Cycle Sort – Python

Last Updated : 24 Feb, 2025

Cycle sort is an in-place, unstable sorting algorithm that is particularly useful when sorting arrays containing elements with a small range of values.

It is optimal in terms of several memory writes. It minimizes the number of memory writes to sort (Each value is either written zero times, if it’s already in its correct position or written one time to its correct position.)

It is based on the idea that the array to be sorted can be divided into cycles. Cycles can be visualized as a graph. We have n nodes and an edge directed from node i to node j if the element at i-th index must be present at j-th index in the sorted array.
Cycle in arr[] = {2, 4, 5, 1, 3}

Cycle in arr[] = {4, 3, 2, 1}

We one by one consider all cycles. We first consider the cycle that includes first element. We find correct position of first element, place it at its correct position, say j. We consider old value of arr[j] and find its correct position, we keep doing this till all elements of current cycle are placed at correct position, i.e., we don’t come back to cycle starting point.

def cycleSort(array):
    writes = 0

    # Loop through the array to find cycles to rotate.
    for cycleStart in range(0, len(array) - 1):
        item = array[cycleStart]

        # Find where to put the item.
        pos = cycleStart
        for i in range(cycleStart + 1, len(array)):
            if array[i] < item:
                pos += 1

        # If the item is already there, this is not a cycle.
        if pos == cycleStart:
            continue

        # Otherwise, put the item there or right after any duplicates.
        while item == array[pos]:
            pos += 1
        array[pos], item = item, array[pos]
        writes += 1

        # Rotate the rest of the cycle.
        while pos != cycleStart:

            # Find where to put the item.
            pos = cycleStart
            for i in range(cycleStart + 1, len(array)):
                if array[i] < item:
                    pos += 1

            # Put the item there or right after any duplicates.
            while item == array[pos]:
                pos += 1
            array[pos], item = item, array[pos]
            writes += 1

    return writes


# driver code
arr = [1, 8, 3, 9, 10, 10, 2, 4]
n = len(arr)
cycleSort(arr)

print("After sort : ")
for i in range(0, n):
    print(arr[i], end=' ')