C# 汉诺塔问题简单演示

汉诺塔问题是学习递归的入门问题，这里用C#简单实现了一个汉诺塔之间传递盘子的小程序

通过简单绘图实现盘子在几个塔之间的转换：

namespace 汉诺塔{    //盘子类    class HanioItem    {        public int HanoiItemHeight { get; set; }//盘子的高度        public int HanoiItemWidth { get; set; }//盘子的宽度        public Point HanoiItemPoint { get; set; }//画盘子的起始点    }}

 

namespace 汉诺塔{         public partial class FrmShow : Form    {        List<HanioItem> HanioItemsA = new List<HanioItem>();//塔A中的盘子集合        List<HanioItem> HanioItemsB = new List<HanioItem>();//塔B中的盘子集合        List<HanioItem> HanioItemsC = new List<HanioItem>();//塔C中的盘子集合        Pen p;//画笔        Graphics hanioPicA;//塔A的画布        Graphics hanioPicB;//塔B的画布        Graphics hanioPicC;//塔C的画布                int tag;//盘子个数                  public FrmShow()        {                        InitializeComponent();                  }        /// <summary>        /// 初始化3个PictureBox画布        /// </summary>        public void InitialTools()        {                       p = new Pen(Color.Black);             hanioPicA = HanoiPicA.CreateGraphics();             hanioPicB = HanoiPicB.CreateGraphics();             hanioPicC = HanoiPicC.CreateGraphics();        }                    public void InitialGraphics()        {            int HanioItemHeight = 15;//塔中盘子的高度            int HanioStartItemWidth = 90;//第一个盘子的宽            Point HanioStartItemP = new Point(15, 135);//第一个盘子起始点            InitialTools();                               tag = Convert.ToInt16(this.Tag.ToString());            HanioItemsA.Clear();            HanioItemsB.Clear();            HanioItemsC.Clear();                                  //初始化塔A上的盘子                     int diffrence = (90 - 30) / tag;//两个盘子之间宽度之差            for (int i = 1; i <= tag; i++)            {                HanioItem item = new HanioItem();                item.HanoiItemWidth = HanioStartItemWidth;                item.HanoiItemHeight = HanioItemHeight;                item.HanoiItemPoint = HanioStartItemP;                HanioItemsA.Add(item);                HanioStartItemWidth -= diffrence;                HanioStartItemP.X += diffrence / 2;                          }            //为汉诺塔画盘子            ShowHanoiGraphics();        }        /// <summary>        /// 画3个塔中的盘子        /// </summary>        private void ShowHanoiGraphics()        {                       hanioPicA.Clear(this.BackColor);            hanioPicB.Clear(this.BackColor);            hanioPicC.Clear(this.BackColor);            //为汉诺塔A画初始线条                       hanioPicA.DrawLine(p, 0, 150, 120, 150);            hanioPicA.DrawLine(p, 60, 0, 60, 150);            //为汉诺塔B画初始线条                      hanioPicB.DrawLine(p, 0, 150, 120, 150);            hanioPicB.DrawLine(p, 60, 0, 60, 150);            //为汉诺塔C画初始线条                        hanioPicC.DrawLine(p, 0, 150, 120, 150);            hanioPicC.DrawLine(p, 60, 0, 60, 150);            //画A塔的盘子            for (int i = 0; i < HanioItemsA.Count; i++)             {                hanioPicA.DrawRectangle(p, HanioItemsA[i].HanoiItemPoint.X, HanioItemsA[i].HanoiItemPoint.Y - i * 15, HanioItemsA[i].HanoiItemWidth, HanioItemsA[i].HanoiItemHeight);            }                      //画B塔的盘子            for (int i = 0; i < HanioItemsB.Count; i++)            {                hanioPicB.DrawRectangle(p, HanioItemsB[i].HanoiItemPoint.X, HanioItemsB[i].HanoiItemPoint.Y - i * 15, HanioItemsB[i].HanoiItemWidth, HanioItemsB[i].HanoiItemHeight);            }                      //画C塔的盘子            for (int i = 0; i < HanioItemsC.Count; i++)            {                hanioPicC.DrawRectangle(p, HanioItemsC[i].HanoiItemPoint.X, HanioItemsC[i].HanoiItemPoint.Y - i * 15, HanioItemsC[i].HanoiItemWidth, HanioItemsC[i].HanoiItemHeight);            }                  }        /// <summary>        /// 汉诺塔核心递归函数        /// </summary>        /// <param name="n">盘子个数</param>        /// <param name="A">塔A</param>        /// <param name="B">塔B</param>        /// <param name="C">塔C</param>        private void Hanio(int n, List<HanioItem> A, List<HanioItem> B, List<HanioItem> C)        {            if (n == 1)            {                HanioMove(A, C);            }            else            {                Hanio(n - 1, A, C, B);                HanioMove(A, C);                Hanio(n-1,B,A,C);            }        }               /// <summary>        /// 盘子移动画图实现        /// </summary>              private void HanioMove(List<HanioItem> X, List<HanioItem> Y)        {                            HanioItem item = new HanioItem();            item = X[X.Count-1];            X.Remove(item);//塔X移除一个盘子            Y.Add(item); //塔Y添加一个盘子                        ShowHanoiGraphics();            System.Threading.Thread.Sleep(1000);            }        private void btnOK_Click(object sender, EventArgs e)        {                     Hanio(tag, HanioItemsA, HanioItemsB, HanioItemsC);        }        private void FrmShow_Paint(object sender, PaintEventArgs e)        {                             InitialGraphics();        }               }}