遞歸枚舉排列、組合的C#源碼

Combinatorics.cs代碼清單

using System;
using System.Collections;
using System.Data;

     /// <summary>
     /// 組合數學函數集
     /// </summary>
     public class Combinatorics
     {        
         #region 公共函數

         
         /// <summary>
         /// 把二維整形數組轉換為數據表
         /// </summary>
         public static DataTable TwoDemisionIntArrayToDataTable(int[, ]source)
         {
              DataTable dt = new DataTable();
              DataRow dr;
              int i, j;
         
              int b1 = source.GetUpperBound(0), b2 = source.GetUpperBound(1);                //獲取二維表的各維長度                         

              for (i = 0; i <= b1; i ++ )                                                         //以第二維長度創建數據表的各字段
                   dt.Columns.Add(i.ToString(), System.Type.GetType("System.Int32"));

              for (i = 0; i <= b2; i ++ )                                                         //對各返回排列循環
              {
                   dr = dt.NewRow();                                                              //準備插入新行
                   for (j = 0; j <= b1; j ++ )                                                    //在新行中逐個填入返回排列的各元素次序                
                       dr[j.ToString()] = source[j, i];                                      //用序數指針獲取原元素的值
                   dt.Rows.Add(dr);                                                               //插入新行
              }

              return dt;
         }    

         /// <summary>
         /// 連乘積函數         
         /// </summary>
         public static int Product(int start, int finish)
         {
              int factorial = 1;
              for (int i = start; i <= finish; i ++ )
                   factorial *= i;
              return factorial;
         }                  

         /// <summary>
         /// 階乘函數       
         /// </summary>
         public static int Factorial(int n)
         {
              return Product(2, n);
         }                           

         /// <summary>
         /// 排列數函數         
         /// </summary>
         public static int ArrangeCount(int m, int n)
         {
              return Product(n - m + 1, n);        
         }
         
         /// <summary>
         /// 生成排列表函數     
         /// </summary>
         public static int[, ]Arrange(int m, int n)
         {
              int A = ArrangeCount(m, n);               //求得排列數，安排返回數組的第一維
              int[, ]arrange = new int[m, A];           //定義返回數組
              ArrayList e = new ArrayList();            //設置元素表
              for (int i = 0; i < n; i ++ )
                   e.Add(i + 1);
              Arrange(ref arrange, e, m, 0, 0);
              return arrange;
         }

         /// <summary>
         /// 組合數函數         
         /// </summary>
         public static int CombinationCount(int m, int n)
         {
              int a = Product(n - m + 1, n), b = Product(2, m);       //a=n-m+1 * ... * n ; b = m!
              return (int) a/b;                                            //c=a/b                              
         }

         /// <summary>
         /// 生成組合表函數     
         /// </summary>
         public static int[, ]Combination(int m, int n)
         {
              int A = CombinationCount(m, n);                //求得排列數，安排返回數組的第一維
              int[, ]combination = new int[m, A];            //定義返回數組
              ArrayList e = new ArrayList();                 //設置元素表
              for (int i = 0; i < n; i ++ )
                   e.Add(i + 1);
              Combination(ref combination, e, m, 0, 0);
              return combination;
         }
         

         #endregion
         
         #region 內部核心

         /// <summary>
         /// 排列函數
         /// </summary>
         /// <param name="reslut">返回值數組</param>
         /// <param name="elements">可供選擇的元素數組</param>
         ///  <param name="m">目標選定元素個數</param>           
         /// <param name="x">當前返回值數組的列坐標</param>
         /// <param name="y">當前返回值數組的行坐標</param>
         private static void Arrange(ref int[, ]reslut, ArrayList elements, int m, int x, int y)
         {             
              int sub = ArrangeCount(m - 1, elements.Count - 1);                    //求取當前子排列的個數
              for (int i = 0; i < elements.Count; i++, y += sub)                    //每個元素均循環一次,每次循環後移動行指針
              {                  
                  int val = RemoveAndWrite(elements, i, ref reslut, x, y, sub);                                                                                    
                   if (m > 1)                                                                 //遞歸條件為子排列數大於1
                       Arrange(ref reslut, elements, m - 1, x + 1, y);
                   elements.Insert(i, val);                                              //恢復剛才刪除的元素                  
              }
         }
         
