# C++ Program for Cycle Sort?

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Cycle sort is an in-place, unstable sorting algorithm, a comparison sort that is theoretically optimal in terms of the total number of writes to the original array, unlike any other in-place sorting algorithm. It is based on the idea that the permutation to be sorted can be factored into cycles, which can individually be rotated to give a sorted result.

Unlike nearly every other sort, items are never written elsewhere in the array simply to push them out of the way of the action. Each value is either written zero times, if it's already in its correct position or written one time to its correct position. This matches the minimal number of overwrites required for a completed in-place sort.

Minimizing the number of writes is useful when making writes to some huge data set is very expensive, such as with EEPROMs like Flash memory where each write reduces the lifespan of the memory.

Input: a[]={7,4,3,5,2,1,6}
Output: 1 2 3 4 5 6 7

## Explanation

arr[] = {10, 5, 2, 3}
index = 0 1 2 3
cycle_start = 0
item = 10 = arr
Find position where we put the item,
pos = cycle_start
while (arr[i] < item)
pos++;
We put 10 at arr and change item to
old value of arr.
arr[] = {10, 5, 2, 10}
item = 3
Again rotate rest cycle that start with index '0'
Find position where we put the item = 3
we swap item with element at arr now
arr[] = {10, 3, 2, 10}
item = 5
Again rotate rest cycle that start with index '0' and item = 5
we swap item with element at arr.
arr[] = {10, 3, 5, 10 }
item = 2
Again rotate rest cycle that start with index '0' and item = 2
arr[] = {2, 3, 5, 10}
Above is one iteration for cycle_stat = 0.
Repeat above steps for cycle_start = 1, 2, ..n-2

## Example

#include<iostream>
using namespace std;
void cycleSort(int a[], int n) {
int writes = 0;
for (int c_start = 0; c_start <= n - 2; c_start++) {
int item = a[c_start];
int pos = c_start;
for (int i = c_start + 1; i < n; i++)
if (a[i] < item)
pos++;
if (pos == c_start)
continue;
while (item == a[pos])
pos += 1;
if (pos != c_start) {
swap(item, a[pos]);
writes++;
}
while (pos != c_start) {
pos = c_start;
for (int i = c_start + 1; i < n; i++)
if (a[i] < item)
pos += 1;
while (item == a[pos])
pos += 1;
if (item != a[pos]) {
swap(item, a[pos]);
writes++;
}
}
}
}
int main() {
int a[] ={7,4,3,5,2,1,6};
int n = 7;
cycleSort(a, n);
for (int i = 0; i < n; i++)
cout << a[i] << " ";
return 0;
}