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C++ Program to Implement Sorting of Less than 100 Numbers in O(n) Complexity
To sort some small numbers in linear time we can use the counting sort technique.
Counting sort is a stable sorting technique, which is used to sort objects according the keys that are small numbers. It counts the number of keys whose key values are same. This sorting technique is efficient when difference between different keys are not so big, otherwise it can increase the space complexity.
The complexity of counting Sort Technique
Time Complexity: O(n + r)
Space Complexity: O(n + r)
Input − A list of unsorted data: 2 5 6 2 3 10 3 6 7 8 Output − Array after Sorting: 2 2 3 3 5 6 6 7 8 10
Algorithm
countingSort(array, size)
Input − An array of data, and the total number in the array
Output − The sorted Array
Begin max = get maximum element from array. define count array of size [max+1] for i := 0 to max do count[i] = 0 //set all elements in the count array to 0 done for i := 1 to size do increase count of each number which have found in the array done for i := 1 to max do count[i] = count[i] + count[i + 1] //find cumulative frequency done for i := size to 1 decrease by 1 do store the number in the output array decrease count[i] done return the output array End
Example Code
#include <iostream>
using namespace std;
void counting_sort(int array[], int n) {
int i, j;
int count[n];
for (i = 0; i < n; i++)
count[i] = 0;
for (i = 0; i < n; i++)
(count[array[i]])++;
for (i = 0, j = 0; i < n; i++)
for (; count[i] > 0; (count[i])--)
array[j++] = i;
}
int main() {
int array[100], i, num;
cout << "Enter the size of array : ";
cin >> num;
cout << "Enter the " << num << " elements to be sorted:" << endl;
for (i = 0; i < num; i++)
cin >> array[i];
cout << "\nThe array of elements before sorting : " <<endl;
for (i = 0; i < num; i++)
cout << array[i] << " ";
cout << "\nThe array of elements after sorting : " << endl;
counting_sort(array, num);
for (i = 0; i < num; i++)
cout << array[i] << " ";
return 0;
}Output
Enter the size of array : 8 Enter the 8 elements to be sorted: 54 89 23 20 18 88 65 31 The array of elements before sorting : 54 89 23 20 18 88 65 31 The array of elements after sorting : 54 89 23 20 18 88 65 31
Updated on: 30-Jul-2019
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