         /// <summary>
         /// 組合函數
         /// </summary>
         /// <param name="reslut">返回值數組</param>
         /// <param name="elements">可供選擇的元素數組</param>
         ///  <param name="m">目標選定元素個數</param>           
         /// <param name="x">當前返回值數組的列坐標</param>
         /// <param name="y">當前返回值數組的行坐標</param>
         private static void Combination(ref int[, ]reslut, ArrayList elements, int m, int x, int y)
         {             
              ArrayList tmpElements = new ArrayList();                              //所有本循環使用的元素都將暫時存放在這個數組
              int elementsCount = elements.Count;                                        //先記錄可選元素個數
              int sub;
              for (int i = elementsCount - 1; i >= m - 1; i--, y += sub)            //從elementsCount-1(即n-1)到m-1的循環,每次循環後移動行指針
              {
                   sub = CombinationCount(m-1,i);                                   //求取當前子組合的個數
                   int val = RemoveAndWrite(elements, 0, ref reslut, x, y, sub);                                                                 
                   tmpElements.Add(val);                                                 //把這個可選元素存放到臨時數組,循環結束後一併恢復到elements數組中                 
                   if (sub > 1 || (elements.Count + 1 == m && elements.Count > 0))  //遞歸條件為 子組合數大於1 或 可選元素個數+1等於當前目標選擇元素個數且可選元素個數大於1
                       Combination(ref reslut, elements, m - 1, x + 1, y);                                 
              }
              elements.InsertRange(0, tmpElements);                                 //一次性把上述循環刪除的可選元素恢復到可選元素數組中           
         }

         /// <summary>
         /// 返回由Index指定的可選元素值,並在數組中刪除之,再從y行開始在x列中連續寫入subComb個值
         /// </summary>
         private static int RemoveAndWrite(ArrayList elements, int index, ref int[, ]reslut, int x, int y, int count)
         {
              int val = (int) elements[index];
              elements.RemoveAt(index);
              for (int i = 0; i < count; i ++ )
                   reslut[x, y + i] = val;              
              return val;
         }        
         
         #endregion 
     }




測試窗體frmTest.cs代碼清單: 

using System;
using System.Drawing;
using System.Collections;
using System.ComponentModel;
using System.Windows.Forms;
using System.Data;

namespace CombinatoricsLib
{
     /// <summary>
     /// Form1 的摘要說明。
     /// </summary>
     public class frmTest : System.Windows.Forms.Form
     {
         private System.Windows.Forms.DataGrid gridShow;
         private System.Windows.Forms.NumericUpDown numM;
         private System.Windows.Forms.Button btnGo;
         private System.Windows.Forms.DomainUpDown domainFunction;
         private System.Windows.Forms.StatusBar statusBar1;
         private System.Windows.Forms.StatusBarPanel panelErrMsg;
         private System.Windows.Forms.NumericUpDown numN;
         /// <summary>
         /// 必需的設計器變量。
         /// </summary>
         private System.ComponentModel.Container components = null;

         public frmTest()
         {
              //
              // Windows 窗體設計器支持所必需的
              //
              InitializeComponent();

              //
              // TODO: 在 InitializeComponent 調用後添加任何構造函數代碼
              //
         }

         /// <summary>
         /// 清理所有正在使用的資源。
         /// </summary>
         protected override void Dispose( bool disposing )
         {
              if( disposing )
              {
                   if (components != null) 
                   {
                       components.Dispose();
                   }
              }
              base.Dispose( disposing );
         }

