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# Counting Sort

• Difficulty Level : Easy
• Last Updated : 16 Mar, 2023

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 (a kind of hashing). Then do some arithmetic operations to calculate the position of each object in the output sequence.

## Characteristics of counting sort:

• Counting sort makes assumptions about the data, for example, it assumes that values are going to be in the range of 0 to 10 or 10 – 99, etc, Some other assumption counting sort makes is input data will be all real numbers.
• Like other algorithms this sorting algorithm is not a comparison-based algorithm, it hashes the value in a temporary count array and uses them for sorting.
• It uses a temporary array making it a non-In Place algorithm.
Recommended Practice

Example:

• For simplicity, consider the data in the range of 0 to 9.
• Input data: {1, 4, 1, 2, 7, 5, 2}
• Take a count array to store the count of each unique object.

Follow the below illustration for a better understanding of the counting sort algorithm

## Illustration:

• Now, store the count of each unique element in the count array
• If any element repeats itself, simply increase its count.

• Here, the count of each unique element in the count array is as shown below:
• Index:  0  1  2  3  4  5  6  7  8  9
• Count: 0  2  2  0   1  1  0  1  0  0

• 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.
• Find the index of each element of the original array in the count array. This gives the cumulative count.

• Rotate the array clockwise for one time.
• Index:  0 1 2 3 4 5 6 7 8 9
• Count: 0 0 2 4 4 5 6 6 7 7

•   Output each object from the input sequence followed by increasing its count by 1.
•   Process the input data: {1, 4, 1, 2, 7, 5, 2}. The position of 1 is 0.
•   Put data 1 at index 0 in output. Increase count by 1 to place next data 1 at an index 1 greater than this index.

• After placing each element in its correct position, decrease its count by one.

Below is the implementation of the above algorithm:

## C++

 `// C++ Program for counting sort` `#include ` `#include ` `using` `namespace` `std;` `#define RANGE 255`   `// The main function that sort` `// the given string arr[] in` `// alphabetical 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 individual` `    ``// 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"``;`   `    ``// Function call` `    ``countSort(arr);`   `    ``cout << ``"Sorted character array is "` `<< arr;` `    ``return` `0;` `}`   `// This code is contributed by rathbhupendra`

## C

 `// C Program for counting sort` `#include ` `#include ` `#define RANGE 255`   `// The main function that sort the given string arr[] in` `// alphabetical 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 individual` `    ``// 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"``; ``//"applepp";`   `    ``// Function call` `    ``countSort(arr);`   `    ``printf``(``"Sorted character array is %s"``, arr);` `    ``return` `0;` `}`

## Java

 `// Java implementation of Counting Sort`   `import` `java.io.*;`   `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 individual` `        ``// 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 code` `    ``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'` `};`   `        ``// Function call` `        ``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 */`

## Python3

 `# Python3 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``(``len``(arr))]`   `    ``# Create a count array to store count of individual` `    ``# 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 code` `if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `"geeksforgeeks"` `    ``ans ``=` `countSort(arr)` `    ``print``(``"Sorted character array is % s"` `%` `("".join(ans)))`   `# This code is contributed by Nikhil Kumar Singh`

## C#

 `// 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 individual 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 code` `    ``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.`

## PHP

 `= 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` `?>`

## Javascript

 `Javas` `cript`

Output

`Sorted character array is eeeefggkkorss`

Time Complexity: O(N + K) where N is the number of elements in the input array and K is the range of input.
Auxiliary Space: O(N + K)

## Counting Sort for an Array with negative elements:

To solve the problem follow the below idea:

The problem with the previous counting sort was that we could not sort the elements if we have negative numbers in them. Because there are no negative array indices.

So what we do is, find the minimum element and we will store the count of that minimum element at the zero index

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ` `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"``;` `}`   `// Driver code` `int` `main()` `{` `    ``vector<``int``> arr = { -5, -10, 0, -3, 8, 5, -1, 10 };`   `    ``// Function call` `    ``countSort(arr);` `    ``printArray(arr);` `    ``return` `0;` `}`

## Java

 `// Java program for the above approach` `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` `};`   `        ``// Function call` `        ``countSort(arr);` `        ``printArray(arr);` `    ``}` `}`   `// This code is contributed by princiRaj1992`

