Circle Sort algorithm

Circle Sort

Circle sort algorithm can be visualized by drawing concentric circles on an array of integers. The elements of the array lying on the same circle diametrically opposite to each other are compared and if found in the wrong order they are swapped. This goes on in a recursive fashion in which the array is divided into sub-arrays on which the above process is repeated until we get pairs of sorted elements which when put together form a sorted array.

In short below two steps are repeated while there are swap operations involved in the steps.

• Compare the first element to the last element, then the second element to the second last element, etc.
• Then split the array in two and recurse until there is only one single element in the array.

It can be better explained by the image below.

• C++

// CPP implementation of Circle Sort #include<bits/stdc++.h> using namespace std;   // Function to perform circular swaps recursively // This function returns true if there was a swap // operation performed. bool circleSortRec(int a[], int low, int high) {     bool swapped = false;       // base case     if (low == high)         return false;       // storing the upper and lower bounds     // of list to be used later in the     // recursive case     int lo = low, hi = high;       while (lo < hi)     {         // swaps the pair of elements         // if true         if (a[lo] > a[hi])         {             swap(a[lo], a[hi]);             swapped = true;         }         lo++;         hi--;     }       // special case arises only for list     // of odd size     if (lo == hi)         if (a[lo] > a[hi + 1])         {             swap(a[low], a[hi+1]);             swapped = true;         }       // recursive case to check the     // traverse lists as sub lists     int mid = (high - low) / 2;     bool firstHalf = circleSortRec(a, low, low+mid);     bool secondHalf = circleSortRec(a, low+mid+1, high);       return swapped || firstHalf || secondHalf; }   // This function mainly calls circleSortRec void circleSort(int a[], int n) {     // Keep calling circleSortRec while     // there is a swap operation.     while (circleSortRec(a, 0, n-1))     {        ;     } }   // Driver program int main() {     int a[] = {7, 5, 3, 1, 2, 4, 6, 8};     int n = sizeof(a)/sizeof(a[0]);       printf("\nUnsorted : ");     for (int i=0; i<n; i++)         cout << a[i] << " ";       circleSort(a, n);       printf("\nSorted : ");     for (int i=0; i<n; i++)         cout << a[i] << " ";       return 0; }

Output :

Unsorted :  [6, 5, 3, 1, 8, 7, 2, 4]
Sorted :  [1, 2, 3, 4, 5, 6, 7, 8]