Shell sort, also known as Shell sort or Shell's method, is an in-place comparison sort. It can be seen as either a generalization of sorting by exchange (bubble sort) or sorting by insertion (insertion sort).The method starts by sorting pairs of elements far apart from each other, then progressively reducing the gap between elements to be compared. Starting with far apart elements, it can move some out-of-place elements into position faster than a simple nearest neighbor exchange. The running time of Shell sort is heavily dependent on the gap sequence it uses. Pseudocode: # Sort an array a[0...n-1]. gaps = [701, 301, 132, 57, 23, 10, 4, 1] # Start with the largest gap and work down to a gap of 1 [[foreach]] (gap in gaps) { # 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 (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 temp = a[i] # shift earlier gap-sorted elements up until the correct location for a[i] is found for (j = i; j >= gap and a[j - gap] > temp; j -= gap) { a[j] = a[j - gap] } # put temp (the original a[i]) in its correct location a[j] = temp } } So,Shell Sort 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 sub-lists of every h’th element is sorted. Time Complexity: Time complexity of above implementation of shell-sort 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. Sample Code: /** * @author Abhinaw.Tripathi * */ public class ShellSortApp { 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) { for (int i = gap; i < n; i += 1) { int temp = arr[i]; int j; for (j = i; j >= gap && arr[j - gap] > temp; j -= gap) arr[j] = arr[j - gap]; arr[j] = temp; } } return 0; } public static void main(String[] args) { int arr[] = {12, 34, 54, 2, 3}; System.out.println("Array before sorting"); printArray(arr); ShellSortApp ob = new ShellSortApp(); ob.sort(arr); System.out.println("Array after sorting"); printArray(arr); } }
Result:
Array before sorting
12 34 54 2 3
Array after sorting
2 3 12 34 54