         #region Windows 窗體設計器生成的代碼
         /// <summary>
         /// 設計器支持所需的方法 - 不要使用代碼編輯器修改
         /// 此方法的內容。
         /// </summary>
         private void InitializeComponent()
         {
              this.gridShow = new System.Windows.Forms.DataGrid();
              this.domainFunction = new System.Windows.Forms.DomainUpDown();
              this.numM = new System.Windows.Forms.NumericUpDown();
              this.numN = new System.Windows.Forms.NumericUpDown();
              this.btnGo = new System.Windows.Forms.Button();
              this.statusBar1 = new System.Windows.Forms.StatusBar();
              this.panelErrMsg = new System.Windows.Forms.StatusBarPanel();
              ((System.ComponentModel.ISupportInitialize)(this.gridShow)).BeginInit();
              ((System.ComponentModel.ISupportInitialize)(this.numM)).BeginInit();
              ((System.ComponentModel.ISupportInitialize)(this.numN)).BeginInit();
              ((System.ComponentModel.ISupportInitialize)(this.panelErrMsg)).BeginInit();
              this.SuspendLayout();
              // 
              // gridShow
              // 
              this.gridShow.AlternatingBackColor = System.Drawing.Color.Lavender;
              this.gridShow.BackColor = System.Drawing.Color.WhiteSmoke;
              this.gridShow.BackgroundColor = System.Drawing.Color.LightGray;
              this.gridShow.BorderStyle = System.Windows.Forms.BorderStyle.None;
              this.gridShow.CaptionBackColor = System.Drawing.Color.LightSteelBlue;
              this.gridShow.CaptionForeColor = System.Drawing.Color.MidnightBlue;
              this.gridShow.DataMember = "";
              this.gridShow.FlatMode = true;
              this.gridShow.Font = new System.Drawing.Font("Tahoma", 8F);
              this.gridShow.ForeColor = System.Drawing.Color.MidnightBlue;
              this.gridShow.GridLineColor = System.Drawing.Color.Gainsboro;
              this.gridShow.GridLineStyle = System.Windows.Forms.DataGridLineStyle.None;
              this.gridShow.HeaderBackColor = System.Drawing.Color.MidnightBlue;
              this.gridShow.HeaderFont = new System.Drawing.Font("Tahoma", 8F, System.Drawing.FontStyle.Bold);
              this.gridShow.HeaderForeColor = System.Drawing.Color.WhiteSmoke;
              this.gridShow.LinkColor = System.Drawing.Color.Teal;
              this.gridShow.Location = new System.Drawing.Point(24, 88);
              this.gridShow.Name = "gridShow";
              this.gridShow.ParentRowsBackColor = System.Drawing.Color.Gainsboro;
              this.gridShow.ParentRowsForeColor = System.Drawing.Color.MidnightBlue;
              this.gridShow.ReadOnly = true;
              this.gridShow.SelectionBackColor = System.Drawing.Color.CadetBlue;
              this.gridShow.SelectionForeColor = System.Drawing.Color.WhiteSmoke;
              this.gridShow.Size = new System.Drawing.Size(648, 344);
              this.gridShow.TabIndex = 0;
              // 
              // domainFunction
              // 
              this.domainFunction.BackColor = System.Drawing.SystemColors.Info;
              this.domainFunction.Font = new System.Drawing.Font("細明體", 36F, System.Drawing.FontStyle.Regular, System.Drawing.GraphicsUnit.Point, ((System.Byte)(134)));
              this.domainFunction.ForeColor = System.Drawing.Color.Teal;
              this.domainFunction.Items.Add("C");
              this.domainFunction.Items.Add("A");
              this.domainFunction.Location = new System.Drawing.Point(24, 8);
              this.domainFunction.Name = "domainFunction";
              this.domainFunction.ReadOnly = true;
              this.domainFunction.Size = new System.Drawing.Size(48, 62);
              this.domainFunction.TabIndex = 1;
              this.domainFunction.Text = "C";
              // 
              // numM
              // 
              this.numM.BackColor = System.Drawing.Color.PeachPuff;
              this.numM.Font = new System.Drawing.Font("細明體", 12F, System.Drawing.FontStyle.Regular, System.Drawing.GraphicsUnit.Point, ((System.Byte)(134)));
              this.numM.ForeColor = System.Drawing.Color.Teal;
              this.numM.Location = new System.Drawing.Point(80, 8);
              this.numM.Maximum = new System.Decimal(new int[] {
                                                                            20,
                                                                            0,
                                                                            0,
                                                                            0});
              this.numM.Minimum = new System.Decimal(new int[] {
                                                                            1,
                                                                            0,
                                                                            0,
                                                                            0});
              this.numM.Name = "numM";
              this.numM.Size = new System.Drawing.Size(56, 26);
              this.numM.TabIndex = 4;
              this.numM.Value = new System.Decimal(new int[] {
                                                                         2,
