2.3.26

上次更新:2019-04-17
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解答

在切换为插入排序之前先记录一下当前子数组的大小。
在排序类内添加一个大小为 M+1 的数组,用于记录每种数组大小出现的次数。

结果如下(N=100000):
M=10

M=20

M=50

代码

using System;
using System.ComponentModel;
using System.Drawing;
using System.Linq;
using System.Windows.Forms;
using Quick;

namespace _2._3._26
{
    public partial class Form2 : Form
    {
        private int M;
        private int N;

        public Form2(int m, int n)
        {
            InitializeComponent();
            this.M = m;
            this.N = n;
        }

        /// <summary>
        /// 启动页面时启动后台测试。
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void Form2_Shown(object sender, EventArgs e)
        {
            this.Text = "正在绘图";
            this.backgroundWorker1.RunWorkerAsync();
        }

        /// <summary>
        /// 后台测试方法。
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void backgroundWorker1_DoWork(object sender, DoWorkEventArgs e)
        {
            BackgroundWorker worker = sender as BackgroundWorker;
            QuickSortInsertion quickSortInsertion = new QuickSortInsertion
            {
                M = this.M
            };
            int[] data = SortCompare.GetRandomArrayInt(this.N);
            worker.ReportProgress(50);
            quickSortInsertion.Sort(data);
            e.Result = quickSortInsertion.Counts;
        }

        /// <summary>
        /// 更新后台进度方法。
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void backgroundWorker1_ProgressChanged(object sender, ProgressChangedEventArgs e)
        {
            this.Text = "正在绘图,已完成 " + e.ProgressPercentage + " %";
        }

        /// <summary>
        /// 测试完毕,进行绘图的方法。
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void backgroundWorker1_RunWorkerCompleted(object sender, RunWorkerCompletedEventArgs e)
        {
            if (e.Error != null)
            {
                MessageBox.Show(e.Error.Message);
            }
            //新建画布
            Graphics graphics = this.CreateGraphics();

            //翻转默认坐标系
            graphics.TranslateTransform(0, this.Height);
            graphics.ScaleTransform(1, -1);

            int[] countsOrigin = e.Result as int[];
            int[] counts = new int[countsOrigin.Length - 1];
            for (int i = 0; i < counts.Length; i++)
            {
                counts[i] = countsOrigin[i + 1];
            }

            //获取最大值
            double max = counts.Max();
            //计算间距
            double unit = this.Width / (3.0 * counts.Length + 1);
            double marginTop = 100;
            //计算直方图的矩形
            Rectangle[] rects = new Rectangle[counts.Length];
            rects[0].X = (int)unit;
            rects[0].Y = 0;
            rects[0].Width = (int)(2 * unit);
            rects[0].Height = (int)((counts[0] / max) * (this.Height - marginTop));
            for (int i = 1; i < counts.Length; ++i)
            {
                rects[i].X = (int)(rects[i - 1].X + 3 * unit);
                rects[i].Y = 0;
                rects[i].Width = (int)(2 * unit);
                rects[i].Height = (int)((counts[i] / (max + 1)) * (this.Height - marginTop));
            }

            //绘图
            graphics.FillRectangles(Brushes.Black, rects);

            //释放资源
            graphics.Dispose();

            this.Text = "绘图结果,最高次数:" + counts.Max() + " 最低次数:" + counts.Min();
        }
    }
}

快速排序类

using System;
using System.Diagnostics;
using Quick;

namespace _2._3._26
{
    /// <summary>
    /// 快速排序类。
    /// </summary>
    public class QuickSortInsertion : BaseSort
    {
        /// <summary>
        /// 切换到插入排序的阈值。
        /// </summary>
        public int M { get; set; }

        public int[] Counts;

        /// <summary>
        /// 默认构造函数。
        /// </summary>
        public QuickSortInsertion()
        {
            this.M = 8;
        }

        /// <summary>
        /// 用快速排序对数组 a 进行升序排序。
        /// </summary>
        /// <typeparam name="T">需要排序的类型。</typeparam>
        /// <param name="a">需要排序的数组。</param>
        public override void Sort<T>(T[] a)
        {
            this.Counts = new int[this.M + 1];
            for (int i = 0; i < this.M + 1; i++)
            {
                this.Counts[i] = 0;
            }
            Shuffle(a);
            Sort(a, 0, a.Length - 1);
            Debug.Assert(IsSorted(a));
        }

        /// <summary>
        /// 用快速排序对数组 a 的 lo ~ hi 范围排序。
        /// </summary>
        /// <typeparam name="T">需要排序的数组类型。</typeparam>
        /// <param name="a">需要排序的数组。</param>
        /// <param name="lo">排序范围的起始下标。</param>
        /// <param name="hi">排序范围的结束下标。</param>
        protected void Sort<T>(T[] a, int lo, int hi) where T: IComparable<T>
        {
            if (hi <= lo)                   // 别越界
                return;
            if (hi - lo <= this.M)
            {
                this.Counts[hi - lo]++;
                // 调用插入排序
                for (int i = lo; i <= hi; i++)
                    for (int k = i; k > lo && Less(a[k], a[k - 1]); k--)
                        Exch(a, k, k - 1);
                return;
            }
            int j = Partition(a, lo, hi);
            Sort(a, lo, j - 1);
            Sort(a, j + 1, hi);
        }

        /// <summary>
        /// 对数组进行切分,返回枢轴位置。
        /// </summary>
        /// <typeparam name="T">需要切分的数组类型。</typeparam>
        /// <param name="a">需要切分的数组。</param>
        /// <param name="lo">切分的起始点。</param>
        /// <param name="hi">切分的末尾点。</param>
        /// <returns>枢轴下标。</returns>
        private int Partition<T>(T[] a, int lo, int hi) where T : IComparable<T>
        {
            int i = lo, j = hi + 1;
            T v = a[lo];
            while (true)
            {
                while (Less(a[++i], v))
                    if (i == hi)
                        break;
                while (Less(v, a[--j]))
                    if (j == lo)
                        break;
                if (i >= j)
                    break;
                Exch(a, i, j);
            }
            Exch(a, lo, j);
            return j;
        }

        /// <summary>
        /// 打乱数组。
        /// </summary>
        /// <typeparam name="T">需要打乱的数组类型。</typeparam>
        /// <param name="a">需要打乱的数组。</param>
        private void Shuffle<T>(T[] a)
        {
            Random random = new Random();
            for (int i = 0; i < a.Length; i++)
            {
                int r = i + random.Next(a.Length - i);
                T temp = a[i];
                a[i] = a[r];
                a[r] = temp;
            }
        }
    }
}

另请参阅

BackgroundWorker 组件 | Microsoft Docs
Quick 库

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