Counting Sort

Counting Sort

• 1.
  COUNTING SORT Design andAnalysis of Algorithm
• 2.
  COUNTING SORT  Step-1:Create a count array to store the count of each unique object.  Step-2: Modify count array by adding the previous number.  Step-3: Create output array by decrese count array.
• 3.
  Let the Arrayin range 0 to 5 1 4 3 2 3 5 2 Create an array that will hold the count of each number, with index ranges from 0 to 5 Count Input 0 1 2 2 1 1 [0] [1] [2] [3] [4] [5]
• 4.
  Modify count arrayby adding the previous number: Input 1 4 3 2 3 5 2 Sum Count 0 1 3 5 6 7 [0] [1] [2] [3] [4] [5]
• 5.
  Output each objectfrom the input sequence followed by decreasing count by 1: 1 4 3 2 3 5 2 Input Sum Count 0 1 3 5 6 7 [0] [1] [2] [3] [4] [5] output [1] [2] [3] [4] [5] [6] [7]
• 6.
  1 4 32 3 5 2 Input Sum Count 0 1 3 5 1 1 [0] [1] [2] [3] [4] [5] 1output Output each object from the input sequence followed by decreasing count by 1: [1] [2] [3] [4] [5] [6] [7]
• 7.
  1 4 32 3 5 2 Input 0 0 3 5 6 7 [0] [1] [2] [3] [4] [5] 1 4output [1] [2] [3] [4] [5] [6] [7] Sum Count
• 8.
  1 4 32 3 5 2 Input 0 0 3 5 5 7 [0] [1] [2] [3] [4] [5] 1 3 4output [1] [2] [3] [4] [5] [6] [7] Sum Count
• 9.
  1 4 32 3 5 2 Input 0 0 3 4 5 7 [0] [1] [2] [3] [4] [5] 1 2 3 4output [1] [2] [3] [4] [5] [6] [7] Sum Count
• 10.
  1 4 32 3 5 2 Input 0 0 2 4 5 7 [0] [1] [2] [3] [4] [5] 1 2 3 3 4output [1] [2] [3] [4] [5] [6] [7] Sum Count
• 11.
  1 4 32 3 5 2 Input 0 0 2 3 5 7 [0] [1] [2] [3] [4] [5] 1 2 3 3 4 5output [1] [2] [3] [4] [5] [6] [7] Sum Count
• 12.
  1 4 32 3 5 2 Input 0 0 2 3 5 6 [0] [1] [2] [3] [4] [5] 1 2 2 3 3 4 5output [1] [2] [3] [4] [5] [6] [7] Sum Count
• 13.
  1 4 32 3 5 2 Input 0 0 1 3 5 6 [0] [1] [2] [3] [4] [5] 1 2 2 3 3 4 5output [1] [2] [3] [4] [5] [6] [7] Sum Count
• 14.
  ARRAY IS NOWSORTED
• 15.
  TIME COMPLEXITY for i<-1to k do………………………..constant time c[i]<- 0……………………………..constant time for j<- 1 to n do…………………………………n time c[A[j]]<- c[A[j]]+1……………………………………..n time for i<-2 to k do……………………………………….constant time c[i]<- c[i]+c[i-1]………………………………………..constant time for j<- n down to 1 do…………………………………n B[c[A[i]]]<- A[j]……………………………………………………..n C[A[i]]<- C[A[j]] +1…………………………………………….n T(n) =c+c+n+n+c+c+n+n+n =5n+4c Big(O)=n