a -special syntax for it: the {\bf for-each loop}. So we could write: - -\begin{lstlisting} - for (Actor actor : neighbors) { - System.out.println(actor); - } -\end{lstlisting} - -We know that the neighbors are {\tt Actors}, but we don't know -what kind: they could be {\tt Bug}s, {\tt Rock}s, etc. -To find the Rocks, we use the {\tt instanceof} operator, which -checks whether an object is an instance of a class. - -\begin{lstlisting} - for (Actor actor : neighbors) { - if (actor instanceof Rock) { - actor.setColor(Color.blue); - } - } -\end{lstlisting} - -To make all this work, we need to import the classes we use: - -\begin{lstlisting} -import info.gridworld.actor.Actor; -import info.gridworld.actor.Bug; -import info.gridworld.actor.Rock; -import info.gridworld.grid.Grid; -import info.gridworld.grid.Location; - -import java.awt.Color; -import java.util.ArrayList; -\end{lstlisting} - - -\section{Interfaces} -\index{interface} - -GridWorld also uses Java {\bf interfaces}, so I want to explain what -they are. ``Interface'' means different things in different contexts, -but in Java it refers to a specific language feature: -an interface is a class definition where the methods have no bodies. - -In a normal class definition, each method has a prototype and a -body (see Section~\ref{documentation}). A prototype is also called a -{\bf specification} because it specifies the name, parameters, and -return type of the method. The body is called the {\bf implementation} -because it implements the specification. - -In a Java interface the methods have no bodies, so it specifies -the methods without implementing them. - -For example, {\tt java.awt.Shape} is an interface with prototypes for -{\tt contains}, {\tt intersects}, and several other methods. {\tt - java.awt.Rectangle} provides implementations for those methods, so -we say that ``Rectangle implements Shape.'' In fact, the first line -of the {\tt Rectangle} class definition is: - -\begin{lstlisting} -public class Rectangle extends Rectangle2D implements Shape, Serializable -\end{lstlisting} - -Rectangle inherits methods from {\tt Rectangle2D} and provides -implementations for the methods in {\tt Shape} and {\tt Serializable}. - -In GridWorld the Location class implements the {\tt - java.lang.Comparable} interface by providing {\tt compareTo}, which -is similar to {\tt compareCards} in Section~\ref{compare}. -% -GridWorld also defines a new interface, {\tt Grid}, that specifies -the methods a {\tt Grid} should provide. And it includes two -implementations, {\tt BoundedGrid} and {\tt UnboundedGrid}. - -The Student Manual uses the abbreviation {\bf API}, which stands for -``application programming interface.'' The API is the set of methods -that are available for you, the application programmer, to use. See -\url{http://en.wikipedia.org/wiki/Application_programming_interface}. - - -\section{{\tt public} and {\tt private}} - -Remember in Chapter~\ref{chap01} I said I would explain why the {\tt - main} method has the keyword {\tt public}? Finally, the time has -come. - -{\tt public} means that the method can be invoked from other classes. -The alternative is {\tt private}, which means the method can only -be invoked inside the class where it is defined. - -Instance variables can also be {\tt public} or {\tt private}, with -the same result: a private instance variable can be accessed only -inside the class where it is defined. - -The primary reason to make methods and instance variables private -is to limit interactions between classes in order to manage -complexity. - -For example, the Location class keeps its instance variables private. -It has accessor methods {\tt getRow} and {\tt getCol}, but it provides -no methods that modify the instance variables. In effect, Location -objects are immutable, which means that they can be shared without -worrying about unexpected behavior due to aliasing. - -Making methods private helps keep the API simple. Classes often -include helper methods that are used to implement other methods, but -making those methods part of the public API might be unnecessary -and error-prone. - -Private methods and instance variables are language features -that help programmers ensure {\bf data encapsulation}, which means -that objects in one class are isolated from other classes. - - -\section{Game of Life} - -The mathematician John Conway invented -the ``Game of Life,'' which he called a ``zero-player game'' -because no players are needed to choose strategies or make decisions. -After you set up the initial conditions, you watch the game -play itself. But that turns out to be more interesting than it sounds; -you can read about it at -\url{http://en.wikipedia.org/wiki/Conways_Game_of_Life}. - -The goal of this exercises is to implement the Game of Life in -GridWorld. The game board is the grid, and the pieces are Rocks. - -The game proceeds in turns, or {\bf time steps}. At the beginning -of the time step, each Rock is either ``alive'' or ``dead''. On the -screen, the color of the Rock indicates its status. -% -The status of each Rock depends on the status of its -{\bf neighbors}. Each Rock has 8 neighbors, except the Rocks along -the edge of the Grid. Here are the rules: - -\begin{itemize} - -\item If a dead Rock has exactly three neighbors, it comes to life! -Otherwise it stays dead. - -\item If a live Rock has 2 or 3 neighbors, it survives. Otherwise it dies. - -\end{itemize} - -Some consequences of these rules: -If all Rocks are dead, no Rocks come to life. If you start with a -single live Rock, it dies. But if you have 4 Rocks in a square, they -keep each other alive, so that's a stable configuration. - -Most simple starting configurations either die out quickly or reach a -stable configuration. But there are a few starting conditions that -display remarkable complexity. One of those is the r-pentomino: it -starts with only 5 Rocks, runs for 1103 timesteps and ends in a stable -configuration with 116 live Rocks (see -\url{http://www.conwaylife.com/wiki/R-pentomino}). - -The following sections are suggestions for implementing Game of Life -in GridWorld. You can download my solution at -\url{http://thinkapjava.com/code/LifeRunner.java} and -\url{http://thinkapjava.com/code/LifeRock.java}. - - -\section{{\tt LifeRunner}} - -Make a copy of {\tt BugRunner.java} named {\tt LifeRunner.java} -and add methods with the following prototypes: - -\begin{lstlisting} - /** - * Makes a Game of Life grid with an r-pentomino. - */ - public static