# 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 number of elements in input array and ‘Range’ is number of possible values in array.

Working of Algorithm :

1. Find minimum and maximum values in array. Let the minimum and maximum values be ‘min’ and ‘max’ respectively. Also find range as ‘max-min-1’.
2. Set up an array of initially empty “pigeonholes” the same size as of the range.
3. Visit each element of the array and then put each element in its pigeonhole. An element arr[i] is put in hole at index arr[i] – min.
4. 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 “.

## C++

```/* C program to implement Pigeonhole Sort */
#include <bits/stdc++.h>
using namespace std;

/* Sorts the array using pigeonhole algorithm */
void pigeonholeSort(int arr[], int n)
{
// Find minimum and maximum values in arr[]
int min = arr[0], max = arr[0];
for (int i = 1; i < n; i++)
{
if (arr[i] < min)
min = arr[i];
if (arr[i] > max)
max = arr[i];
}
int range = max - min + 1; // Find range

// Create an array of vectors. Size of array
// range. Each vector represents a hole that
// is going to contain matching elements.
vector<int> holes[range];

// Traverse through input array and put every
// element in its respective hole
for (int i = 0; i < n; i++)
holes[arr[i]-min].push_back(arr[i]);

// Traverse through all holes one by one. For
// every hole, take its elements and put in
// array.
int index = 0;  // index in sorted array
for (int i = 0; i < range; i++)
{
vector<int>::iterator it;
for (it = holes[i].begin(); it != holes[i].end(); ++it)
arr[index++]  = *it;
}
}

// Driver program to test the above function
int main()
{
int arr[] = {8, 3, 2, 7, 4, 6, 8};
int n = sizeof(arr)/sizeof(arr[0]);

pigeonholeSort(arr, n);

printf("Sorted order is : ");
for (int i = 0; i < n; i++)
printf("%d ", arr[i]);

return 0;
}
```

## Java

```/* 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)>
```

## Python3

```# Python program to implement Pigeonhole Sort */

# source code : "https://en.wikibooks.org/wiki/
#   Algorithm_Implementation/Sorting/Pigeonhole_sort"
def pigeonhole_sort(a):
# size of range of values in the list
# (ie, number of pigeonholes we need)
my_min = min(a)
my_max = max(a)
size = my_max - my_min + 1

# our list of pigeonholes
holes = [0] * size

# Populate the pigeonholes.
for x in a:
assert type(x) is int, "integers only please"
holes[x - my_min] += 1

# Put the elements back into the array in order.
i = 0
for count in range(size):
while holes[count] > 0:
holes[count] -= 1
a[i] = count + my_min
i += 1

a = [8, 3, 2, 7, 4, 6, 8]
print("Sorted order is : ", end = ' ')

pigeonhole_sort(a)

for i in range(0, len(a)):
print(a[i], end = ' ')

```

Output:

`Sorted order is : 2 3 4 6 7 8 8 `

Pigeonhole sort has limited use as requirements are rarely met. For arrays where range is much larger than n, bucket sort is a generalization that is more efficient in space and time.

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,

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