Shell Sort

The shell sorting technique is based on the insertion sort. In the insertion sort sometimes we need to shift large block to insert an item in the correct location. Using shell sort, we can avoid a large number of shifting. The sorting is done with a specific interval. After each pass, the interval is reduced to make the smaller interval.

The complexity of the Shell Sort Technique

• Time Complexity: O(n log n) for best case, and for other cases, it depends on the gap sequence.
• Space Complexity: O(1)

Input and Output

Input:
The unsorted list: 23 56 97 21 35 689 854 12 47 66
Output:
Array before Sorting: 23 56 97 21 35 689 854 12 47 66
Array after Sorting: 12 21 23 35 47 56 66 97 689 854

Algorithm

shellSort(array, size)

Input − An array of data, and the total number in the array

Output − The sorted Array

Begin
   for gap := size / 2, when gap > 0 and gap is updated with gap / 2 do
      for j:= gap to size– 1 do
         for k := j-gap to 0, decrease by gap value do
            if array[k+gap] >= array[k]
               break
            else
               swap array[k + gap] with array[k]
         done
      done
   done
End

Example

#include<iostream>
using namespace std;

void swapping(int &a, int &b) { //swap the content of a and b
   int temp;
   temp = a;
   a = b;
   b = temp;
}

void display(int *array, int size) {
   for(int i = 0; i<size; i++)
      cout << array[i] << " ";
   cout << endl;
}

void shellSort(int *arr, int n) {
   int gap, j, k;
   for(gap = n/2; gap > 0; gap = gap / 2) {      //initially gap = n/2, decreasing by gap /2
      for(j = gap; j<n; j++) {
         for(k = j-gap; k>=0; k -= gap) {
            if(arr[k+gap] >= arr[k])
               break;
            else
               swapping(arr[k+gap], arr[k]);
         }
      }
   }
}

int main() {
   int n;
   cout << "Enter the number of elements: ";
   cin >> n;
   int arr[n]; //create an array with given number of elements
   cout << "Enter elements:" << endl;

   for(int i = 0; i<n; i++) {
      cin >> arr[i];
   }

   cout << "Array before Sorting: ";
   display(arr, n);
   shellSort(arr, n);
   cout << "Array after Sorting: ";
   display(arr, n);
}

Output

Enter the number of elements: 10
Enter elements:
23 56 97 21 35 689 854 12 47 66
Array before Sorting: 23 56 97 21 35 689 854 12 47 66
Array after Sorting: 12 21 23 35 47 56 66 97 689 854