CycleSorter.cs

using System.Collections.Generic;

namespace Algorithms.Sorters.Comparison
{
    /// <summary>
    /// 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.
    /// 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.
    /// </summary>
    /// <typeparam name="T">Type array input.</typeparam>
    public class CycleSorter<T> : IComparisonSorter<T>
    {
        /// <summary>
        /// Sorts input array using Cycle sort.
        /// </summary>
        /// <param name="array">Input array.</param>
        /// <param name="comparer">Integer comparer.</param>
        public void Sort(T[] array, IComparer<T> comparer)
        {
            for (var i = 0; i < array.Length - 1; i++)
            {
                MoveCycle(array, i, comparer);
            }
        }

        private static void MoveCycle(T[] array, int startingIndex, IComparer<T> comparer)
        {
            var item = array[startingIndex];
            var pos = startingIndex + CountSmallerElements(array, startingIndex + 1, item, comparer);

            if (pos == startingIndex)
            {
                return;
            }

            pos = SkipSameElements(array, pos, item, comparer);

            var temp = array[pos];
            array[pos] = item;
            item = temp;

            while (pos != startingIndex)
            {
                pos = startingIndex + CountSmallerElements(array, startingIndex + 1, item, comparer);
                pos = SkipSameElements(array, pos, item, comparer);

                temp = array[pos];
                array[pos] = item;
                item = temp;
            }
        }

        private static int SkipSameElements(T[] array, int nextIndex, T item, IComparer<T> comparer)
        {
            while (comparer.Compare(array[nextIndex], item) == 0)
            {
                nextIndex++;
            }

            return nextIndex;
        }

        private static int CountSmallerElements(T[] array, int startingIndex, T element, IComparer<T> comparer)
        {
            var smallerElements = 0;
            for (var i = startingIndex; i < array.Length; i++)
            {
                if (comparer.Compare(array[i], element) < 0)
                {
                    smallerElements++;
                }
            }

            return smallerElements;
        }
    }
}