Heap Sort

Heap Sort is interesting because the use of the 'heapify' method that creates a binary tree as a flat array. First, a binary tree, also known as a heap, is created, and then the same function is used to sort the elements. In a heap, the first node in the array at zero (0) is the top node of the binary tree. The next two (2) items are the two (2) subnodes of the top node, and so on. For each node at a position (positionIndex), its 2 subnodes are in the following positions:

• int left = 2 * positionIndex + 1;
• int right = 2 *  positionIndex + 2;

The CommonMethods.Swap() function is a reusable class, since swapping values by position is a common action during these example sorts.

Class

using System;

namespace Algorithms
{
    class HeapSort
    {
        public int[]  Sort()
        {
            //creates array
            int[] arrayToSort = { 11, 1, 22, 2, 33, 3, 44, 4, 55, 5, 66, 6, 7, 77, 88 };
           
            //creates a heap
            BuildHeap(arrayToSort);

            //sorts a heap
            //takes the largest element @ first position and moves to end
            //reuses the same heapify function, but in reverse, to sort the array
            int size = arrayToSort.Length;
            for (int counter = size - 1; counter > 0; counter--)
            {
                CommonMethods.Swap(arrayToSort, 0, counter);
                HeapifyRecursive(arrayToSort, 0, counter);
            }
            return arrayToSort;
        }

        //a heap, in this case, is a binary tree
        //the largest element is in the first position
        //the next two positions are the 2 subelements of this node, and so on
        //it looks at each element, then reporders them so it maintains the heap structure
        public int[] BuildHeap(int[] arrayToSort)
        {
            int size = arrayToSort.Length;
            int start = (arrayToSort.Length / 2) - 1;
          
            for (int counter = start; counter >= 0; counter--)
            {
                HeapifyRecursive(arrayToSort, counter, size);
            }
            return arrayToSort;
        }

        public void HeapifyRecursive(int[] arrayToSort, int idx, int max)
        {
            int left = 2 * idx + 1;
            int right = 2 * idx + 2;
            int largest;
            if (left < max && arrayToSort[left] > arrayToSort[idx])
            {
                largest = left;
            }
            else
            {
                largest = idx;
            }

            if (right < max && arrayToSort[right] > arrayToSort[largest])
            {
                largest = right;
            }

            if (largest != idx)
            {
                CommonMethods.Swap(arrayToSort, idx, largest);
                HeapifyRecursive(arrayToSort, largest, max);
            }
        }
    }
}