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Counting Sort Algorithm Assignment Help


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What is Counting Sort Algorithm?


Counting_Sort (P, Q, r)
1: for j = 1 to r
2: S[ j ] = 0;
3: for k = 1 to n 
4: S[P[ k ]] += 1;
5: for j = 2 to r
6: S[ j ] = S[ j ] + S[j - 1];
7: for k = n down to 1
8: 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



Follow similar step, we got

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


Follow similar step, we got

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



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