C#解决汉诺塔问题DEMO

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();
    }      
  }
}