Counting Sort

Counting sort is a stable sorting technique, which is used to sort objects according to the keys that are small numbers. It counts the number of keys whose key values are same. This sorting technique is effective when the difference between different keys are not so big, otherwise, it can increase the space complexity.

The complexity of counting Sort Technique

• Time Complexity: O(n+r)
• Space Complexity: O(n+r)

Input and Output

Input:
A list of unsorted data: 2 5 6 2 3 10 3 6 7 8
Output:
Array before Sorting: 2 5 6 2 3 10 3 6 7 8
Array after Sorting: 2 2 3 3 5 6 6 7 8 10

Algorithm

counting sort(array, size)

Input: An array of data, and the total number in the array

Output: The sorted Array

Begin
   max = get maximum element from array.
   define count array of size [max+1]

   for i := 0 to max do
      count[i] = 0 //set all elements in the count array to 0
   done

   for i := 1 to size do
      increase count of each number which have found in the array
   done

   for i := 1 to max do
      count[i] = count[i] + count[i+1] //find cumulative frequency
   done

   for i := size to 1 decrease by 1 do
      store the number in the output array
      decrease count[i]
   done

   return the output array
End

Example

#include<iostream>
#include<algorithm>
using namespace std;

void display(int *array, int size) {
   for(int i = 1; i<=size; i++)
      cout << array[i] << " ";
   cout << endl;
}

int getMax(int array[], int size) {
   int max = array[1];
   for(int i = 2; i<=size; i++) {
      if(array[i] > max)
         max = array[i];
   }

   return max; //the max element from the array
}

void countSort(int *array, int size) {
   int output[size+1];
   int max = getMax(array, size);
   int count[max+1]; //create count array (max+1 number of elements)

   for(int i = 0; i<=max; i++)
      count[i] = 0; //initialize count array to all zero
   for(int i = 1; i <=size; i++)
      count[array[i]]++; //increase number count in count array.
   for(int i = 1; i<=max; i++)
      count[i] += count[i-1]; //find cumulative frequency

   for(int i = size; i>=1; i--) {
      output[count[array[i]]] = array[i];
      count[array[i]] -= 1; //decrease count for same numbers
   }

   for(int i = 1; i<=size; i++) {
      array[i] = output[i]; //store output array to main array
   }
}

int main() {
   int n;
   cout << "Enter the number of elements: ";
   cin >> n;
   int arr[n+1]; //create an array with given number of elements
   cout << "Enter elements:" << endl;

   for(int i = 1; i<=n; i++) {
      cin >> arr[i];
   }

   cout << "Array before Sorting: ";
   display(arr, n);
   countSort(arr, n);
   cout << "Array after Sorting: ";
   display(arr, n);
}

Output

Enter the number of elements: 10
Enter elements:
2 5 6 2 3 10 3 6 7 8
Array before Sorting: 2 5 6 2 3 10 3 6 7 8
Array after Sorting: 2 2 3 3 5 6 6 7 8 10