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This sample code uses no temp variables, aka "extra space"

public class ArraySort
    {
        public static void Sort02(int[] array)
        {
            if (array == null || array.Length == 1)
                return;

            if (array.Length == 2)
            {
                Swap(array, 0, 1);
                return;
            }

            for (int left = -1, right = array.Length, index = right - 1; index > left && index > -1; index--)
            {
                if ((array.Length - index) % 2 == 1)
                {
                    // Updating the left side...
                    Swap(array, index, ++left);
                }
                else
                {
                    // Updating the right side..
                    Swap(array, index, --right);
                }
            }

            // At this point for even lengthed arrays, the majority of the Array 
            // should be sorted less its middle two elements.
            if (array.Length % 2 == 0)
                Swap(array, array.Length / 2, array.Length / 2 - 1);
        }

        private static void Swap(int[] array, int indexA, int indexB)
        {
            // TODO: validate input
            int temp = array[indexA];
            array[indexA] = array[indexB];
            array[indexB] = temp;
        }
    }

This sample code uses some temp variables, aka "extra space"

using static ArraySorting.LastUpdatedSide;

namespace ArraySorting
{
    public enum LastUpdatedSide { LeftSide = 0, RightSide = 1 };

    public class ArraySort
    {
        public static void Sort01(int[] array)
        {
            if (array == null || array.Length == 1)
                return;

            if (array.Length == 2)
            {
                Swap(array, 0, 1);
                return;
            }

            int left = -1;
            int right = array.Length;
            int index = right - 1;
            LastUpdatedSide lastUpdatedSide = RightSide;

            for (; index > left && index > -1; index--)
            {
                if (lastUpdatedSide == RightSide)
                {
                    // Updating the left side...
                    Swap(array, index, ++left);
                    lastUpdatedSide = LeftSide;
                }
                else
                {
                    // Updating the right side..
                    Swap(array, index, --right);
                    lastUpdatedSide = RightSide;
                }
            }

            // At this point for even lengthed arrays, the majority of the Array 
            // should be sorted less its middle two elements.
            if (array.Length % 2 == 0)
                Swap(array, --right, ++left);
        }
  
        private static void Swap(int[] array, int indexA, int indexB)
        {
            // TODO: validate input
            int temp = array[indexA];
            array[indexA] = array[indexB];
            array[indexB] = temp;
        }

    }
}