递归枚举排列、组合的C#源码

 

         using System;    

using System.Collections;
using System.Data;
     /// <summary>
     /// 组合数学函数集
     /// </summary>
public class Combinatorics
{
    #region 公共函数
    /// <summary>
    /// 把二维整形数组转换为数据表
    /// </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);                //获取二维表的各维长度
        for (i = 0; i <= b1; i++)                                                         //以第二维长度创建数据表的各字段
            dt.Columns.Add(i.ToString(), System.Type.GetType("System.Int32"));
        for (i = 0; i <= b2; i++)                                                         //对各返回排列循环
        {
            dr = dt.NewRow();                                                              //准备插入新行
            for (j = 0; j <= b1; j++)                                                    //在新行中逐个填入返回排列的各元素次序
                dr[j.ToString()] = source[j, i];                                      //用序数指针获取原元素的值
            dt.Rows.Add(dr);                                                               //插入新行
        }
        return dt;
    }
    /// <summary>
    /// 连乘积函数
    /// </summary>
    public static int Product(int start, int finish)
    {
        int factorial = 1;
        for (int i = start; i <= finish; i++)
            factorial *= i;
        return factorial;
    }
    /// <summary>
    /// 阶乘函数
    /// </summary>
    public static int Factorial(int n)
    {
        return Product(2, n);
    }
    /// <summary>
    /// 排列数函数
    /// </summary>
    public static int ArrangeCount(int m, int n)
    {
        return Product(n - m + 1, n);
    }
    /// <summary>
    /// 生成排列表函数
    /// </summary>
    public static int[,] Arrange(int m, int n)
    {
        int A = ArrangeCount(m, n);               //求得排列数，安排返回数组的第一维
        int[,] arrange = new int[m, A];           //定义返回数组
        ArrayList e = new ArrayList();            //设置元素表
        for (int i = 0; i < n; i++)
            e.Add(i + 1);
        Arrange(ref arrange, e, m, 0, 0);
        return arrange;
    }
    /// <summary>
    /// 组合数函数
    /// </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>
    /// 生成组合表函数
    /// </summary>
    public static int[,] Combination(int m, int n)
    {
        int A = CombinationCount(m, n);                //求得排列数，安排返回数组的第一维
        int[,] combination = new int[m, A];            //定义返回数组
        ArrayList e = new ArrayList();                 //设置元素表
        for (int i = 0; i < n; i++)
            e.Add(i + 1);
        Combination(ref combination, e, m, 0, 0);
        return combination;
    }
    #endregion
    #region 内部核心
    /// <summary>
    /// 排列函数
    /// </summary>
    /// <param name="reslut">返回值数组</param>
    /// <param name="elements">可供选择的元素数组</param>
    ///  <param name="m">目标选定元素个数</param>
    /// <param name="x">当前返回值数组的列坐标</param>
    /// <param name="y">当前返回值数组的行坐标</param>
    private static void Arrange(ref int[,] reslut, ArrayList elements, int m, int x, int y)
    {
        int sub = ArrangeCount(m - 1, elements.Count - 1);                    //求取当前子排列的个数
        for (int i = 0; i < elements.Count; i++, y += sub)                    //每个元素均循环一次,每次循环后移动行指针
        {
            int val = RemoveAndWrite(elements, i, ref reslut, x, y, sub);
            if (m > 1)                                                                 //递归条件为子排列数大于1
                Arrange(ref reslut, elements, m - 1, x + 1, y);
            elements.Insert(i, val);                                              //恢复刚才删除的元素
        }
    }
    /// <summary>
    /// 组合函数
    /// </summary>
    /// /// <param name="reslut">返回值数组</param>
    /// <param name="elements">可供选择的元素数组</param>
    ///  <param name="m">目标选定元素个数</param>
    /// <param name="x">当前返回值数组的列坐标</param>
    /// <param name="y">当前返回值数组的行坐标</param>
    private static void Combination(ref int[,] reslut, ArrayList elements, int m, int x, int y)
    {
        ArrayList tmpElements = new ArrayList();                              //所有本循环使用的元素都将暂时存放在这个数组
        int elementsCount = elements.Count;                                        //先记录可选元素个数
        int sub;
        for (int i = elementsCount - 1; i >= m - 1; i--, y += sub)            //从elementsCount-1(即n-1)到m-1的循环,每次循环后移动行指针
        {
            sub = CombinationCount(m - 1, i);                                   //求取当前子组合的个数
            int val = RemoveAndWrite(elements, 0, ref reslut, x, y, sub);
            tmpElements.Add(val);                                                 //把这个可选元素存放到临时数组,循环结束后一并恢复到elements数组中
            if (sub > 1 || (elements.Count + 1 == m && elements.Count > 0))  //递归条件为 子组合数大于1 或 可选元素个数+1等于当前目标选择元素个数且可选元素个数大于1
                Combination(ref reslut, elements, m - 1, x + 1, y);
        }
        elements.InsertRange(0, tmpElements);                                 //一次性把上述循环删除的可选元素恢复到可选元素数组中
    }
    /// <summary>
    /// 返回由Index指定的可选元素值,并在数组中删除之,再从y行开始在x列中连续写入subComb个值
    /// </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
}

