ShellSort

Difficulty Level : Medium
Last Updated : 17 Aug, 2021

ShellSort is mainly a variation of Insertion Sort. In insertion sort, we move elements only one position ahead. When an element has to be moved far ahead, many movements are involved. The idea of shellSort is to allow exchange of far items. In shellSort, we make the array h-sorted for a large value of h. We keep reducing the value of h until it becomes 1. An array is said to be h-sorted if all sublists of every h’th element is sorted.

Following is the implementation of ShellSort.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

C++

// C++ implementation of Shell Sort
#include  <iostream>
using namespace std;
 
/* function to sort arr using shellSort */
int shellSort(int arr[], int n)
{
    // Start with a big gap, then reduce the gap
    for (int gap = n/2; gap > 0; gap /= 2)
    {
        // Do a gapped insertion sort for this gap size.
        // The first gap elements a[0..gap-1] are already in gapped order
        // keep adding one more element until the entire array is
        // gap sorted
        for (int i = gap; i < n; i += 1)
        {
            // add a[i] to the elements that have been gap sorted
            // save a[i] in temp and make a hole at position i
            int temp = arr[i];
 
            // shift earlier gap-sorted elements up until the correct
            // location for a[i] is found
            int j;           
            for (j = i; j >= gap && arr[j - gap] > temp; j -= gap)
                arr[j] = arr[j - gap];
             
            //  put temp (the original a[i]) in its correct location
            arr[j] = temp;
        }
    }
    return 0;
}
 
void printArray(int arr[], int n)
{
    for (int i=0; i<n; i++)
        cout << arr[i] << " ";
}
 
int main()
{
    int arr[] = {12, 34, 54, 2, 3}, i;
    int n = sizeof(arr)/sizeof(arr[0]);
 
    cout << "Array before sorting: \n";
    printArray(arr, n);
 
    shellSort(arr, n);
 
    cout << "\nArray after sorting: \n";
    printArray(arr, n);
 
    return 0;
}

Java

// Java implementation of ShellSort
class ShellSort
{
    /* An utility function to print array of size n*/
    static void printArray(int arr[])
    {
        int n = arr.length;
        for (int i=0; i<n; ++i)
            System.out.print(arr[i] + " ");
        System.out.println();
    }
 
    /* function to sort arr using shellSort */
    int sort(int arr[])
    {
        int n = arr.length;
 
        // Start with a big gap, then reduce the gap
        for (int gap = n/2; gap > 0; gap /= 2)
        {
            // Do a gapped insertion sort for this gap size.
            // The first gap elements a[0..gap-1] are already
            // in gapped order keep adding one more element
            // until the entire array is gap sorted
            for (int i = gap; i < n; i += 1)
            {
                // add a[i] to the elements that have been gap
                // sorted save a[i] in temp and make a hole at
                // position i
                int temp = arr[i];
 
                // shift earlier gap-sorted elements up until
                // the correct location for a[i] is found
                int j;
                for (j = i; j >= gap && arr[j - gap] > temp; j -= gap)
                    arr[j] = arr[j - gap];
 
                // put temp (the original a[i]) in its correct
                // location
                arr[j] = temp;
            }
        }
        return 0;
    }
 
    // Driver method
    public static void main(String args[])
    {
        int arr[] = {12, 34, 54, 2, 3};
        System.out.println("Array before sorting");
        printArray(arr);
 
        ShellSort ob = new ShellSort();
        ob.sort(arr);
 
        System.out.println("Array after sorting");
        printArray(arr);
    }
}
/*This code is contributed by Rajat Mishra */

Python3

# Python3 program for implementation of Shell Sort
 
def shellSort(arr):
    gap = len(arr) // 2 # initialize the gap
 
    while gap > 0:
        i = 0
        j = gap
         
        # check the array in from left to right
        # till the last possible index of j
        while j < len(arr):
     
            if arr[i] >arr[j]:
                arr[i],arr[j] = arr[j],arr[i]
             
            i += 1
            j += 1
         
            # now, we look back from ith index to the left
            # we swap the values which are not in the right order.
            k = i
            while k - gap > -1:
 
                if arr[k - gap] > arr[k]:
                    arr[k-gap],arr[k] = arr[k],arr[k-gap]
                k -= 1
 
        gap //= 2
 
 
# driver to check the code
arr2 = [12, 34, 54, 2, 3]
print("input array:",arr2)
 
shellSort(arr2)
print("sorted array",arr2)
 
