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:
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 functionint 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;} |
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!
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