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Hashing PPT

This document discusses hashing and different techniques for implementing dictionaries using hashing. It begins by explaining that dictionaries store elements using keys to allow for quick lookups. It then discusses different data structures that can be used, focusing on hash tables. The document explains that hashing allows for constant-time lookups on average by using a hash function to map keys to table positions. It discusses collision resolution techniques like chaining, linear probing, and double hashing to handle collisions when the hash function maps multiple keys to the same position.

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CSCE 3110 Data Structures & Algorithm Analysis Rada Mihalcea http://www.cs.unt.edu/~rada/CSCE3110 Hashing Reading: Chap.5, Weiss
Dictionaries stores elements so that they can be located quickly using keys. For eg A Dictionary may hold bank accounts. In which key will be account number. And each account may stores many additional information. Dictionaries
How to Implement a Dictionary? Different data structure to realize a key Array , Linked list Binary tree Hash table Red/Black tree AVL Tree B-Tree
Why Hashing?? The sequential search algorithm takes time proportional to the data size, i.e, O(n). Binary search improves on liner search reducing the search time to O(log n). With a BST, an O(log n) search efficiency can be obtained; but the worst-case complexity is O(n). To guarantee the O(log n) search time, BST height balancing is required ( i.e., AVL trees).
Why Hashing?? (Cntd.) Suppose that we want to store 10,000 students records (each with a 5-digit ID) in a given container. · A linked list implementation would take O(n) time. · A height balanced tree would give O(log n) access time. · Using an array of size 100,000 would give O(1) access time but will lead to a lot of space wastage.
Why Hashing?? (Cntd.) Is there some way that we could get O(1) access without wasting a lot of space? The answer is hashing.
Hashing Another important and widely useful technique for implementing dictionaries Constant time per operation (on the average) Like an array, come up with a function to map the large range into one which we can manage.
Basic Idea Use hash function to map keys into positions in a hash table Ideally If Student A has ID(Key) k and h is hash function, then A’s Details is stored in position h(k) of table To search for A, compute h(k) to locate position. If no element, dictionary does not contain A.
Example Let keys be ID of 100 students And ID in form of like 345610. Now, we decided to take A[100] And, Hash function is , say , LAST TWO DIGIT So, 103062 will go to location 62 And same if some one have 113062 Then again goes to the location 62 THIS EVENT IS CALLED COLLISION
Collision Resolution Chaining Linear Probe Double hashing
Chaining
Hash Functions A Good Hash function is one which distribute keys evenly among the slots. And It is said that Hash Function is more art than a science. Becoz it need to analyze the data. Key Hash Function Slot
Hash Function(cntd.) Need of choose a good Hash function Quick Compute. Distributes keys in uniform manner throughout the table. How to deal with Hashing non integer Key??? 1.Find some way of turning keys into integer. eg if key is in character then convert it into integer using ASCII 2.Then use standard Hash Function on the integer.
Hash Function (contd.) Hash code map Keys Integer Compression map Integer A[0….m-1] The Mapping of keys to indices of a hash table is called a hash function. The Hash Function is ussually the composition of two maps:
Collision Resolution (contd.) Now, there is two more techniques to deal with collision Linear Probing Double Hashing
Linear probe Linearprobeinsert(k) If(table is full) {error} probe =h(k) while(table[probe] is occupied) {probe = (probe + 1) % m //m is no. of slots } Table[probe]=k
Linear Probe(contd.) If the current location is used, Try the next table Location. Used less memory than chaining as one does not have to store all those link(i.e. address of others). Slower than chaining as one might have to walk along the table for a long time.
Linear Probe (contd.)
Linear probe (contd.) Deletion in Linear probe
Double Hashing h1(k) - Position in the table where we first check for the key h2(k) – Determine offset when h1(k) is already occupied In Linear probing offset is always 1.
Double Hashing (contd.) Doublehashing insert(k) If (table is full) {error } Probe=h1(k); offset=h2(k); While (table[probe] is occupied) {probe=(probe + offset)%m } table[probe]=k;
Double Hashing(contd.)
Double Hashing(contd.)
Double Hashing(contd.)
Double Hashing(contd.)
Double Hashing(contd.)
Double Hashing(contd.)
Double Hashing(contd.)
Double Hashing(contd.)
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