# This code is contributed by Shubham Prashar (SirPrashar)

C#

// C# implementation of ShellSort
using System;
 
class ShellSort
{
    /* An utility function to
       print array of size n*/
    static void printArray(int []arr)
    {
        int n = arr.Length;
        for (int i=0; i<n; ++i)
        Console.Write(arr[i] + " ");
        Console.WriteLine();
    }
 
    /* function to sort arr using shellSort */
    int sort(int []arr)
    {
        int n = arr.Length;
 
        // Start with a big gap,
        // then reduce the gap
        for (int gap = n/2; gap > 0; gap /= 2)
        {
            // Do a gapped insertion sort for this gap size.
            // The first gap elements a[0..gap-1] are already
            // in gapped order keep adding one more element
            // until the entire array is gap sorted
            for (int i = gap; i < n; i += 1)
            {
                // add a[i] to the elements that have
                // been gap sorted save a[i] in temp and
                // make a hole at position i
                int temp = arr[i];
 
                // shift earlier gap-sorted elements up until
                // the correct location for a[i] is found
                int j;
                for (j = i; j >= gap && arr[j - gap] > temp; j -= gap)
                    arr[j] = arr[j - gap];
 
                // put temp (the original a[i])
                // in its correct location
                arr[j] = temp;
            }
        }
        return 0;
    }
 
    // Driver method
    public static void Main()
    {
        int []arr = {12, 34, 54, 2, 3};
        Console.Write("Array before sorting :\n");
        printArray(arr);
 
        ShellSort ob = new ShellSort();
        ob.sort(arr);
 
        Console.Write("Array after sorting :\n");
        printArray(arr);
    }
}
 
// This code is contributed by nitin mittal.

Javascript

<script>
// Javascript implementation of ShellSort
 
/* An utility function to print array of size n*/
function printArray(arr)
{
    let n = arr.length;
        for (let i = 0; i < n; ++i)
            document.write(arr[i] + " ");
        document.write("<br>");
}
 
/* function to sort arr using shellSort */
function sort(arr)
{
    let n = arr.length;
  
        // Start with a big gap, then reduce the gap
        for (let gap = Math.floor(n/2); gap > 0; gap = Math.floor(gap/2))
        {
         
            // Do a gapped insertion sort for this gap size.
            // The first gap elements a[0..gap-1] are already
            // in gapped order keep adding one more element
            // until the entire array is gap sorted
            for (let i = gap; i < n; i += 1)
            {
             
                // add a[i] to the elements that have been gap
                // sorted save a[i] in temp and make a hole at
                // position i
                let temp = arr[i];
  
                // shift earlier gap-sorted elements up until
                // the correct location for a[i] is found
                let j;
                for (j = i; j >= gap && arr[j - gap] > temp; j -= gap)
                    arr[j] = arr[j - gap];
  
                // put temp (the original a[i]) in its correct
                // location
                arr[j] = temp;
            }
        }
        return arr;
}
 
// Driver method
let arr = [12, 34, 54, 2, 3];
document.write("Array before sorting<br>");
printArray(arr);
 
arr = sort(arr);
document.write("Array after sorting<br>");
printArray(arr);
 
// This code is contributed by unknown2108
</script>

Output:

Array before sorting:
12 34 54 2 3
Array after sorting:
2 3 12 34 54

Time Complexity: Time complexity of above implementation of shellsort is O(n²). In the above implementation gap is reduce by half in every iteration. There are many other ways to reduce gap which lead to better time complexity. See this for more details.

References:
https://www.youtube.com/watch?v=pGhazjsFW28
http://en.wikipedia.org/wiki/Shellsort