Counting Sort Algorithm Assignment Help

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What is Counting Sort Algorithm?

 Counting_Sort (P, Q, r)1: for j = 1 to r2: S[ j ] = 0;3: for k = 1 to n 4: S[P[ k ]] += 1;5: for j = 2 to r6: S[ j ] = S[ j ] + S[j - 1];7: for k = n down to 18: Q[S[P[ k ]]] = P[ k ];9: S[P[ k ]] -= 1;

## Example: Find the shortest sequence.

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5

B:

 1 2 3 4 5 6 7 8

Solution:

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 1

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 1 1

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 1 1 1

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 1 1 1 1

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 1 1+1 =2 1 1

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 1 2 1+1=2 1

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 1+1=2 2 2 1

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 2 2 2+1=3 1

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 2 0 2 3 0 1

Second Step:

C:

 0 1 2 3 4 5 2 0 2 3 0 1

C:

 0 1 2 3 4 5 2 0 +2 2 3 0 1

C:

 0 1 2 3 4 5 2 2 2 3 0 1

C:

 0 1 2 3 4 5 2 2 2+2 3 0 1

C:

 0 1 2 3 4 5 2 2 4 7 7 8

C:

 0 1 2 3 4 5 2 2 4 7 7 8

Third Step:

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 2 2 4 7 7 8

B:

 1 2 3 4 5 6 7 8 3

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 2 2 4 7 7 8

B:

 1 2 3 4 5 6 7 8 0 3

A:

 1 2 3 4 5 6 7 8 2 5 3 0 2 3 0 3

C:

 0 1 2 3 4 5 2 2 4 7 7 8

B:

 1 2 3 4 5 6 7 8 0 0 2 2 3 3 3 5