void makeLifeWorld(int rows, int cols) - - /** - * Fills the grid with LifeRocks. - */ - public static void makeRocks(ActorWorld world) -\end{lstlisting} - -{\tt makeLifeWorld} should create a Grid of Actors and an ActorWorld, -then invoke {\tt makeRocks}, which should put a {\tt LifeRock} at -every location in the Grid. - - -\section{{\tt LifeRock}} - -Make a copy of {\tt BoxBug.java} named {\tt LifeRock.java}. -{\tt LifeRock} should extend {\tt Rock}. Add an {\tt act} method -that does nothing. At this point you should be able to run the -code and see a Grid full of Rocks. - -To keep track of the status of the Rocks, you can add a new instance -variable, or you can use the Color of the Rock to indicate status. -Either way, write methods with these prototypes: - -\begin{lstlisting} - /** - * Returns true if the Rock is alive. - */ - public boolean isAlive() - - /** - * Makes the Rock alive. - */ - public void setAlive() - - /** - * Makes the Rock dead. - */ - public void setDead() -\end{lstlisting} - -Write a constructor that invokes {\tt setDead} and confirm that -all Rocks are dead. - - -\section{Simultaneous updates} - -In the Game of Life, all Rocks are updated simultaneously; that is, -each rock checks the status of its neighbors before any Rocks -change their status. Otherwise the behavior of the system would -depend on the order of the updates. - -In order to implement simultaneous updates, I suggest that you write -an {\tt act} method that has two phases: during the first phase, -all Rocks count their neighbors and record the results; during the -second phase, all Rocks update their status. - -Here's what my {\tt act} method looks like: - -\begin{lstlisting} - /** - * Check what phase we're in and calls the appropriate method. - * Moves to the next phase. - */ - public void act() { - if (phase == 1) { - numNeighbors = countLiveNeighbors(); - phase = 2; - } else { - updateStatus(); - phase = 1; - } - } -\end{lstlisting} - -{\tt phase} and {\tt numNeighbors} are instance variables. -And here are the prototypes for {\tt countLiveNeighbors} and -{\tt updateStatus}: - -\begin{lstlisting} - /** - * Counts the number of live neighbors. - */ - public int countLiveNeighbors() - - /** - * Updates the status of the Rock (live or dead) based on - * the number of neighbors. - */ - public void updateStatus() -\end{lstlisting} - -Start with a simple version of {\tt updateStatus} that changes live -rocks to dead and vice versa. Now run the program and confirm that -the Rocks change color. Every two steps in the World correspond to -one timestep in the Game of Life. - -Now fill in the bodies of {\tt countLiveNeighbors} and -{\tt updateStatus} according to the rules and see if the system behaves -as expected. - - -\section{Initial conditions} - -To change the initial conditions, you can use the GridWorld pop-up -menus to set the status of the Rocks by invoking {\tt setAlive}. -Or you can write methods to automate the process. - -In {\tt LifeRunner}, add a method called {\tt makeRow} that creates -an initial configuration with {\tt n} live Rocks in a row in the middle -of the grid. What happens for different values of {\tt n}? - -Add a method called {\tt makePentomino} that creates -an r-pentomino in the middle of the Grid. The initial configuration -should look like this: - -\includegraphics[height=2in]{figs/LifeRunner.pdf} - -If you run this configuration for more than a few steps, it reaches the -end of the Grid. The boundaries of the Grid change the behavior of -the system; in order to see the full evolution of the r-pentomino, -the Grid has to be big enough. You might have to experiment to find -the right size, and depending on the speed of your computer, it -might take a while. - -The Game of Life web page describes other initial conditions that -yield interesting results (\url{http://www.conwaylife.com/}). Choose -one you like and implement it. - -There are also variations of the Game of Life based on different rules. -Try one out and see if you find anything interesting. - -\section{Exercises} - -\begin{exercise} -Starting with a copy of {\tt BlueBug.java}, write a class definition -for a new kind of {\tt Bug} that finds and eats flowers. You can -``eat'' a flower by invoking {\tt removeSelfFromGrid} on it. -\end{exercise} - -\begin{exercise} -Now you know what you need to know to read Part 3 of the -GridWorld Student Manual and do the exercises. -\end{exercise} - -\begin{exercise} -If you implemented the Game of Life, you are well prepared for -Part 4 of the GridWorld Student Manual. Read it and do the exercises. -\end{exercise} - - -Congratulations, you're done! - - -\appendix - -\chapter{Graphics} -\label{graphics} - -\section{Java 2D Graphics} -\index{class!Graphics} -\index{Graphics} -\index{class!Frame} -\index{Frame} - -This appendix provides examples and exercises that demonstrate Java -graphics. There are several ways to create graphics in Java; the -simplest is to use {\tt java.awt.Graphics}. -Here is a complete example: - -\begin{lstlisting} -import java.awt.Canvas; -import java.awt.Graphics; -import javax.swing.JFrame; - -public class MyCanvas extends Canvas { - - public static void main(String[] args) { - // make the frame - JFrame frame = new JFrame(); - frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); - - // add the canvas - Canvas canvas = new MyCanvas(); - canvas.setSize(400, 400); - frame.getContentPane().add(canvas); - - // show the frame - frame.pack(); - frame.setVisible(true); - } - - public void paint(Graphics g) { - // draw a circle - g.fillOval(100, 100, 200, 200); - } -} -\end{lstlisting} -% -You can download this code from -\url{http://thinkapjava.com/code/MyCanvas.java}. - -The first lines import the classes we need from {\tt java.awt} -and {\tt javax.swing}. - -{\tt MyCanvas} extends {\tt Canvas}, which means that a -{\tt MyCanvas} object is a kind of {\tt Canvas} that provides -methods for drawing graphical objects. - -In {\tt main} we - -\begin{enumerate} - -\item Create a {\tt JFrame}, which is a window that can contain the - canvas, buttons, menus, and other window components; - -\item Create {\tt MyCanvas}, set its width and height, and add it - to the frame; and - -\item Display the frame on the screen. - -\end{enumerate} - -{\tt paint} is a special method that gets invoked -when {\tt MyCanvas} needs to be drawn. -If you run this code, you should see a black circle on a gray -background. - - -\section{{\tt Graphics} methods} -\index{method!Graphics} -\index{setColor} -\index{drawOval} - -To