Shell Sort
Shell Sort: Shell sort is a sorting algorithm. It is an extended version of the insertion sort.
- In this sorting, we compare the elements that are distant apart rather than the adjacent.
- We start by comparing elements that are at a certain distance apart. So, if there are N elements then we start with a value gap < N.
- In each iteration we keep decreasing the value of the gap until the difference becomes 1.
- In the last iteration, the shell sort acts as an insertion-type.
Complexity table of shell sort
| Complexity | Best case | Average case | Worst case |
| Time | O(n) | O((nlog(n))2) | O((nlog(n))2) |
| Space | O(1) |
Algorithm of shell sort
Shell_Sort (array, size) for interval i ? size /2 down to 1. for each interval "i" in the array. sort all the elements at interval "i". end Shell_Sort.
Shell sort example
Suppose you have the following array, which you have to sort.
| 14 | 18 | 19 | 37 | 23 | 40 | 29 | 30 | 11 |
The size of array is 9, so n = 9.
Now, find the value of the Gap.
Gap = floor(n / 2)
= floor (9 / 2)
= floor(4.5)
= 4
Pass = 1 Gap = 4
Gap 4 means, if we consider the first element at index 0 then next element will be at index 0+4 = 4., and third element will be at index 4 + 4 = 8.
Similarly, if we consider the element at index 1 then next element will be at index 1 + 4 = 5, and third element will be at index 5 + 4 = 9. But there is no 9th index in the above array so we will just have index 1 and 5.
Similarly, if we consider the element at index 2, 3, and 4 respectively then next element will be at index 2 + 4 = 6, 3 + 4 = 7, and 4 + 4 = 8 respectively.
Compare the elements.
A[0] > A[4] = 14 > 23 // false
A[1] > A[5] = 18 > 40 // false
A[2] > A[6] = 19 > 29 // false
A[3] > A[7] = 37 > 30 // true i.e., swap the both element positions.
A[4] > A[8] = 23 > 11 // true i.e., swap the both element positions.
A[1] > A[4] = 14 > 11 // true i.e., swap the both element positions.
Pass 1 is complete.
Pass 2: Gap = floor(Gap / 2)
Gap = floor(4 / 2) // in pass 1,
Gap was 4.
Gap = 2
Gap 2 means, if we consider the first element at index 0 then next element will be at index 0+2 = 2, and similarly this process applied till the end of index.
Compare the elements.
A[0] > A[2] = 11 > 19 // false
A[]1 > A[3] = 18 > 30 // false
A[2] > A[4] = 19 > 14 // true, i.e. swap the both element positions.
A[1] > A[2] = 11 > 14 // false
A[3] > A[5] = 30 > 40 //false
A[4] > A[6] = 19 > 29 // false
A[5] > A[7] = 40 > 37 // true, i.e. swap the both element positions.
A[3] > A[5] = 30 > 37 // false
A[6] > A[8] = 29 > 23 // true, i.e. swap the both element positions.
A[4] > A[6] = 19 > 23 // false
Pass 2 is complete.
Pass 3: Gap = floor(Gap/2)
Gap = floor(2 / 2) // in pass 2, Gap was 2.
Gap = 1 // i.e. last pass when gap is 1, shell sort is like the insertion sort. Compare the elements.
A[0] > A[1] = 11 > 18 // false
A[1] > A[2] = 18 > 14 // true i.e. swap the both element positions.
A[0] > A[1] = 11 > 14 // false
A[2] > A[3] = 18 > 30 // false A[3] > A[4] = 30 > 19 // true i.e. swap the both element positions. A[2] > A[3] = 18 > 19 // false
A[4] > A[5] = 30 > 37 // false A[5] > A[6] = 37 > 23 // true i.e. swap the both element positions. A[4] > A[5] = 30 > 23 // true i.e. swap the both element positions. A[3] > A[4] = 19 > 23 // false
A[6] > A[7] = 37 > 40 // false A[7] > A[8] = 40 > 29 // true i.e. swap the both element positions. A[6] > A[7] = 37 > 29 // true i.e. swap the both element positions. A[5] > A[6] = 30 > 29 // true i.e. swap the both element positions. A[4] > A[5] = 23 > 29 // false
Pass 3 is complete, and array is fully sorted.
Shell sort program in C language:
#include <stdio.h>
// Shell sort void shellSort(int array[], int n) {
// Rearrange elements at each n/2, n/4, n/8, ... intervals
for (int gap = n / 2; gap > 0; gap /= 2) {
for (int i = gap; i < n; i += 1) {
int temp = array[i];
int j;
for (j = i; j >= gap && array[j - gap] > temp; j -= gap) {
array[j] = array[j - gap];
}
array[j] = temp;
}
}
}
// Print an array
void printArray(int array[], int size) {
for (int i = 0; i < size; ++i) {
printf("%d ", array[i]);
}
printf("\n");
} // Driver code
int main()
{
int data[] = {9, 8, 3, 7, 5, 6, 4, 1};
int size = sizeof(data) / sizeof(data[0]);
shellSort(data, size);
printf("Sorted array: \n");
printArray(data, size);
}