C++ Program for Gnome Sort

Algorithm Steps

1. If you are at the start of the array then go to the right element (from arr[0] to arr[1]).
2. If the current array element is larger or equal to the previous array element then go one step right

                   if (arr[i] >= arr[i-1])
                      i++;

1. If the current array element is smaller than the previous array element then swap these two elements and go one step backwards

                       if (arr[i] < arr[i-1])
                       {
                           swap(arr[i], arr[i-1]);
                           i--;
                       }

1. Repeat steps 2) and 3) till ‘i’ reaches the end of the array (i.e- ‘n-1’)
2. If the end of the array is reached then stop and the array is sorted.

CPP

// A C++ Program to implement Gnome Sort
#include <iostream>
using namespace std;

// A function to sort the algorithm using gnome sort
void gnomeSort(int arr[], int n)
{
 int index = 0;

 while (index < n) {
  if (index == 0)
   index++;
  if (arr[index] >= arr[index - 1])
   index++;
  else {
   swap(arr[index], arr[index - 1]);
   index--;
  }
 }
 return;
}

// A utility function ot print an array of size n
void printArray(int arr[], int n)
{
 cout << "Sorted sequence after Gnome sort: ";
 for (int i = 0; i < n; i++)
  cout << arr[i] << " ";
 cout << "\n";
}

// Driver program to test above functions.
int main()
{
 int arr[] = { 34, 2, 10, -9 };
 int n = sizeof(arr) / sizeof(arr[0]);

 gnomeSort(arr, n);
 printArray(arr, n);

 return (0);
}

Output:

Sorted sequence after Gnome sort: -9 2 10 34

Time Complexity: O(n²). As there is no nested loop (only one while) it may seem that this is a linear O(n) time algorithm. But the time complexity is O(n^2) as the variable ‘index’ in the program doesn’t always get incremented, it gets decremented too. 
Auxiliary Space: O(1)

Please refer complete article on Gnome Sort for more details!