draw on the Canvas, you invoke methods on the -Graphics object. The previous example uses {\tt fillOval}. -Other methods include {\tt drawLine}, {\tt drawRect} and more. -You can read the documentation of these methods at -\url{http://download.oracle.com/javase/6/docs/api/java/awt/Graphics.html}. - -Here is the prototype for {\tt fillOval}: - -\begin{lstlisting} -public void fillOval(int x, int y, int width, int height) -\end{lstlisting} - -The parameters specify -a {\bf bounding box}, which is the rectangle -in which the oval is drawn (as shown in the figure). The -bounding box itself is not drawn. - -\index{bounding box} - - -\includegraphics{figs/circle.pdf} - -{\tt x} and {\tt y} specify the -the location of the upper-left corner -of the bounding box in the Graphics -{\bf coordinate system}. - - -\section{Coordinates} -\index{coordinate} -\index{Cartesian coordinate} -\index{graphics coordinate} - -You are probably familiar with Cartesian coordinates in two -dimensions, where each location is identified by an x-coordinate -(distance along the x-axis) and a y-coordinate. By convention, -Cartesian coordinates increase to the right and up, as shown in the -figure. - - -\includegraphics[width=5in]{figs/coordinates.pdf} - - -By convention, computer graphics systems to use a -coordinate system where the origin is in the -upper-left corner, and the direction of the -positive y-axis is {\em down}. Java follows this convention. - -\index{pixel} - -Coordinates are measured in {\bf pixels}; each pixel corresponds to -a dot on the screen. A typical screen is about -1000 pixels wide. Coordinates are always integers. If you want to -use a floating-point value as a coordinate, you have to round it off -(see Section~\ref{rounding}). - - -\section{Color} - -To choose the color of a shape, invoke {\tt setColor} on the Graphics -object: - -\begin{lstlisting} - g.setColor(Color.red); -\end{lstlisting} -% -{\tt setColor} changes the current color; everything that gets drawn -is the current color. - -{\tt Color.red} is a value provided by the {\tt Color} -class; to use it you have to import {\tt java.awt.Color}. -Other colors include: - -\begin{verbatimtab} -black blue cyan darkGray gray lightGray -magenta orange pink red white yellow -\end{verbatimtab} -% -You can create other colors by specifying red, green and blue (RGB) -components. -See \url{http://download.oracle.com/javase/6/docs/api/java/awt/Color.html}. - -You can control the background color of the {\tt Canvas} by -invoking {\tt Canvas.setBackground}. - - -\section{Mickey Mouse} -\index{Mickey Mouse} - -Let's say we want to draw a picture of Mickey Mouse. We can use the -oval we just drew as the face, and then add ears. To make the code -more readable, let's use {\tt Rectangles} to represent bounding boxes. - -Here's a method that takes a Rectangle and invokes {\tt fillOval}. - -\begin{lstlisting} - public void boxOval(Graphics g, Rectangle bb) { - g.fillOval(bb.x, bb.y, bb.width, bb.height); - } -\end{lstlisting} - -And here's a method that draws Mickey: - -\begin{lstlisting} - public void mickey(Graphics g, Rectangle bb) { - boxOval(g, bb); - - int dx = bb.width/2; - int dy = bb.height/2; - Rectangle half = new Rectangle(bb.x, bb.y, dx, dy); - - half.translate(-dx/2, -dy/2); - boxOval(g, half); - - half.translate(dx*2, 0); - boxOval(g, half); - } -\end{lstlisting} - -The first line draws the face. The next three lines create -a smaller rectangle for the ears. We translate the rectangle -up and left for the first ear, then right for the second ear. - -The result looks like this: - -\includegraphics[height=2in]{figs/mickey.pdf} - -You can download this code from -\url{http://thinkapjava.com/code/Mickey.java}. - - -\section{Glossary} - -\begin{description} - -\item[coordinate:] A variable or value that specifies a location -in a two-dimensional graphical window. - -\item[pixel:] The unit in which coordinates are measured. - -\item[bounding box:] A common way to specify the coordinates of -a rectangular area. - -\index{coordinate} -\index{pixel} -\index{bounding box} - -\end{description} - - -\section{Exercises} - -\begin{exercise} -Draw the flag of Japan, a red circle on white background -that is wider than it is tall. -\end{exercise} - - -\begin{exercise} -Modify {\tt Mickey.java} to draw ears on the ears, and ears on those -ears, and more ears all the way down until the smallest ears are -only 3 pixels wide. - -The result should look like Mickey Moose: - -\includegraphics[height=2in]{figs/moose.pdf} - -Hint: you should only have to add or modify a few lines of code. - -You can download a solution from -\url{http://thinkapjava.com/code/MickeySoln.java}. - -\end{exercise} - - -\begin{exercise} -\begin{enumerate} - -\item Download -\url{http://thinkapjava.com/code/Moire.java} and import it into -your development environment. - -\item Read the {\tt paint} method and draw a sketch of -what you expect it to do. Now run it. Did you get what you -expected? For an explanation of what is going on, see -\url{http://en.wikipedia.org/wiki/Moire_pattern}. - -\item Modify the program so that the space between the circles is -larger or smaller. See what happens to the image. - -\item Modify the program so that the circles are drawn in the center -of the screen and concentric, as in the following figure (left). -The distance between the circles should be small enough -that the Moir\'{e} interference is apparent. - -\includegraphics[height=1.5in]{figs/moire.pdf} - -\item Write a method named {\tt radial} that draws a radial set -of line segments as shown in the figure (right), but they should be close -enough together to create a Moir\'{e} pattern. - -\item Just about any kind of graphical pattern can generate -Moir\'{e}-like interference patterns. Play around and see what you -can create. - -\end{enumerate} -\end{exercise} - - -\chapter{Input and Output in Java} -\label{javaio} - -\section{System objects} -\label{system} -\index{System object} -\index{object!System} - -The {\tt System} class provides -methods and objects that get input from the keyboard, -print text on the screen, and do file input and output (I/O). -% -{\tt System.out} is the object that displays -on the screen. When you invoke {\tt print} and {\tt println}, you -invoke them on {\tt System.out}. - -You can even use {\tt System.out} to print {\tt System.out}: - -\begin{lstlisting} -System.out.println(System.out); -\end{lstlisting} -% -The result is: - -\begin{verbatimtab} -java.io.PrintStream@80cc0e5 -\end{verbatimtab} -% -When Java prints an object, it prints the type -of the object ({\tt PrintStream}), the package -where the type is defined ({\tt java.io}), and a -unique identifier for the object. On my machine the identifier -is {\tt 80cc0e5}, but if you run the same code you will -probably get something different. - -There is also an object named {\tt System.in} that makes it -possible to get input from the keyboard. Unfortunately, -it does not make it easy to get input from the keyboard. - - -\section{Keyboard input} -\label{keyboard} -\index{keyboard} -\index{input!keyboard} - -First, you have to use {\tt System.in} to create a new -{\tt InputStreamReader}. - -\begin{lstlisting} - InputStreamReader in = new InputStreamReader(System.in); -\end{lstlisting} -% -Then you use {\tt in} to create a new {\tt BufferedReader}: - -\begin{lstlisting} - BufferedReader keyboard = new BufferedReader(in); -\end{lstlisting} -% -Finally you can invoke {\tt readLine} on {\tt keyboard}, -to take input from the keyboard and convert it to a -String. - -\begin{lstlisting} - String s = keyboard.readLine(); - System.out.println(s); -\end{lstlisting} -% -There is only one problem. There are things that can go wrong when -you invoke {\tt readLine}, and they might throw an {\tt IOException}. A -method that throws an exception has to include it in the -prototype, like this: - -\begin {lstlisting} -public static void main(String[] args) throws IOException { - // body of main -} -\end{lstlisting} - - -\section{File input} -\label{fileIO} -\index{file input} -\index{input!file} - -Here's a program that reads lines from a file and prints them: - -\begin{lstlisting} -import java.io.*; - -public class Words { - - public static void main(String[] args) - throws FileNotFoundException, IOException { - - processFile("words.txt"); - } - - public static void processFile(String filename) - throws FileNotFoundException, IOException { - - FileReader fileReader = new FileReader(filename); - BufferedReader in = new BufferedReader(fileReader); - - while (true) { - String s = in.readLine(); - if (s == null) break; - System.out.println(s); - } - } -} -\end{lstlisting} - -This first line imports {\tt java.io}, the package that contains -{\tt FileReader}, {\tt BufferedReader}, and the rest of -the elaborate class hierarchy Java uses to do -common, simple things. The {\tt *} means it imports all classes -in the package. -\index{import statement} -\index{statement!import} - -Here's what the same program looks like in Python: - -\begin{verbatim} -for word in open('words.txt'): - print word -\end{verbatim} - -I'm not kidding. That's the whole program, and it does the same thing. - - -\section{Catching exceptions} - -In the previous example, {\tt processFile} can throw -{\tt FileNotFoundException} and {\tt IOException}. And since -{\tt main} calls {\tt processFile}, it has to declare the -same exceptions. In a larger program, {\tt main} might -declare every exception there is. - -The alternative is to {\bf catch} the exception with a -{\tt try} statement. Here's an example: -\index{try statement} -\index{statement!try} - -\begin{lstlisting} - public static void main(String[] args) { - try { - processFile("words.txt"); - } catch (Exception ex) { - System.out.println("That didn't work. Here's why:"); - ex.printStackTrace(); - } - } -\end{lstlisting} - -The structure is similar to an {\tt if} statement. If the first -``branch'' runs without causing an Exception, the second branch -is skipped. - -If the first branch causes an Exception, the flow of execution jumps -to the second branch, which tries to deal with the exceptional -condition (by saying ``error'' in a polite way). In this case it prints -an error message and the stack trace. - -You can download this code from -\url{http://thinkapjava.com/code/Words.java} -and the word list from -\url{http://thinkapjava.com/code/words.txt}. -Make sure both files are in the same folder. -(If you are using an IDE like NetBeans or Eclipse, make -sure the words.txt file is in your project directory.) - -Now go do Exercises~\ref{palindrome}, \ref{abecedarian}, and \ref{dupledrome}. - - - -\chapter{Program development} -\label{development} - -\section{Strategies} - -I present different program development strategies throughout -the book, so I wanted to pull them together here. -% -The foundation of all strategies is {\bf incremental development}, -which goes like this: - -\begin{enumerate} - -\item Start with a working program that does something visible, - like printing something. - -\item Add a small number of lines of code at a time, - and test the program after every change. - -\item Repeat until the program does what it is supposed to do. - -\end{enumerate} - -After every change, the program should produce some visible effect -that tests the new code. This approach to programming can save -a lot of time. - -Because you only add a few lines of code at a time, it -is easy to find syntax errors. -% -And because each version of the -program produces a visible result, you are constantly testing your -mental model of how the program works. If your mental model is -wrong, you are confronted with the conflict (and have a chance -to correct it) before you write a lot of bad code. - -The challenge of incremental development is that is it not -easy to figure out a path from the starting place -to a complete and correct program. -% -To help with that, there are several strategies to choose from: - -\begin{description} - -\item[Encapsulation and generalization:] If you don't know yet how -to divide the computation into methods, start writing code in -{\tt main}, then look for coherent chunks to encapsulate in -a method, and generalize them appropriately. - -\item[Rapid prototyping:] If you know what method to write, but not -how to write it, start with a rough draft that handles the simplest -case, then test it with other cases, extending and correcting as you go. - -\item[Bottom-up:] Start by writing simple methods, then assemble them -into a solution. - -\item[Top-down:] Use pseudocode to design the structure of the -computation and identify the methods you'll need. Then write the -methods and replace the pseudocode with real code. - -\end{description} - -Along the way, you might need some scaffolding. For example, each -class should have a {\tt toString} method that lets you print the -state of an object in human-readable form. This method is useful -for debugging, but usually not part of a finished program. - -\section{Failure modes} - -If you are spending a lot of time debugging, it is probably -because you are using an ineffective development strategy. Here -are the failure modes I see most often (and occasionally fall into): - -\begin{description} - -\item[Non-incremental developement:] If you write more than a few - lines of code without compiling and testing, you are asking for - trouble. One time when I asked a student how the homework was - coming along, he said, ``Great! I have it all written. Now I just - have to debug it.'' - -\item[Attachment to bad code:] If you write more than a few lines of - code without compiling and testing, you may not be able to debug it. - Ever. Sometimes the only strategy is (gasp!)