Java Program for Pigeonhole Sort

Pigeonhole sorting is a sorting algorithm that is suitable for sorting lists of elements where the number of elements and the number of possible key values are approximately the same.
It requires O(n + Range) time where n is the number of elements in the input array and ‘Range’ is the number of possible values in the array.

Step-by-step approach:

• Find minimum and maximum values in the array. Let the minimum and maximum values be ‘min’ and ‘max’ respectively. Also, find the range as ‘max-min+1’.
• Set up an array of initially empty “pigeonholes” the same size as the range.
• Visit each element of the array and then put each element in its pigeonhole. An element arr[i] is put in the hole at index arr[i] – min.
• Start the loop all over the pigeonhole array in order and put the elements from non-empty holes back into the original array.

Comparison with Counting Sort : 
It is similar to counting sort, but differs in that it “moves items twice: once to the bucket array and again to the final destination “. 

Below is the implementation of the above approach:

/* Java program to implement Pigeonhole Sort */

import java.lang.*;
import java.util.*;

public class GFG {
    public static void pigeonhole_sort(int arr[], int n)
    {
        int min = arr[0];
        int max = arr[0];
        int range, i, j, index;

        for (int a = 0; a < n; a++) {
            if (arr[a] > max)
                max = arr[a];
            if (arr[a] < min)
                min = arr[a];
        }

        range = max - min + 1;
        int[] phole = new int[range];
        Arrays.fill(phole, 0);

        for (i = 0; i < n; i++)
            phole[arr[i] - min]++;

        index = 0;

        for (j = 0; j < range; j++)
            while (phole[j]-- > 0)
                arr[index++] = j + min;
    }

    public static void main(String[] args)
    {
        GFG sort = new GFG();
        int[] arr = { 8, 3, 2, 7, 4, 6, 8 };

        System.out.print("Sorted order is : ");

        sort.pigeonhole_sort(arr, arr.length);

        for (int i = 0; i < arr.length; i++)
            System.out.print(arr[i] + " ");
    }
}

// Code contributed by Mohit Gupta_OMG <(0_o)>

Sorted order is : 2 3 4 6 7 8 8 

Time complexity: O(n + range), where n is the number of elements in the array and range is the range of the input data.
Auxiliary space: O(range)

Advantages of Pigeonhole sort:

• It is a non-comparison based sort making it faster in application.
• It is a stable sorting algorithm.
• It performs sorting in linear time.

Disadvantages of Pigeonhole sort:

• It is not easy to know the range of the numbers to sort.
• This number might only work with zero and positive integers.
• Pigeonhole Sort

Please refer to the complete article on Pigeonhole Sort for more details!