# Counting Sort

Counting Sort is an sorting algorithm, which sorts the integers( or Objects) given in a specific range.

Algorithm: Time Complexity O(n)

• Take two arrays, Count[] and Result[] and given array is input[].
• Count[] will store the counts of each integer in the given array.
• Update the Count[] so that each index will store the sum till previous step. (Count[i]=Count[i] + Count[i-1]). Now updated Count[] array will reflect the actual position of each integer in Result[].
• Now navigate the input array taking one element at a time, Count[input[i]] will tell you the index position of input[i] in Result[]. When you do that, decrease the count in Count[input[i]] by 1. See Example

Code:

 import java.util.Arrays; public class CountingSort { public int[] sort(int[] A) { int[] Result = new int[A.length + 1]; int[] Count = new int[A.length + 1]; for (int i = 0; i < Count.length; i++) { Count[i] = 0; // put count for every element as 0 } // Count[] will store the counts of each integer in the given array for (int i = 0; i < A.length; i++) { int x = Count[A[i]]; x++; Count[A[i]] = x; } // • Update the Count[] so that each index will store the sum till // previous step. (Count[i]=Count[i] + Count[i-1]). // Now updated Count[] array will reflect the actual position of each // integer in Result[]. for (int i = 1; i < Count.length; i++) { Count[i] = Count[i] + Count[i – 1]; } // • Now navigate the input array taking one element at a time, // Count[input[i]] will tell you the index position of input[i] in // Result[]. When you do that, decrease the count in Count[input[i]] by // 1. for (int i = A.length – 1; i >= 0; i—) { int x = Count[A[i]]; Result[x] = A[i]; x—; Count[A[i]] = x; } return Result; } public static void main(String[] args) { // TODO Auto-generated method stub int input[] = { 2, 1, 4, 5, 7, 1, 1, 8, 9, 10, 11, 14, 15, 3, 2, 4 }; System.out.println("Orginal Array " + Arrays.toString(input)); CountingSort c = new CountingSort(); int[] B = c.sort(input); System.out.println("Sorted Array : " + Arrays.toString(B)); } }

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CountingSort.java
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Output :

```Orginal Array [2, 1, 4, 5, 7, 1, 1, 8, 9, 10, 11, 14, 15, 3, 2, 4]
Sorted Array : [0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 9, 10, 11, 14, 15]
```