Counting Sort

Counting sort is a sorting technique based on keys between a specific range. It works by counting the number of objects having distinct key values (kind of hashing). Then doing some arithmetic to calculate the position of each object in the output sequence.

Let us understand it with the help of an example. 

For simplicity, consider the data in the range 0 to 9. 
Input data: 1, 4, 1, 2, 7, 5, 2
  1) Take a count array to store the count of each unique object.
  Index:     0  1  2  3  4  5  6  7  8  9
  Count:     0  2  2  0   1  1  0  1  0  0

  2) Modify the count array such that each element at each index 
  stores the sum of previous counts. 
  Index:     0  1  2  3  4  5  6  7  8  9
  Count:     0  2  4  4  5  6  6  7  7  7

The modified count array indicates the position of each object in 
the output sequence.
 
  3) Output each object from the input sequence followed by 
  decreasing its count by 1.
  Process the input data: 1, 4, 1, 2, 7, 5, 2. Position of 1 is 2.
  Put data 1 at index 2 in output. Decrease count by 1 to place 
  next data 1 at an index 1 smaller than this index.

Following is implementation of counting sort.



C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ Program for counting sort 
#include<bits/stdc++.h> 
#include<string.h>
using namespace std; 
#define RANGE 255 
  
// The main function that sort 
// the given string arr[] in 
// alphabatical order 
void countSort(char arr[]) 
{ 
    // The output character array 
    // that will have sorted arr 
    char output[strlen(arr)]; 
  
    // Create a count array to store count of inidividul 
    // characters and initialize count array as 0 
    int count[RANGE + 1], i; 
    memset(count, 0, sizeof(count)); 
  
    // Store count of each character 
    for(i = 0; arr[i]; ++i) 
        ++count[arr[i]]; 
  
    // Change count[i] so that count[i] now contains actual 
    // position of this character in output array 
    for (i = 1; i <= RANGE; ++i) 
        count[i] += count[i-1]; 
  
    // Build the output character array 
    for (i = 0; arr[i]; ++i) 
    { 
        output[count[arr[i]]-1] = arr[i]; 
        --count[arr[i]]; 
    } 
  
    /* 
    For Stable algorithm 
    for (i = sizeof(arr)-1; i>=0; --i) 
    { 
        output[count[arr[i]]-1] = arr[i]; 
        --count[arr[i]]; 
    } 
      
    For Logic : See implementation 
    */
  
    // Copy the output array to arr, so that arr now 
    // contains sorted characters 
    for (i = 0; arr[i]; ++i) 
        arr[i] = output[i]; 
} 
  
// Driver  code
int main() 
{ 
    char arr[] = "geeksforgeeks";
  
    countSort(arr); 
  
    cout<< "Sorted character array is " << arr; 
    return 0; 
} 
  
// This code is contributed by rathbhupendra

chevron_right






                        filter_none









C














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// C Program for counting sort 


#include <stdio.h> 


#include <string.h> 


#define RANGE 255 


  


// The main function that sort the given string arr[] in 


// alphabatical order 


void countSort(char arr[]) 


{ 


    // The output character array that will have sorted arr 


    char output[strlen(arr)]; 


  


    // Create a count array to store count of inidividul 


    // characters and initialize count array as 0 


    int count[RANGE + 1], i; 


    memset(count, 0, sizeof(count)); 


  


    // Store count of each character 


    for(i = 0; arr[i]; ++i) 


        ++count[arr[i]]; 


  


    // Change count[i] so that count[i] now contains actual 


    // position of this character in output array 


    for (i = 1; i <= RANGE; ++i) 


        count[i] += count[i-1]; 


  


    // Build the output character array 


    for (i = 0; arr[i]; ++i) 


    { 


        output[count[arr[i]]-1] = arr[i]; 


        --count[arr[i]]; 


    } 


  


    /* 


     For Stable algorithm  


     for (i = sizeof(arr)-1; i>=0; --i) 


    { 


        output[count[arr[i]]-1] = arr[i]; 


        --count[arr[i]]; 


    } 


     


    For Logic : See implementation 


    */


  


    // Copy the output array to arr, so that arr now 


    // contains sorted characters 


    for (i = 0; arr[i]; ++i) 


        arr[i] = output[i]; 


} 


  


// Driver program to test above function 


int main() 


{ 


    char arr[] = "geeksforgeeks";//"applepp"; 


  


    countSort(arr); 


  


    printf("Sorted character array is %sn", arr); 


    return 0; 


} 



















                        chevron_right







                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// Java implementation of Counting Sort 


class CountingSort 


{ 


    void sort(char arr[]) 


    { 


        int n = arr.length; 


  


        // The output character array that will have sorted arr 


        char output[] = new char[n]; 


  


        // Create a count array to store count of inidividul 


        // characters and initialize count array as 0 


        int count[] = new int[256]; 


        for (int i=0; i<256; ++i) 


            count[i] = 0; 


  


        // store count of each character 


        for (int i=0; i<n; ++i) 


            ++count[arr[i]]; 


  