~to delete the bad - code and start over (using an incremental strategy). But beginners - are often emotionally attached to their code, even if it doesn't - work. The only way out of this trap is to be ruthless. - -\item[Random-walk programming:] I sometimes work with students who - seem to be programming at random. They make a change, run the - program, get an error, make a change, run the program, etc. The - problem is that there is no apparent connection between the outcome - of the program and the change. -% - If you get an error message, take the time to read it. - More generally, take time to think. - -\item[Compiler submission:] Error messages are useful, but they - are not always right. For example, if the message says, ``Semi-colon - expected on line 13,'' that means there is a syntax error near - line 13. But putting a semi-colon on line 13 is not always the - solution. Don't submit to the will of the compiler. - -\end{description} - -The next chapter makes more suggestions for effective debugging. - - -\chapter{Debugging} -\label{debug} -\index{debugging} - -The best debugging strategy depends on what kind of error -you have: - -\begin{itemize} - -\item Syntax errors are produced by the compiler and indicate that - there is something wrong with the syntax of the program. Example: - omitting the semi-colon at the end of a statement. -\index{syntax error} - -\item Exceptions are produced if something goes wrong while the - program is running. Example: an infinite recursion eventually - causes a {\tt StackOverflowException}. -\index{exception} -\index{run-time error} - -\item Logic errors cause the program to do the wrong thing. Example: - an expression may not be evaluated in the order you expect, yielding - an unexpected result. -\index{logic error} - -\end{itemize} - -\index{error!syntax} -\index{error!run-time} -\index{error!logic} - -The following sections are organized by error type; -some techniques are useful for more than one type. - - -\section{Syntax errors} - -The best kind of debugging is the kind you don't have to do -because you avoid making errors in the first place. In the -previous section, I suggested development strategies that -minimize errors and makes it easy to find them when you do. -% -The key is to start with a working program and add small -amounts of code at a time. When there is an error, you will -have a pretty good idea where it is. - -Nevertheless, you might find yourself in one of the following -situations. For each situation, I make some suggestions about -how to proceed. - - -\subsection*{The compiler is spewing error messages.} -\index{error messages} -\index{compiler} - -If the compiler reports 100 error messages, that doesn't mean -there are 100 errors in your program. When the compiler encounters -an error, it often gets thrown off track for a while. It tries to -recover and pick up again after the first error, but sometimes -it reports spurious errors. - -Only the first error message is truly reliable. I suggest -that you only fix one error at a time, and then recompile the -program. You may find that one semi-colon ``fixes'' 100 errors. - - -\subsection*{I'm getting a weird compiler message and it -won't go away.} - -First of all, read the error message carefully. It is written in -terse jargon, but often there is a carefully hidden kernel of -information. - -If nothing else, the message will tell you where in the program the -problem occurred. Actually, it tells you where the compiler was -when it noticed a problem, which is not necessarily where the error -is. Use the information the compiler gives you as a guideline, -but if you don't see an error where the compiler is pointing, -broaden the search. - -Generally the error will be prior to the location of the error -message, but there are cases where it will be somewhere else -entirely. For example, if you get an error message at a method -invocation, the actual error may be in the method definition. - -If you don't find the error quickly, take a breath and look more -broadly at the entire program. Make sure the program is indented -properly; that makes it easier to spot syntax errors. - -Now, start looking for common errors: -\index{syntax} - -\begin{enumerate} - -\item Check that all parentheses and brackets are -balanced and properly nested. All method definitions should be nested -within a class definition. All program statements should be within a -method definition. - -\item Remember that upper case letters are not the same as -lower case letters. - -\item Check for semi-colons at the end of statements (and -no semi-colons after squiggly-braces). - -\item Make sure that any strings in the code have matching -quotation marks. Make sure that you use double-quotes for -Strings and single quotes for characters. - -\item For each assignment statement, make sure that the type -on the left is the same as the type on the right. Make sure -that the expression on the left is a variable name or something -else that you can assign a value to (like an element of an array). - -\item For each method invocation, make sure that the arguments -you provide are in the right order, and have right type, and that the -object you are invoking the method on is the right type. - -\item If you are invoking a value method, make sure you -are doing something with the result. If you are invoking a -void method, make sure you are {\em not} trying to do something -with the result. - -\item If you are invoking an object method, make sure you are -invoking it on an object with the right type. If you are invoking -a class method from outside the class where it is defined, make -sure you specify the class name. - -\item Inside an object method you can refer to the instance -variables without specifying an object. If you try that in -a class method, you get a message like, ``Static -reference to non-static variable.'' - -\end{enumerate} - -If nothing works, move on to the next section... - - -\subsection*{I can't get my program to compile no matter -what I do.