                                                                         0,
                                                                         0,
                                                                         0});
              // 
              // numN
              // 
              this.numN.BackColor = System.Drawing.Color.Bisque;
              this.numN.Font = new System.Drawing.Font("細明體", 12F);
              this.numN.ForeColor = System.Drawing.Color.Teal;
              this.numN.Location = new System.Drawing.Point(80, 40);
              this.numN.Maximum = new System.Decimal(new int[] {
                                                                            25,
                                                                            0,
                                                                            0,
                                                                            0});
              this.numN.Minimum = new System.Decimal(new int[] {
                                                                            1,
                                                                            0,
                                                                            0,
                                                                            0});
              this.numN.Name = "numN";
              this.numN.Size = new System.Drawing.Size(56, 26);
              this.numN.TabIndex = 5;
              this.numN.Value = new System.Decimal(new int[] {
                                                                         4,
                                                                         0,
                                                                         0,
                                                                         0});
              // 
              // btnGo
              // 
              this.btnGo.BackColor = System.Drawing.Color.PaleTurquoise;
              this.btnGo.Location = new System.Drawing.Point(184, 24);
              this.btnGo.Name = "btnGo";
              this.btnGo.Size = new System.Drawing.Size(88, 32);
              this.btnGo.TabIndex = 6;
              this.btnGo.Text = "Go!";
              this.btnGo.Click += new System.EventHandler(this.btnGo_Click);
              // 
              // statusBar1
              // 
              this.statusBar1.Location = new System.Drawing.Point(0, 453);
              this.statusBar1.Name = "statusBar1";
              this.statusBar1.Panels.AddRange(new System.Windows.Forms.StatusBarPanel[] {
                                                                                                         this.panelErrMsg});
              this.statusBar1.ShowPanels = true;
              this.statusBar1.Size = new System.Drawing.Size(704, 32);
              this.statusBar1.TabIndex = 7;
              this.statusBar1.Text = "statusBar1";
              // 
              // panelErrMsg
              // 
              this.panelErrMsg.AutoSize = System.Windows.Forms.StatusBarPanelAutoSize.Contents;
              this.panelErrMsg.Text = "Idle";
              this.panelErrMsg.Width = 39;
              // 
              // frmTest
              // 
              this.AutoScaleBaseSize = new System.Drawing.Size(6, 14);
              this.ClientSize = new System.Drawing.Size(704, 485);
              this.Controls.Add(this.statusBar1);
              this.Controls.Add(this.btnGo);
              this.Controls.Add(this.numN);
              this.Controls.Add(this.numM);
              this.Controls.Add(this.domainFunction);
              this.Controls.Add(this.gridShow);
              this.MaximizeBox = false;
              this.Name = "frmTest";
              this.StartPosition = System.Windows.Forms.FormStartPosition.CenterScreen;
              this.Text = "frmTest";
              ((System.ComponentModel.ISupportInitialize)(this.gridShow)).EndInit();
              ((System.ComponentModel.ISupportInitialize)(this.numM)).EndInit();
              ((System.ComponentModel.ISupportInitialize)(this.numN)).EndInit();
              ((System.ComponentModel.ISupportInitialize)(this.panelErrMsg)).EndInit();
              this.ResumeLayout(false);

         }
         #endregion

         /// <summary>
         /// 應用程序的主入口點。
         /// </summary>
         [STAThread]
         static void Main() 
         {
              Application.Run(new frmTest());
         }

         private void btnGo_Click(object sender, System.EventArgs e)
         {
              int[, ]reslut;
              int m = (int)numM.Value, n = (int)numN.Value;
              
              if (m <= n)
              {
                   panelErrMsg.Text = "Running...";
                   if (domainFunction.Text == "A")                
                       reslut = Combinatorics.Arrange(m, n);
                   else
                       reslut = Combinatorics.Combination(m, n);                        
                   panelErrMsg.Text = "Showing...";
                   gridShow.DataSource = Combinatorics.TwoDemisionIntArrayToDataTable(reslut);
                   panelErrMsg.Text = "Idle";
              }
              else          
                   panelErrMsg.Text = "Input number is invalid";
         }
     }
}