## Python3

 `# Python3 program for counting sort` `# which takes negative numbers as well`   `# The function that sorts the given arr[]`     `def` `count_sort(arr):` `    ``max_element ``=` `int``(``max``(arr))` `    ``min_element ``=` `int``(``min``(arr))` `    ``range_of_elements ``=` `max_element ``-` `min_element ``+` `1` `    ``# Create a count array to store count of individual` `    ``# elements and initialize count array as 0` `    ``count_arr ``=` `[``0` `for` `_ ``in` `range``(range_of_elements)]` `    ``output_arr ``=` `[``0` `for` `_ ``in` `range``(``len``(arr))]`   `    ``# Store count of each character` `    ``for` `i ``in` `range``(``0``, ``len``(arr)):` `        ``count_arr[arr[i]``-``min_element] ``+``=` `1`   `    ``# Change count_arr[i] so that count_arr[i] now contains actual` `    ``# position of this element in output array` `    ``for` `i ``in` `range``(``1``, ``len``(count_arr)):` `        ``count_arr[i] ``+``=` `count_arr[i``-``1``]`   `    ``# Build the output character array` `    ``for` `i ``in` `range``(``len``(arr)``-``1``, ``-``1``, ``-``1``):` `        ``output_arr[count_arr[arr[i] ``-` `min_element] ``-` `1``] ``=` `arr[i]` `        ``count_arr[arr[i] ``-` `min_element] ``-``=` `1`   `    ``# Copy the output array to arr, so that arr now` `    ``# contains sorted characters` `    ``for` `i ``in` `range``(``0``, ``len``(arr)):` `        ``arr[i] ``=` `output_arr[i]`   `    ``return` `arr`     `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``-``5``, ``-``10``, ``0``, ``-``3``, ``8``, ``5``, ``-``1``, ``10``]` `    ``ans ``=` `count_sort(arr)` `    ``print``(``str``(ans))`

## C#

 `// C# program for the above approach` `using` `System;` `using` `System.Collections.Generic;` `using` `System.Linq;` `class` `GFG {` `    ``static` `void` `countSort(``int``[] arr)` `    ``{` `        ``int` `max = arr.Max();` `        ``int` `min = arr.Min();` `        ``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++) {` `            ``Console.Write(arr[i] + ``" "``);` `        ``}` `        ``Console.WriteLine(``""``);` `    ``}`   `    ``// 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 rutvik_56.`

## Javascript

 ``

Output

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

Time complexity: O(N), where N is the total number of elements
Auxiliary Space: O(N)

## Another Approach for counting sort for positive numbers

In this approach, we are going to do the same thing as explained above but we will be implementing using the map data structure of C++.

## C++

 `#include ` `using` `namespace` `std;`   `vector<``int``> countingSort(vector<``int``> vec, ``int` `n)` `{` `    ``for` `(``int` `i = 0; i> vec[i], i++)` `        ``;` `    ``map<``int``, ``int``> count;` `    ``// Here we are initializing every element of count to 0` `    ``// from 1 to n` `    ``for` `(``int` `i = 0; i < n; count[i] = 0, i++)` `        ``;` `    ``// Here we are storing count of every element` `    ``for` `(``int` `i = 0; i < n; count[vec[i]]++, i++)` `        ``;` `    ``vector<``int``> sortedArr;` `    ``int` `i = 0;` `    ``while` `(n > 0) {` `        ``// Here we are checking if the count[element] = 0` `        ``// then incrementing for the next Element` `        ``if` `(count[i] == 0) {` `            ``i++;` `        ``}` `        ``// Here we are inserting the element into the` `        ``// sortedArr decrementing count[element] and n by 1` `        ``else` `{` `            ``sortedArr.push_back(i);` `            ``count[i]--;` `            ``--n;` `        ``}` `    ``}` `    ``return` `sortedArr;` `}`   `void` `printArr(vector<``int``> vec, ``int` `n)` `{` `    ``cout << ``"Sorted Array: "``;` `    ``for` `(``int` `i = 0; i < n; cout << vec[i] << ``" "``, i++)` `        ``;` `    ``cout << endl;` `}` `signed` `main()` `{` `    ``vector<``int``> vec1 = { 6, 0, 7, 8, 7, 2, 0 };` `    ``vector<``int``> sortedArr1` `        ``= countingSort(vec1, vec1.size());` `    ``printArr(sortedArr1, sortedArr1.size());`   `    ``vector<``int``> vec2 = { 4, 8, 1, 0, 1, 1, 0, 0 };` `    ``vector<``int``> sortedArr2` `        ``= countingSort(vec2, vec2.size());` `    ``printArr(sortedArr2, sortedArr2.size());`   `    ``return` `0;` `}`