} - -If the compiler says there is an error and you don't see it, that -might be because you and the compiler are not looking at the same -code. Check your development environment to make sure the program -you are editing is the program the compiler is compiling. If you -are not sure, try putting an obvious and deliberate syntax error -right at the beginning of the program. Now compile again. If -the compiler doesn't find the new error, there is probably something -wrong with the way you set up the development environment. - -If you have examined the code thoroughly, and you're sure the compiler -is compiling the right code, it is time for desperate measures: -{\bf debugging by bisection}. -\index{bisection!debugging by} -\index{debugging by bisection} - -\begin{itemize} - -\item Make a copy of the file you are working on. If you are -working on {\tt Bob.java}, make a copy called {\tt Bob.java.old}. - -\item Delete about half the code from {\tt Bob.java}. Try compiling -again. - -\begin{itemize} - -\item If the program compiles now, you know the error is in -the other half. Bring back about half of the code you deleted and -repeat. - -\item If the program still doesn't compile, the error must be in -this half. Delete about half of the code and repeat. - -\end{itemize} - -\item Once you have found and fixed the error, start bringing back -the code you deleted, a little bit at a time. - -\end{itemize} - -This process is ugly, but it goes faster than you might think, -and it is very reliable. - - -\subsection*{I did what the compiler told me to do, but it -still doesn't work.} - -Some compiler messages come with tidbits of advice, like -``class Golfer must be declared -abstract. It does not define int compareTo(java.lang.Object) from -interface java.lang.Comparable.'' It sounds like the compiler -is telling you to declare Golfer as an abstract class, and if -you are reading this book, you probably don't know what that is -or how to do it. - -Fortunately, the compiler is wrong. The solution in this case -is to make sure {\tt Golfer} has a method called {\tt compareTo} -that takes an {\tt Object} as a parameter. - -Don't let the compiler lead you by the nose. Error -messages give you evidence that something is wrong, but -the remedies they suggest are unreliable. - - -\section{Run-time errors} - -\subsection*{My program hangs.} -\index{infinite loop} -\index{infinite recursion} -\index{hanging} - -If a program stops and seems to be doing nothing, we -say it is {\bf hanging}. Often that means that it is caught in -an infinite loop or an infinite recursion. - -\begin{itemize} - -\item If there is a particular loop that you suspect is the -problem, add a print statement immediately before the loop -that says -``entering the loop'' and another immediately after that -says ``exiting the loop.'' - -Run the program. If you get the first message and not -the second, you've got an infinite loop. Go to the section -titled ``Infinite loop.'' - -\item Most of the time an infinite recursion will cause the program -to run for a while and then produce a StackOverflowException. -If that happens, go to the section titled ``Infinite recursion.'' - -If you are not getting a StackOverflowException, but you suspect -there is a problem with a recursive method, you can still use -the techniques in the infinite recursion section. - -\item If neither of those suggestions helps, you might not -understand the flow of execution in your program. -Go to the section titled ``Flow of execution.'' - -\end{itemize} - - -\subsubsection*{Infinite loop} - -If you think you have an infinite loop and you know -which loop it is, add a print statement at -the end of the loop that prints the values of the variables in -the condition, and the value of the condition. - -For example, - -\begin{lstlisting} - while (x > 0 && y < 0) { - // do something to x - // do something to y - - System.out.println("x: " + x); - System.out.println("y: " + y); - System.out.println("condition: " + (x > 0 && y < 0)); - } -\end{lstlisting} -% -Now when you run the program you see three lines of output -for each time through the loop. The last time through the -loop, the condition should be {\tt false}. If the loop keeps -going, you will see the values of {\tt x} and {\tt y} -and you might figure out why they are not updated correctly. - - -\subsubsection*{Infinite recursion} - -Most of the time an infinite recursion will cause the program -to throw a {\tt StackOverflowException}. But if the program is -slow it may take a long time to fill the stack. - -If you know which method is causing an infinite recursion, check that -there is a base case. There should be some condition -that makes the method return without making a recursive -invocation. If not, you need to rethink the algorithm and -identify a base case. - -If there is a base case, but the program doesn't seem to be reaching -it, add a print statement at the beginning of the method that prints -the parameters. Now when you run the program you see a few lines -of output every time the method is invoked, and you see the values of -the parameters. If the parameters are not moving toward the base case, -you might see why not. - - -\subsubsection*{Flow of execution} -\index{flow of execution} - -If you are not sure how the flow of execution is moving through -your program, add print statements to the beginning of each -method with a message like ``entering method foo,'' where -{\tt foo} is the name of the method. - -Now when you run the program it prints a trace of each -method as it is invoked. - -You can also print the arguments each method receives. When you run -the program, check whether the values are reasonable, and check -for one of the most common errors---providing arguments in the wrong -order. - - -\subsection*{When I run the program I get an Exception.