漢諾塔問題是學習遞歸的入門問題，這里用C#簡單實現了一個漢諾塔之間傳遞盤子的小程序
通過簡單繪圖實現盤子在幾個塔之間的轉換：
namespace 漢諾塔{ //盤子類 class HanioItem { public int HanoiItemHeight { get; set; }//盤子的高度 public int HanoiItemWidth { get; set; }//盤子的寬度 public Point HanoiItemPoint { get; set; }//畫盤子的起始點 }}namespace 漢諾塔{ public partial class FrmShow : Form { List<HanioItem> HanioItemsA = new List<HanioItem>();//塔A中的盤子集合 List<HanioItem> HanioItemsB = new List<HanioItem>();//塔B中的盤子集合 List<HanioItem> HanioItemsC = new List<HanioItem>();//塔C中的盤子集合 Pen p;//畫筆 Graphics hanioPicA;//塔A的畫布 Graphics hanioPicB;//塔B的畫布 Graphics hanioPicC;//塔C的畫布 int tag;//盤子個數 public FrmShow() { InitializeComponent(); } /// <summary> /// 初始化3個PictureBox畫布 /// </summary> public void InitialTools() { p = new Pen(Color.Black); hanioPicA = HanoiPicA.CreateGraphics(); hanioPicB = HanoiPicB.CreateGraphics(); hanioPicC = HanoiPicC.CreateGraphics(); } public void InitialGraphics() { int HanioItemHeight = 15;//塔中盤子的高度 int HanioStartItemWidth = 90;//第一個盤子的寬 Point HanioStartItemP = new Point(15, 135);//第一個盤子起始點 InitialTools(); tag = Convert.ToInt16(this.Tag.ToString()); HanioItemsA.Clear(); HanioItemsB.Clear(); HanioItemsC.Clear(); //初始化塔A上的盤子 int diffrence = (90 - 30) / tag;//兩個盤子之間寬度之差 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; } //為漢諾塔畫盤子 ShowHanoiGraphics(); } /// <summary> /// 畫3個塔中的盤子 /// </summary> private void ShowHanoiGraphics() { hanioPicA.Clear(this.BackColor); hanioPicB.Clear(this.BackColor); hanioPicC.Clear(this.BackColor); //為漢諾塔A畫初始線條 hanioPicA.DrawLine(p, 0, 150, 120, 150); hanioPicA.DrawLine(p, 60, 0, 60, 150); //為漢諾塔B畫初始線條 hanioPicB.DrawLine(p, 0, 150, 120, 150); hanioPicB.DrawLine(p, 60, 0, 60, 150); //為漢諾塔C畫初始線條 hanioPicC.DrawLine(p, 0, 150, 120, 150); hanioPicC.DrawLine(p, 60, 0, 60, 150); //畫A塔的盤子 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); } //畫B塔的盤子 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); } //畫C塔的盤子 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> /// 漢諾塔核心遞歸函數 /// </summary> /// <param name="n">盤子個數</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> /// 盤子移動畫圖實現 /// </summary> private void HanioMove(List<HanioItem> X, List<HanioItem> Y) { HanioItem item = new HanioItem(); item = X[X.Count-1]; X.Remove(item);//塔X移除一個盤子 Y.Add(item); //塔Y添加一個盤子 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(); } }}新聞熱點
疑難解答