## Java

 `// Java code to implement the approach` `import` `java.io.*;` `import` `java.util.*;` `import` `java.util.HashMap;`   `class` `GFG {`   `static` `ArrayList countingSort(ArrayList vec, Integer n)` `{` `    ``HashMap count = ``new` `HashMap<>();`   `    ``// Here we are initializing every element of count to 0` `    ``// from 1 to n` `    ``Integer i;` `    ``for` `(i = ``0``; i < n; i++)` `    ``count.put(i,``0``);`   `    ``// Here we are storing count of every element` `    ``for` `(i = ``0``; i < n; i++)` `    ``{` `    ``if``(count.containsKey(vec.get(i)))` `        ``count.put(vec.get(i),count.get(vec.get(i))+``1``);` `    ``else` `        ``count.put(vec.get(i),``1``);` `    ``}` `    ``ArrayList sortedArr=``new` `ArrayList();` `    ``i = ``0``;` `    ``while` `(n > ``0``)` `    ``{`   `    ``// Here we are checking if the count[element] = 0` `    ``// then incrementing for the next Element` `    ``if` `(count.get(i) == ``0``) {` `        ``i++;` `    ``}`   `    ``// Here we are inserting the element Integero the` `    ``// sortedArr decrementing count[element] and n by 1` `    ``else` `{` `        ``sortedArr.add(i);` `        ``count.put(i,count.get(i)-``1``);` `        ``n--;` `    ``}` `    ``}` `    ``return` `sortedArr;` `}`   `static` `void` `printArr(ArrayList vec, Integer n)` `{` `    ``System.out.print(``"Sorted Array: "``);` `    ``for` `(Integer i = ``0``; i < n; i++)` `    ``System.out.print(vec.get(i) + ``" "``);` `    ``System.out.print(``"\n"``);` `}` `public` `static` `void` `main (String[] args)` `{` `    ``ArrayList vec1 = ``new` `ArrayList(Arrays.asList( ``6``, ``0``, ``7``, ``8``, ``7``, ``2``, ``0` `));` `    ``ArrayList sortedArr1 = countingSort(vec1, vec1.size());` `    ``printArr(sortedArr1, sortedArr1.size());`   `    ``ArrayList vec2 = ``new` `ArrayList(Arrays.asList( ``4``, ``8``, ``1``, ``0``, ``1``, ``1``, ``0``, ``0`  `));` `    ``ArrayList sortedArr2 = countingSort(vec2, vec2.size());` `    ``printArr(sortedArr2, sortedArr2.size());` `}` `}`   `// This code was contributed by Pushpesh Raj.`

## Python3

 `def` `countingSort(vec, n):` `    ``#for (int i = 0; i> vec[i], i++)` `    ``count``=``dict``();` `    `  `    ``# Here we are initializing every element of count to 0` `    ``# from 1 to n` `    ``for` `i ``in` `range``(``0``,n):` `        ``count[i] ``=` `0``;` `        `  `    ``# Here we are storing count of every element` `    ``for` `i ``in` `range``(``0``,n):` `        ``if` `vec[i] ``in` `count.keys():` `            ``count[vec[i]] ``+``=` `1``;` `        ``else``:` `            ``count[vec[i]] ``=` `1``;`   `        `  `    ``sortedArr ``=` `[];` `    ``i ``=` `0``;` `    ``while` `(n > ``0``):` `        ``# Here we are checking if the count[element] = 0` `        ``# then incrementing for the next Element` `        ``if` `(count[i] ``=``=` `0``) :` `            ``i ``+``=` `1``;` `        `  `        ``# Here we are inserting the element into the` `        ``# sortedArr decrementing count[element] and n by 1` `        ``else``:` `            ``sortedArr.append(i);` `            ``count[i] ``-``=` `1``;` `            ``n ``=` `n ``-` `1``;` `        `  `    ``return` `sortedArr;`     `def` `printArr(vec, n):` `    ``print``(``"Sorted Array: "``);` `    ``for` `i ``in` `range``(``0``,n):` `        ``print``(vec[i], ``" "``);`   `vec1 ``=` `[ ``6``, ``0``, ``7``, ``8``, ``7``, ``2``, ``0` `];` `sortedArr1 ``=` `countingSort(vec1, ``len``(vec1));` `printArr(sortedArr1, ``len``(sortedArr1));`   `vec2 ``=` `[ ``4``, ``8``, ``1``, ``0``, ``1``, ``1``, ``0``, ``0` `];` `sortedArr2 ``=` `countingSort(vec2, ``len``(vec2));` `printArr(sortedArr2, ``len``(sortedArr2));`   `# This code is contributed by ritaagarwal.`

