Algorithms:HeapSort

HeapSort is an sort algorithms, using heap tree(Full Binary Tree) for help.

Implementing this sort should execute three steps

1. Adjust an entire array to a heap tree(big heap tree for ascending, small heap tree for descending sort)

2. Get the root of the heap tree arr[0] and swap it with last one of the no-sort array, that will consider as the item of the sort array.

3. Re-adjust the new no-sort array, till the no-sort array has only one item.

Code is below:

        /// <summary>
        /// Heap Sort
        /// </summary>
        /// <param name="arr"></param>
        public static void HeapSort(int[] arr)
        {
            if (arr == null)
            {
                throw new ArgumentNullException();
            }

            // Adjust array, make it as big heap
            for (int i = arr.Length / 2 - 1; i >= 0; i--)
            {
                HeapAdjust(arr, i, arr.Length);
            }

            for (int i = arr.Length - 1; i > 0; i--)
            {
                // Swap the first one with last one, both of which in the left no-sort sub array
                // Generated no-sort subarray (a[0]-a[i-1]) and sort subarray(a[i-1]-a[arr.Length-1]).
                int temp = arr[i];
                arr[i] = arr[0];
                arr[0] = temp;

                // Re-adjust left  no-sort subarray to a heap
                HeapAdjust(arr, 0, i);
            }
        }

        /// <summary>
        /// Adjust array to a big heap
        /// </summary>
        /// <param name="arr"></param>
        /// <param name="i"> sub-heap's root index </param>
        /// <param name="len"> sub-array's length </param>
        private static void HeapAdjust(int[] arr, int i, int len)
        {
            if (arr == null)
            {
                throw new ArgumentNullException();
            }

            if (len > arr.Length || i > len - 1 || i < 0)
            {
                throw new ArgumentOutOfRangeException();
            }

            for (int child = 2 * i + 1; child < len; i = child, child = 2 * i + 1)
            {
                // Choose big one of children to compare with parent 
                if (child < len - 1 && arr[child] < arr[child + 1])
                {
                    child++;
                }

                // if the big child is greater than its parent, then swap them.
                if (arr[i] < arr[child])
                {
                    int temp = arr[i];
                    arr[i] = arr[child];
                    arr[child] = temp;
                }
                // if not, break the loop
                else
                {
                    break;
                }
            }
        }