算法 - 堆排序（C#）

以你之姓@ 2022-05-15 14:25 160阅读 0赞

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// --------------------------------------------------------------------------------------------------------------------// <copyright file="Program.cs" company="Chimomo's Company">//// Respect the work.//// </copyright>// <summary>//// Heap sort.//// 堆排序是一种选择排序，时间复杂度为O(nlog<sub>2</sub>n)。// 堆排序的特点是：在排序过程中，将待排序数组看成是一棵完全二叉树的顺序存储结构，利用完全二叉树中父结点和子结点之间的内在关系，在当前无序区中选择关键字最大（或最小）的记录。//// 基本思想// 1.将待排序数组调整为一个大根堆。大根堆的堆顶元素就是这个堆中最大的元素。// 2.将大根堆的堆顶元素和无序区最后一个元素交换，并将无序区最后一个位置列入有序区，然后将新的无序区调整为大根堆。// 3.重复操作，直到无序区消失为止。// 初始时，整个数组为无序区。每一次交换，都是将大根堆的堆顶元素换入有序区，以保证有序区是有序的。//// </summary>// --------------------------------------------------------------------------------------------------------------------namespace CSharpLearning{    using System;    /// <summary>    /// The program.    /// </summary>    public static class Program    {        /// <summary>        /// 程序入口点。        /// </summary>        public static void Main()        {            int[] a = { 1, 14, 6, 2, 8, 66, 9, 3, 0, 10, 5, 34, 76, 809, 4, 7 };            Console.WriteLine("Before Heap Sort...");            foreach (int i in a)            {                Console.Write(i + " ");            }            Console.WriteLine("\r\n--------------------");            Console.WriteLine("In Heap Sort...");            HeapSort(a);            Console.WriteLine("--------------------");            Console.WriteLine("After Heap Sort...");            foreach (int i in a)            {                Console.Write(i + " ");            }            Console.WriteLine(string.Empty);        }        /// <summary>        /// 堆排序方法。        /// </summary>        /// <param name="a">        /// 待排序数组。        /// </param>        private static void HeapSort(int[] a)        {            BuildMaxHeap(a); // 建立大根堆。            Console.WriteLine("Build max heap:");            foreach (int i in a)            {                Console.Write(i + " "); // 打印大根堆。            }            Console.WriteLine("\r\nMax heap in each iteration:");            for (int i = a.Length - 1; i > 0; i--)            {                Swap(ref a[0], ref a[i]); // 将堆顶元素和无序区的最后一个元素交换。                MaxHeaping(a, 0, i); // 将新的无序区调整为大根堆。                // 打印每一次堆排序迭代后的大根堆。                for (int j = 0; j < i; j++)                {                    Console.Write(a[j] + " ");                }                Console.WriteLine(string.Empty);            }        }        /// <summary>        /// 由底向上建堆。由完全二叉树的性质可知，叶子结点是从index=a.Length/2开始，所以从index=(a.Length/2)-1结点开始由底向上进行大根堆的调整。        /// </summary>        /// <param name="a">        /// 待排序数组。        /// </param>        private static void BuildMaxHeap(int[] a)        {            for (int i = (a.Length / 2) - 1; i >= 0; i--)            {                MaxHeaping(a, i, a.Length);            }        }        /// <summary>        /// 将指定的结点调整为堆。        /// </summary>        /// <param name="a">        /// 待排序数组。        /// </param>        /// <param name="i">        /// 需要调整的结点。        /// </param>        /// <param name="heapSize">        /// 堆的大小，也指数组中无序区的长度。        /// </param>        private static void MaxHeaping(int[] a, int i, int heapSize)        {            int left = (2 * i) + 1; // 左子结点。            int right = 2 * (i + 1); // 右子结点。            int large = i; // 临时变量，存放大的结点值。            // 比较左子结点。            if (left < heapSize && a[left] > a[large])            {                large = left;            }            // 比较右子结点。            if (right < heapSize && a[right] > a[large])            {                large = right;            }            // 如有子结点大于自身就交换，使大的元素上移；并且把该大的元素调整为堆以保证堆的性质。            if (i != large)            {                Swap(ref a[i], ref a[large]);                MaxHeaping(a, large, heapSize);            }        }        /// <summary>        /// 交换两个整数的值。        /// </summary>        /// <param name="a">整数a。</param>        /// <param name="b">整数b。</param>        private static void Swap(ref int a, ref int b)        {            int tmp = a;            a = b;            b = tmp;        }    }}// Output:/*Before Heap Sort...1 14 6 2 8 66 9 3 0 10 5 34 76 809 4 7--------------------In Heap Sort...Build max heap:809 14 76 7 10 66 9 3 0 8 5 34 1 6 4 2Max heap in each iteration:76 14 66 7 10 34 9 3 0 8 5 2 1 6 466 14 34 7 10 4 9 3 0 8 5 2 1 634 14 9 7 10 4 6 3 0 8 5 2 114 10 9 7 8 4 6 3 0 1 5 210 8 9 7 5 4 6 3 0 1 29 8 6 7 5 4 2 3 0 18 7 6 3 5 4 2 1 07 5 6 3 0 4 2 16 5 4 3 0 1 25 3 4 2 0 14 3 1 2 03 2 1 02 0 11 00--------------------After Heap Sort...0 1 2 3 4 5 6 7 8 9 10 14 34 66 76 809*/

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