# C++ 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 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.

 `/* C program to implement Pigeonhole Sort */` `#include ` `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; ` `} `

Output:

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

Please refer complete article on Pigeonhole Sort for more details!

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