} -\index{Exception} - -When an exception occurs, Java prints -a message that includes the name of the -exception, the line of the program where the problem occurred, and a -stack trace. -% -The stack trace includes the method that was running, -the method that invoked it, the method that -invoked {\em that}, and so on. - -The first step is to examine the place in the program where -the error occurred and see if you can figure out what happened. - -\begin{description} - -\item[NullPointerException:] You tried to access an instance -variable or invoke a method on an object that is currently -{\tt null}. You should figure out which variable is {\tt null} -and then figure out how it got to be that way. - -Remember that when you declare a variable with an object type, -it is initially {\tt null} until you assign a value to it. -For example, this code causes a NullPointerException: - -\begin{lstlisting} -Point blank; -System.out.println(blank.x); -\end{lstlisting} - -\item[ArrayIndexOutOfBoundsException:] The index you are using -to access an array is either negative or greater than -{\tt array.length-1}. If you can find the site where the -problem is, add a print statement immediately before it to -print the value of the index and the length of the array. -Is the array the right size? Is the index the right value? - -Now work your way backwards through the program and see where -the array and the index come from. Find the nearest assignment -statement and see if it is doing the right thing. - -If either one is a parameter, go to the place where the method -is invoked and see where the values are coming from. - -\item[StackOverFlowException:] See ``Infinite recursion.'' - -\item[FileNotFoundException:] This means Java didn't find the file -it was looking for. If you are using a project-based development -environment like Eclipse, you might have to import the file into -the project. Otherwise make sure the file exists and that the -path is correct. This problem depends on your file system, so it -can be hard to track down. - -\item[ArithmeticException:] Occurs when something goes wrong during -an arithmetic operation, most often division by zero. - -\end{description} - - -\subsection*{I added so many print statements I get inundated with -output.} -\index{print statement} -\index{statement!print} - -One of the problems with using print statements for debugging -is that you can end up buried in output. There are two ways -to proceed: either simplify the output or simplify the program. - -To simplify the output, you can remove or comment out print -statements that aren't helping, or combine them, or format -the output so it is easier to understand. As you develop a program, -you should write code to generate concise, -informative visualizations of what the program is doing. - -To simplify the program, -scale down the problem the program is working on. For example, if you -are sorting an array, sort a {\em small} array. If the program takes -input from the user, give it the simplest input that causes the -error. - -Also, clean up the code. Remove dead code and reorganize the -program to make it easier to read. For example, if you -suspect that the error is in a deeply-nested part of the program, -rewrite that part with simpler structure. If you suspect a -large method, split it into smaller methods and test them -separately. - -The process of finding the minimal test case often leads you to the -bug. For example, if you find that a program works when the array has -an even number of elements, but not when it has an odd number, that -gives you a clue about what is going on. - -Reorganizing the program can help you find subtle -bugs. If you make a change that you think doesn't affect the -program, and it does, that can tip you off. - - -\section{Logic errors} - -\subsection*{My program doesn't work.} - -Logic errors are hard to find because the -compiler and the run-time system provide no information about -what is wrong. Only you know what the program is supposed to -do, and only you know that it isn't doing it. - -The first step is to make a connection between the code and the -behavior you get. You need a hypothesis about what the program -is actually doing. -% -Here are some questions to ask yourself: - -\begin{itemize} - -\item Is there something the program was supposed to do, but -doesn't seem to be happening? Find the section of the code -that performs that function and make sure it is executing when -you think it should. See ``Flow of execution'' above. - -\item Is something happening that shouldn't? Find code in -your program that performs that function and see if it is -executing when it shouldn't. - -\item Is a section of code producing an unexpected effect? Make sure - you understand the code, especially if it invokes - Java methods. Read the documentation for those methods, and - try them out with simple test cases. They might not do what you - think they do. - -\end{itemize} - -To program, you need a mental model what your code does. -If it doesn't do what you expect, the problem might not be -the program; it might be in your head. -\index{model!mental} -\index{mental model} - -The best way to correct your mental model is to break the program -into components (usually the classes and methods) and test -them independently. Once you find the discrepancy -between your model and reality, you can solve the problem. - -Here are some common logic errors to check for: - -\begin{itemize} - -\item Remember that integer division always rounds down. If you -want fractions, use {\tt doubles}. - -\item Floating-point numbers are only approximate, so don't rely -on perfect accuracy. - -\item More generally, use integers for countable things -and floating-point numbers for measurable things. - -\item If you use the assignment operator ({\tt =}) -instead of the equality operator ({\tt ==}) in the -condition of an {\tt if}, {\tt while}, or {\tt for} statement, -you might get an expression that is syntactically legal and -semantically wrong. - -\item When you apply the equality operator ({\tt ==}) to an -object, it checks identity. If you meant to check -equivalence, you should use the {\tt equals} method. - -\item For user defined types, {\tt equals} checks identity. -If you want a different notion of equivalence, you have to -override it. - -\item Inheritance can lead to subtle logic errors, -because you can run inherited code without realizing it. -See ``Flow of Execution'' above. - -\end{itemize} - - -\subsection*{I've got a big hairy expression and it doesn't -do what I expect.