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)); | |

} | |

} |

**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]