        // Change count[i] so that count[i] now contains actual 


        // position of this character in output array 


        for (int i=1; i<=255; ++i) 


            count[i] += count[i-1]; 


  


        // Build the output character array 


        // To make it stable we are operating in reverse order. 


        for (int i = n-1; i>=0; i--) 


        { 


            output[count[arr[i]]-1] = arr[i]; 


            --count[arr[i]]; 


        } 


  


        // Copy the output array to arr, so that arr now 


        // contains sorted characters 


        for (int i = 0; i<n; ++i) 


            arr[i] = output[i]; 


    } 


  


    // Driver method 


    public static void main(String args[]) 


    { 


        CountingSort ob = new CountingSort(); 


        char arr[] = {'g', 'e', 'e', 'k', 's', 'f', 'o', 


                    'r', 'g', 'e', 'e', 'k', 's'


                    }; 


  


        ob.sort(arr); 


  


        System.out.print("Sorted character array is "); 


        for (int i=0; i<arr.length; ++i) 


            System.out.print(arr[i]); 


    } 


} 


/*This code is contributed by Rajat Mishra */



















                        chevron_right







                        filter_none









Python














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















# Python program for counting sort 


  


# The main function that sort the given string arr[] in  


# alphabetical order 


def countSort(arr): 


  


    # The output character array that will have sorted arr 


    output = [0 for i in range(256)] 


  


    # Create a count array to store count of inidividul 


    # characters and initialize count array as 0 


    count = [0 for i in range(256)] 


  


    # For storing the resulting answer since the  


    # string is immutable 


    ans = ["" for _ in arr] 


  


    # Store count of each character 


    for i in arr: 


        count[ord(i)] += 1


  


    # Change count[i] so that count[i] now contains actual 


    # position of this character in output array 


    for i in range(256): 


        count[i] += count[i-1] 


  


    # Build the output character array 


    for i in range(len(arr)): 


        output[count[ord(arr[i])]-1] = arr[i] 


        count[ord(arr[i])] -= 1


  


    # Copy the output array to arr, so that arr now 


    # contains sorted characters 


    for i in range(len(arr)): 


        ans[i] = output[i] 


    return ans  


  


# Driver program to test above function 


arr = "geeksforgeeks"


ans = countSort(arr) 


print "Sorted character array is %s"  %("".join(ans)) 


  


# This code is contributed by Nikhil Kumar Singh 



















                        chevron_right







                        filter_none









C#














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// C# implementation of Counting Sort 


using System; 


  


class GFG { 


      


    static void countsort(char []arr) 


    { 


        int n = arr.Length; 


  


        // The output character array that 


        // will have sorted arr 


        char []output = new char[n]; 


  


        // Create a count array to store  


        // count of inidividul characters  


        // and initialize count array as 0 


        int []count = new int[256]; 


          


        for (int i=0; i<256; ++i) 


            count[i] = 0; 


  


        // store count of each character 


        for (int i=0; i<n; ++i) 


            ++count[arr[i]]; 


  


        // Change count[i] so that count[i]  


        // now contains actual position of  


        // this character in output array 


        for (int i=1; i<=255; ++i) 


            count[i] += count[i-1]; 


  


        // Build the output character array 


        // To make it stable we are operating in reverse order. 


        for (int i = n-1; i>=0; i--) 


        { 


            output[count[arr[i]]-1] = arr[i]; 


            --count[arr[i]]; 


        } 


  


        // Copy the output array to arr, so 


        // that arr now contains sorted  


        // characters 


        for (int i = 0; i<n; ++i) 


            arr[i] = output[i]; 


    } 


  


    // Driver method 


    public static void Main() 


    { 


          


        char []arr = {'g', 'e', 'e', 'k', 's', 'f', 'o', 


                    'r', 'g', 'e', 'e', 'k', 's'


                    }; 


  


        countsort(arr); 


  


        Console.Write("Sorted character array is "); 


        for (int i=0; i<arr.Length; ++i) 


            Console.Write(arr[i]); 


    } 


} 


  


// This code is contributed by Sam007. 



















                        chevron_right







                        filter_none









PHP














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















<?php 


// PHP Program for counting sort 


  


$RANGE = 255; 


  


// The main function that sort  


// the given string arr[] in 


// alphabatical order 


function countSort($arr) 


{ 


    global $RANGE; 


      


    // The output character array  


    // that will have sorted arr 


    $output = array(strlen($arr)); 


    $len = strlen($arr); 


      


    // Create a count array to  


    // store count of inidividul  


    // characters and initialize 


    // count array as 0 


    $count = array_fill(0, $RANGE + 1, 0); 


  


    // Store count of  


    // each character 


    for($i = 0; $i < $len; ++$i) 


        ++$count[ord($arr[$i])]; 


  


    // Change count[i] so that  


    // count[i] now contains  


    // actual position of this 


    // character in output array 


    for ($i = 1; $i <= $RANGE; ++$i) 


        $count[$i] += $count[$i - 1]; 


  


    // Build the output 


    // character array 


    // To make it stable we are operating  


    // in reverse order. 