## C#

 `// C# code to implement the approach` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG {`   `  ``static` `List<``int``> countingSort(List<``int``> vec, ``int` `n)` `  ``{` `    ``Dictionary<``int``, ``int``> count=``new` `Dictionary<``int``,``int``>();`   `    ``// Here we are initializing every element of count to 0` `    ``// from 1 to n` `    ``int` `i;` `    ``for` `(i = 0; i < n; i++)` `      ``count.Add(i,0);`   `    ``// Here we are storing count of every element` `    ``for` `(i = 0; i < n; i++)` `    ``{` `      ``if``(count.ContainsKey(vec[i]))` `        ``count[vec[i]]++;` `      ``else` `        ``count[vec[i]]=1;` `    ``}` `    ``List<``int``> sortedArr=``new` `List<``int``>();` `    ``i = 0;` `    ``while` `(n > 0)` `    ``{`   `      ``// Here we are checking if the count[element] = 0` `      ``// then incrementing for the next Element` `      ``if` `(count[i] == 0) {` `        ``i++;` `      ``}`   `      ``// Here we are inserting the element into the` `      ``// sortedArr decrementing count[element] and n by 1` `      ``else` `{` `        ``sortedArr.Add(i);` `        ``count[i]--;` `        ``n--;` `      ``}` `    ``}` `    ``return` `sortedArr;` `  ``}`   `  ``static` `void` `printArr(List<``int``> vec, ``int` `n)` `  ``{` `    ``Console.Write(``"Sorted Array: "``);` `    ``for` `(``int` `i = 0; i < n; i++)` `      ``Console.Write(vec[i] + ``" "``);` `    ``Console.Write(``"\n"``);` `  ``}` `  ``public` `static` `void` `Main()` `  ``{` `    ``List<``int``> vec1 = ``new` `List<``int``>{ 6, 0, 7, 8, 7, 2, 0 };` `    ``List<``int``> sortedArr1 = countingSort(vec1, vec1.Count);` `    ``printArr(sortedArr1, sortedArr1.Count);`   `    ``List<``int``> vec2 = ``new` `List<``int``>{ 4, 8, 1, 0, 1, 1, 0, 0 };` `    ``List<``int``> sortedArr2 = countingSort(vec2, vec2.Count);` `    ``printArr(sortedArr2, sortedArr2.Count);` `  ``}` `}`   `// This code was contributed by poojaagrawal2.`

## Javascript

 `const countingSort = (vec, n) => {`   `  ``// map to store the count of each element` `  ``const count = {};` `  `  `  ``// initialize every element of count to 0 from 0 to n-1` `  ``for` `(let i = 0; i < n; count[i] = 0, i++);` `  `  `  ``// store count of every element` `  ``for` `(let i = 0; i < n; count[vec[i]]++, i++);` `  ``const sortedArr = [];` `  ``let i = 0;` `  ``while` `(n > 0) ` `  ``{` `  `  `    ``// if the count of the element is 0, then increment i` `    ``// and move to the next element` `    ``if` `(count[i] === 0) {` `      ``i++;` `    ``}` `    `  `    ``// else, insert the element into the sorted array,` `    ``// decrement count[element] and n by 1` `    ``else` `{` `      ``sortedArr.push(i);` `      ``count[i]--;` `      ``n--;` `    ``}` `  ``}` `  ``return` `sortedArr;` `};`   `const printArr = (vec, n) => {` `  ``console.log(``"Sorted Array: "``);` `  ``for` `(let i = 0; i < n; console.log(vec[i] + ``" "``), i++);` `  ``console.log(``"\n"``);` `};`   `const vec1 = [6, 0, 7, 8, 7, 2, 0];` `const sortedArr1 = countingSort(vec1, vec1.length);` `printArr(sortedArr1, sortedArr1.length);`   `const vec2 = [4, 8, 1, 0, 1, 1, 0, 0];` `const sortedArr2 = countingSort(vec2, vec2.length);` `printArr(sortedArr2, sortedArr2.length);`   `// This code is contributed by ishankhandelwals.`

Output

```Sorted Array: 0 0 2 6 7 7 8
Sorted Array: 0 0 0 1 1 1 4 8 ```

Time complexity: O(N), where N is the total number of elements
Auxiliary Space: O(N)

## Important points:

• 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 the range 1 to 10K and the data is 10, 5, 10K, 5K.
• It is not a comparison-based sorting. Its running time complexity is O(n) with space proportional to the range of data.
• Counting sorting is able to achieve this because we are making assumptions about the data we are sorting.
• It is often used as a sub-routine to another sorting algorithm like the radix sort.
• Counting sort uses partial hashing to count the occurrence of the data object in O(1).
• The counting sort can be extended to work for negative inputs also.
• Counting sort is  a stable algorithm. But it can be made stable with some code changes.

## Exercise:

• Modify the above code to sort the input data in the range from M to N.
• Modify the code to make the counting sort stable.
• Thoughts on parallelizing the counting sort algorithm.

#### Related Articles:

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, PigeonHole Sorting

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

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