# algorithm Cycle Sort

## Cycle Sort Basic Information

Cycle Sort is sorting algorithm which uses comparison sort that is theoretically optimal in terms of the total number of writes to original array, unlike any other in-place sorting algorithm. Cycle sort is unstable sorting algorithm. It is based on idea of permutation in which permutations are factored into cycles, which individually rotate and return a sorted output.

Example of Cycle Sort: Auxiliary Space: `O(1)`
Time Complexity: `O(n^2)`

## Pseudocode Implementation

``````(input)
output = 0
for cycleStart from 0 to length(array) - 2
item = array[cycleStart]
pos = cycleStart
for i from cycleStart + 1 to length(array) - 1
if array[i] < item:
pos += 1
if pos == cycleStart:
continue
while item == array[pos]:
pos += 1
array[pos], item = item, array[pos]
writes += 1
while pos != cycleStart:
pos = cycleStart
for i from cycleStart + 1 to length(array) - 1
if array[i] < item:
pos += 1
while item == array[pos]:
pos += 1
array[pos], item = item, array[pos]
writes += 1
return outout
``````

## C# Implementation

``````public class CycleSort
{
public static void SortCycle(int[] input)
{
for (var i = 0; i < input.Length; i++)
{
var item = input[i];
var position = i;
do
{
var k = input.Where((t, j) => position != j && t < item).Count();
if (position == k) continue;
while (position != k && item == input[k])
{
k++;
}
var temp = input[k];
input[k] = item;
item = temp;
position = k;
} while (position != i);
}
}

public static int[] Main(int[] input)
{
SortCycle(input);
return input;
}
}
``````