Shell Sort
Shell sort works by comparing elements that are distant rather than adjacent elements in an array or list where adjacent elements are compared. Shellsort uses an increment sequence. The increment size is reduced after each pass until the increment size is 1. With an increment size of 1, the sort is a basic insertion sort, but by this time the data is guaranteed to be almost sorted, which is insertion sort's "best case". The distance between comparisons decreases as the sorting algorithm runs until the last phase in which adjacent elements are compared hence, it is also known as diminishing increment sort.
Algorithm:
1. n = length of the list, increment = n/2
2. Do the following until increment>0 i = increment until i<n do the following
Store the value at index i in a temporary variable(temp)
j = i until j>= increment do the following
• If temp is less than the value at index jincrement
Replace the value at index j with the value at index jincrement and
decrease j by increment.
• Else break out of the j loop.
Replace the value at index j with temp and increase i by 1.
Divide increment by 2.
Property:
1. BestCase Complexity O(n) when array is already sorted.
2. WorstCase ComplexityIt depends on gap sequence; best known is O( n (log n)2 ) and
occurs when array is sorted in reverse order.
3. AverageCase Complexity It also depends on gap sequence.
4. O(1) extra space and it is not stable.
5. It’s only efficient for medium size lists. it is a complex algorithm and it’s not nearly as
efficient as the merge, heap, and quick sorts.
Shell Sort  C Program Source Code
#include<stdio.h>
void ShellSort(int *array, int number_of_elements)
{
int iter, jter, increment, temp;
for(increment = number_of_elements/2;increment > 0; increment /= 2)
{
for(i = increment; i<number_of_elements; i++)
{
temp = array[i];
for(j = i; j >= increment ;j=increment)
{
if(temp < array[jincrement])
{
array[j] = array[jincrement];
}
else
{
break;
}
}
array[j] = temp;
}
}
}
int main()
{
int number_of_elements;
scanf("%d",&number_of_elements);
int array[number_of_elements];
int iter;
for(iter = 0;iter < number_of_elements;iter++)
{
scanf("%d",&array[iter]);
}
/* Calling this functions sorts the array */
ShellSort(array,number_of_elements);
for(iter = 0;iter < number_of_elements;iter++)
{
printf("%d ",array[iter]);
}
printf("\n");
return 0;
}
Shell Sort  Java Program Source Code
import java.io.*;
class ShellSort
{
void ShellSort(int array[], int number_of_elements)
{
int iter, jter, increment, temp,i,j;
for(increment = number_of_elements/2;increment > 0; increment /= 2)
{
for(i = increment; i<number_of_elements; i++)
{
temp = array[i];
for(j = i; j >= increment ;j=increment)
{
if(temp < array[jincrement])
{
array[j] = array[jincrement];
}
else
{
break;
}
}
array[j] = temp;
}
}
}
int main()throws IOException
{
BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
int number_of_elements;
System.out.println("Enter the number of elements");
number_of_elements=Integer.parseInt(in.readLine());
int array[]=new int[number_of_elements];
int iter;
System.out.println("Enter the elements one by one");
for(iter = 0;iter < number_of_elements;iter++)
{
array[iter]=Integer.parseInt(in.readLine());;
}
/* Calling this functions sorts the array */
ShellSort(array,number_of_elements);
for(iter = 0;iter < number_of_elements;iter++)
{
System.out.print(array[iter]+"\t");
}
System.out.print("\n");
return 0;
}
}
Related Tutorials :
Bubble Sort
 One
of the most elementary sorting algorithms to implement  and also very
inefficient. Runs in quadratic time. A good starting point to understand
sorting in general, before moving on to more advanced techniques and
algorithms. A general idea of how the algorithm works and a the code for
a C program.

Insertion Sort

Another quadratic time sorting algorithm  an example
of dynamic programming. An explanation and step through of how the
algorithm works, as well as the source code for a C program which
performs insertion sort.

Selection Sort

Another quadratic time sorting algorithm  an example
of a greedy algorithm. An explanation and step through of how the
algorithm works, as well as the source code for a C program which
performs selection sort.

Shell Sort

An inefficient but interesting algorithm, the complexity of which is not exactly known.

Merge Sort

An example of a Divide and Conquer algorithm. Works in
O(n log n) time. The memory complexity for this is a bit of a
disadvantage.

Quick Sort

In the average case, this works in O(n log n) time. No
additional memory overhead  so this is better than merge sort in this
regard. A partition element is selected, the array is restructured such
that all elements greater or less than the partition are on opposite
sides of the partition. These two parts of the array are then sorted
recursively.

Heap Sort

Efficient sorting algorithm which runs in O(n log n) time. Uses the Heap data structure.

Binary Search Algorithm

Commonly used algorithm used to find the position of an element in a sorted array. Runs in O(log n) time.

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