} -\index{expression!big and hairy} - -Writing complex expressions is fine as long as they are readable, -but they can be hard to debug. It is often a good idea to -break a complex expression into a series of assignments to -temporary variables. - -For example: - -\begin{lstlisting} -rect.setLocation(rect.getLocation().translate( - -rect.getWidth(), -rect.getHeight())); -\end{lstlisting} -% -Can be rewritten as - -\begin{lstlisting} -int dx = -rect.getWidth(); -int dy = -rect.getHeight(); -Point location = rect.getLocation(); -Point newLocation = location.translate(dx, dy); -rect.setLocation(newLocation); -\end{lstlisting} -% -The explicit version is easier to read, because the variable -names provide additional documentation, and easier to debug, -because you can check the types of the temporary variables -and display their values. - -\index{temporary variable} -\index{variable!temporary} -\index{order of evaluation} -\index{precedence} - -Another problem that can occur with big expressions is -that the order of evaluation may not be what you expect. -For example, to evaluate -$\frac{x}{2 \pi}$, you might write - -\begin{lstlisting} -double y = x / 2 * Math.PI; -\end{lstlisting} -% -That is not correct, because multiplication and division have -the same precedence, and they are evaluated from left to right. -This expression computes $x \pi / 2$. - -If you are not sure of the order of operations, use parentheses to -make it explicit. - -\begin{lstlisting} -double y = x / (2 * Math.PI); -\end{lstlisting} -% -This version is correct, -and more readable for -other people who haven't memorized the order of operations. - - - -\subsection*{My method doesn't return what I expect.} -\index{return statement} -\index{statement!return} - -If you have a return statement with a complex expression, -you don't have a chance to print the value before -returning. Again, you can use a temporary variable. For -example, instead of - -\begin{lstlisting} -public Rectangle intersection(Rectangle a, Rectangle b) { - return new Rectangle( - Math.min(a.x, b.x), - Math.min(a.y, b.y), - Math.max(a.x+a.width, b.x+b.width)-Math.min(a.x, b.x) - Math.max(a.y+a.height, b.y+b.height)-Math.min(a.y, b.y) ); -} -\end{lstlisting} -% -You could write - -\begin{lstlisting} -public Rectangle intersection(Rectangle a, Rectangle b) { - int x1 = Math.min(a.x, b.x); - int y2 = Math.min(a.y, b.y); - int x2 = Math.max(a.x+a.width, b.x+b.width); - int y2 = Math.max(a.y+a.height, b.y+b.height); - Rectangle rect = new Rectangle(x1, y1, x2-x1, y2-y1); - return rect; -} -\end{lstlisting} -% -Now you have the opportunity to display any of -the intermediate variables before returning. And by -reusing {\tt x1} and {\tt y1}, you made the code smaller, too. - - -\subsection*{My print statement isn't doing anything} -\index{print statement} -\index{statement!print} - -If you use the {\tt println} method, the output is displayed -immediately, but if you use {\tt print} (at least in some -environments) the output gets stored without being displayed until the -next newline. If the program terminates without -printing a newline, you may never see the stored output. - -If you suspect that this is happening to, change -some or all of the {\tt print} statements to {\tt println}. - - -\subsection*{I'm really, really stuck and I need help} - -First, get away from the computer for a few minutes. -Computers emit waves that affect the brain, causing the following -symptoms: - -\begin{itemize} - -\item Frustration and rage. - -\item Superstitious beliefs (``the computer hates me'') and -magical thinking (``the program only works when I wear my -hat backwards''). - -\item Sour grapes (``this program is lame anyway''). - -\end{itemize} - -If you suffer from any of these symptoms, get -up and go for a walk. When you are calm, think about the program. -What is it doing? What are possible causes of that -behavior? When was the last time you had a working program, -and what did you do next? - -Sometimes it just takes time to find a bug. I often find bugs when I -let my mind wander. Good places to find bugs are trains, showers, and -bed. - - -\subsection*{No, I really need help.} - -It happens. Even the best programmers get stuck. -Sometimes you need a fresh pair of eyes. - -Before you bring someone else in, make sure you have tried -the techniques described above. Your program should be as simple -as possible, and you should be working on the smallest input -that causes the error. You should have print statements in the -appropriate places (and the output they produce should be -comprehensible). You should understand the problem well enough -to describe it concisely. - -When you bring someone in to help, give -them the information they need. - -\begin{itemize} - -\item What kind of bug is it? Syntax, run-time, or logic? - -\item What was the last thing you did before this error occurred? -What were the last lines of code that you wrote, or what is -the new test case that fails? - -\item If the bug occurs at compile-time or run-time, what is -the error message, and what part of the program does it indicate? - -\item What have you tried, and what have you learned? - -\end{itemize} - -By the time you explain the problem -to someone, you might see the answer. This phenomenon -is so common that some people recommend a debugging technique -called ``rubber ducking.'' Here's how it works: - -\begin{enumerate} - -\item Buy a standard-issue rubber duck. - -\item When you are really stuck on a problem, put the rubber -duck on the desk in front of you and say, ``Rubber duck, I -am stuck on a problem. Here's what's happening...'' - -\item Explain the problem to the rubber duck. - -\item See the solution. - -\item Thank the rubber duck. - -\end{enumerate} - -I am not kidding. See -\url{http://en.wikipedia.org/wiki/Rubber_duck_debugging}. - - -\subsection*{I found the bug!} - -When you find the bug, it is usually obvious how to fix it. But not -always. Sometimes what seems to be a bug is really an indication that -you don't understand the program, or there is an error in your -algorithm. In these cases, you might have to rethink the algorithm, -or adjust your mental model. Take some time away from -the computer to think, work through test cases -by hand, or draw diagrams to represent the computation. - -After you fix the bug, don't just start in making new errors. -Take a minute to think about what kind of bug it was, why you made -the error, how the error manifested itself, and -what you could have done to find it faster. Next time you see something -similar, you will be able to find the bug more quickly. - - -\printindex - -\clearemptydoublepage - -\end{document} - - - diff --git a/up.png b/up.png deleted file mode 100644 index 4e86da1..0000000 Binary files a/up.png and /dev/null differ