    for ($i = $len-1; $i >= 0 ; $i--) 


    { 


        $output[$count[ord($arr[$i])] - 1] = $arr[$i]; 


        --$count[ord($arr[$i])]; 


    } 


  


    // Copy the output array to  


    // arr, so that arr now  


    // contains sorted characters 


    for ($i = 0; $i < $len; ++$i) 


        $arr[$i] = $output[$i]; 


return $arr; 


} 


  


// Driver Code 


$arr = "geeksforgeeks"; //"applepp"; 


  


$arr = countSort($arr); 


  


echo "Sorted character array is " . $arr; 


  


// This code is contributed by mits 


?> 



















                        chevron_right







                        filter_none










Output: 


Sorted character array is eeeefggkkorss


Time Complexity: O(n+k) where n is the number of elements in input array and k is the range of input.

Auxiliary Space: O(n+k)


The problem with the previous counting sort was that we could not sort the elements if we have negative numbers in it. Because there are no negative array indices. So what we do is, we find the minimum element and we will store count of that minimum element at zero index.




C++














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















//Counting sort which takes negative numbers as well 


#include <iostream> 


#include <vector> 


#include <algorithm> 


using namespace std; 


  


void countSort(vector <int>& arr) 


{ 


    int max = *max_element(arr.begin(), arr.end()); 


    int min = *min_element(arr.begin(), arr.end()); 


    int range = max - min + 1; 


      


    vector<int> count(range), output(arr.size()); 


    for(int i = 0; i < arr.size(); i++) 


        count[arr[i]-min]++; 


          


    for(int i = 1; i < count.size(); i++) 


           count[i] += count[i-1]; 


    


    for(int i = arr.size()-1; i >= 0; i--) 


    {  


         output[ count[arr[i]-min] -1 ] = arr[i];  


              count[arr[i]-min]--;  


    } 


      


    for(int i=0; i < arr.size(); i++) 


            arr[i] = output[i]; 


} 


  


void printArray(vector <int> & arr)  


{  


    for (int i=0; i < arr.size(); i++)  


        cout << arr[i] << " ";  


    cout << "\n";  


} 


  


int main() 


{ 


    vector<int> arr = {-5, -10, 0, -3, 8, 5, -1, 10}; 


    countSort (arr); 


    printArray (arr); 


    return 0; 


} 



















                        chevron_right







                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// Counting sort which takes negative numbers as well  


import java.util.*; 


  


class GFG  


{ 


  


    static void countSort(int[] arr)  


    { 


        int max = Arrays.stream(arr).max().getAsInt(); 


        int min = Arrays.stream(arr).min().getAsInt(); 


        int range = max - min + 1; 


        int count[] = new int[range]; 


        int output[] = new int[arr.length]; 


        for (int i = 0; i < arr.length; i++)  


        { 


            count[arr[i] - min]++; 


        } 


  


        for (int i = 1; i < count.length; i++)  


        { 


            count[i] += count[i - 1]; 


        } 


  


        for (int i = arr.length - 1; i >= 0; i--)  


        { 


            output[count[arr[i] - min] - 1] = arr[i]; 


            count[arr[i] - min]--; 


        } 


  


        for (int i = 0; i < arr.length; i++) 


        { 


            arr[i] = output[i]; 


        } 


    } 


  


    static void printArray(int[] arr)  


    { 


        for (int i = 0; i < arr.length; i++)  


        { 


            System.out.print(arr[i] + " "); 


        } 


        System.out.println(""); 


    } 


  


    // Driver code 


    public static void main(String[] args) 


    { 


        int[] arr = {-5, -10, 0, -3, 8, 5, -1, 10}; 


        countSort(arr); 


        printArray(arr); 


    } 


}  


  


// This code is contributed by princiRaj1992 



















                        chevron_right







                        filter_none










Output:


-10 -5 -3 -1 0 5 8 10 


Points to be noted:

1. Counting sort is efficient if the range of input data is not significantly greater than the number of objects to be sorted.  Consider the situation where the input sequence is between range 1 to 10K and the data is 10, 5, 10K, 5K.

2. It is not a comparison based sorting. It running time complexity is O(n) with space proportional to the range of data.

3. It is often used as a sub-routine to another sorting algorithm like radix sort.

4. Counting sort uses a partial hashing to count the occurrence of the data object in O(1).

5. Counting sort can be extended to work for negative inputs also.


Exercise:

1. Modify above code to sort the input data in the range from M to N.

2. Is counting sort stable and online?

3. Thoughts on parallelizing the counting sort algorithm.


 




Snapshots:

scene00721

scene00865

scene01153

scene01297

scene01369

scene02521

scene02881


Quiz on Counting Sort


Coding Practice for Sorting


Other Sorting Algorithms on GeeksforGeeks/GeeksQuiz

Selection Sort, Bubble Sort, Insertion Sort, Merge Sort, Heap Sort, QuickSort, Radix Sort,  Counting Sort,  Bucket Sort,  ShellSort,  Comb Sort, PegionHole Sorting


This article is compiled by Aashish Barnwal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.


Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.





    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts: