Heap Sort

Heap Sort 

1. Build a max heap using exsiting array, which is called Heapify
2. Swap root with the last element, and re-Heapify the root node

Heapify

Heapify(array, n, i) = 1) compare node[i] with children   2)node[i] is already the largest one, no op.  3) child is largest one, swap, then Heapify(array, n, 2*i + 1 or 2i* + 2)

Code

    public class HeapSort
    {
        /// <summary>
        /// Heapify the array
        /// </summary>
        /// <param name="array">array</param>
        /// <param name="n">total size of the heap</param>
        /// <param name="i">starting node</param>
        public void Heapify(int[] array, int n, int i)
        {
            int left = 2*i + 1;
            int right = 2*i + 2;

            int largest = i;

            if (left < n)
            {
                if (array[left] > array[largest])  //  <---- 此处注意，要用array[largest] instead of array[i], 这样我们可以一直跟踪最大的下标， 而不会错误的交换次大的下标
                {
                    largest = left;
                }
            }

            if (right < n)
            {
                if (array[right] > array[largest])
                {
                    largest = right;
                }
            }

            if (largest != i)
            {
                int temp = array[i];
                array[i] = array[largest];
                array[largest] = temp;
                Heapify(array, n, largest);
            }
        }

        public void BuildHeap(int[] array)
        {
            for(int i = array.Length / 2 - 1; i >= 0; i--)
            {
                Heapify(array, array.Length, i);
            }
        }

        public void Sort(int[] array)
        {
            if (array == null || array.Length == 0)
            {
                return;
            }

            BuildHeap(array);

            for(int i = array.Length - 1; i >= 0; i--)
            {
                Swap(ref array[0], ref array[i]);
                Heapify(array, i, 0);
            }
        }

        public void Print(int[] array)
        {
            for(int i = 0; i < array.Length; i++)
            {
                Console.WriteLine(array[i]);
            }
        }

        private void Swap(ref int a, ref int b)
        {
            int temp = a;
            a = b;
            b = temp;
        }
    }

Comments

1. Heap sort is a in place sort.
2. Time complexity is O(NLogN) for Heapify.A quick look over the above algorithm suggests that the running time is , since each call to Heapify costs  and Build-Heap makes  such calls.