# Counting Sort with C++ Example

Submitted by Shubham Singh Rajawat, on June 13, 2017

Learn: Counting Sort in Data Structure using C++ Example: Counting sort is used for small integers it is an algorithm with a complexity of O(n+k) as worst case.

Counting sort is used for small integers it is an algorithm with a complexity of O(n+k) as worst case where 'n' is the number of elements and k is the greatest number among all the elements .

Algorithm:

Method Counting_Sort() contains three arguments A contains the elements entered by user, B array in which sorted elements are stored , n is the size of array A.

First of all we will have to initialize the array C with zero then we will store the frequency of elements in another array C i.e. if the value of an input element is x , we increment C[i](to store the occurrence of each number) then we will modify C[x] so that it will contain the last occurrence of the element x this can be done by storing the sum of C[x] and C[x-1] in C[x].
Now we will traverse the array A from last and find its position from C and that element in B at that address and at last we will modify C so that duplicate element will not end up in the same position in B.

Let us understand this with the help of an example:

```Here , n=7 and A[]={0,1,5,7,8,6,3}

At first C[]={0,0,0,0,0,0,0,0,0}

Now we will modify C[]
C[]={1,1,0,1,0,1,1,1,1}

Now we will modify C[] so that it contains the last occurrence of any element
x at C[x].

C[1]=C[0]+c[1] , C[2]=C[1]+C[2]… and so on
C[]={1,2,2,3,3,4,5,6,7}    /*Index of will start from zero*/

Now we will store the sorted array in B[] by traversing A[]
and checking the position of that element from C[]

/*Index of A[] and B[] will start from one*/
So first A[7]=3  So the position of 3 in B[] is 3 and then we will update C[3]=2
Next A[6]=6 so the position of 6 in B[] is 5 and then we will update C[6]=4
And this will keep on going until we reach the first element then we will get
our sorted array B[].
B[]={0,1,3,5,6,7,8}
```

## Counting sort program using C++

```#include<iostream>
using namespace std;
int k=0;

/*Method to sort the array*/
void Counting_Sort(int A[],int B[],int n)
{
int C[k];
for(int i=0;i<k+1;i++)
{
/*It will initialize the C with zero*/
C[i]=0;
}
for(int j=1;j<=n;j++)
{
/*It will count the occurence of every element x in A
and increment it at position x in C*/
C[A[j]]++;
}
for(int i=1;i<=k;i++)
{
/*It will store the last
occurence of the element i */
C[i]+=C[i-1];
}
for(int j=n;j>=1;j--)
{
/*It will place the elements at their
respective index*/
B[C[A[j]]]=A[j];
/*It will help if an element occurs
more than one time*/
C[A[j]]=C[A[j]]-1;
}
}
int main()
{
int n;
cout<<"Enter the size of the array :";
cin>>n;

/*A stores the elements input by user */
/*B stores the sorted sequence of elements*/
int A[n],B[n];

for(int i=1;i<=n;i++)
{
cin>>A[i];
if(A[i]>k)
{
/*It will modify k if an element
occurs whose value is greater than k*/
k=A[i];
}
}
Counting_Sort(A,B,n);
/*It will print the sorted sequence on the
console*/
for(int i=1;i<=n;i++)
{
cout<<B[i]<<" ";
}

cout<<endl;
return 0;
}
```

Output

```First Run:
Enter the size of the array :10
12 345 89 100 23 0 18 44 111 1
0 1 12 18 23 44 89 100 111 345

Second Run:
Enter the size of the array :5
999 87 12 90 567
12 87 99 567 999
```

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