<textarea style="DISPLAY: none" class="csharp" name="code">using System; using System.Collections; using System.Data; /// &lt;summary&gt; /// 组合数学函数集 /// &lt;/summary&gt; public class Combinatorics { #region 公共函数 /// &lt;summary&gt; /// 把二维整形数组转换为数据表 /// &lt;/summary&gt; public static DataTable TwoDemisionIntArrayToDataTable(int[,] source) { DataTable dt = new DataTable(); DataRow dr; int i, j; int b1 = source.GetUpperBound(0), b2 = source.GetUpperBound(1); //获取二维表的各维长度 for (i = 0; i &lt;= b1; i++) //以第二维长度创建数据表的各字段 dt.Columns.Add(i.ToString(), System.Type.GetType(&quot;System.Int32&quot;)); for (i = 0; i &lt;= b2; i++) //对各返回排列循环 { dr = dt.NewRow(); //准备插入新行 for (j = 0; j &lt;= b1; j++) //在新行中逐个填入返回排列的各元素次序 dr[j.ToString()] = source[j, i]; //用序数指针获取原元素的值 dt.Rows.Add(dr); //插入新行 } return dt; } /// &lt;summary&gt; /// 连乘积函数 /// &lt;/summary&gt; public static int Product(int start, int finish) { int factorial = 1; for (int i = start; i &lt;= finish; i++) factorial *= i; return factorial; } /// &lt;summary&gt; /// 阶乘函数 /// &lt;/summary&gt; public static int Factorial(int n) { return Product(2, n); } /// &lt;summary&gt; /// 排列数函数 /// &lt;/summary&gt; public static int ArrangeCount(int m, int n) { return Product(n - m + 1, n); } /// &lt;summary&gt; /// 生成排列表函数 /// &lt;/summary&gt; public static int[,] Arrange(int m, int n) { int A = ArrangeCount(m, n); //求得排列数，安排返回数组的第一维 int[,] arrange = new int[m, A]; //定义返回数组 ArrayList e = new ArrayList(); //设置元素表 for (int i = 0; i &lt; n; i++) e.Add(i + 1); Arrange(ref arrange, e, m, 0, 0); return arrange; } /// &lt;summary&gt; /// 组合数函数 /// &lt;/summary&gt; 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 } /// &lt;summary&gt; /// 生成组合表函数 /// &lt;/summary&gt; public static int[,] Combination(int m, int n) { int A = CombinationCount(m, n); //求得排列数，安排返回数组的第一维 int[,] combination = new int[m, A]; //定义返回数组 ArrayList e = new ArrayList(); //设置元素表 for (int i = 0; i &lt; n; i++) e.Add(i + 1); Combination(ref combination, e, m, 0, 0); return combination; } #endregion #region 内部核心 /// &lt;summary&gt; /// 排列函数 /// &lt;/summary&gt; /// &lt;param name=&quot;reslut&quot;&gt;返回值数组&lt;/param&gt; /// &lt;param name=&quot;elements&quot;&gt;可供选择的元素数组&lt;/param&gt; /// &lt;param name=&quot;m&quot;&gt;目标选定元素个数&lt;/param&gt; /// &lt;param name=&quot;x&quot;&gt;当前返回值数组的列坐标&lt;/param&gt; /// &lt;param name=&quot;y&quot;&gt;当前返回值数组的行坐标&lt;/param&gt; private static void Arrange(ref int[,] reslut, ArrayList elements, int m, int x, int y) { int sub = ArrangeCount(m - 1, elements.Count - 1); //求取当前子排列的个数 for (int i = 0; i &lt; elements.Count; i++, y += sub) //每个元素均循环一次,每次循环后移动行指针 { int val = RemoveAndWrite(elements, i, ref reslut, x, y, sub); if (m &gt; 1) //递归条件为子排列数大于1 Arrange(ref reslut, elements, m - 1, x + 1, y); elements.Insert(i, val); //恢复刚才删除的元素 } } /// &lt;summary&gt; /// 组合函数 /// &lt;/summary&gt; /// /// &lt;param name=&quot;reslut&quot;&gt;返回值数组&lt;/param&gt; /// &lt;param name=&quot;elements&quot;&gt;可供选择的元素数组&lt;/param&gt; /// &lt;param name=&quot;m&quot;&gt;目标选定元素个数&lt;/param&gt; /// &lt;param name=&quot;x&quot;&gt;当前返回值数组的列坐标&lt;/param&gt; /// &lt;param name=&quot;y&quot;&gt;当前返回值数组的行坐标&lt;/param&gt; private static void Combination(ref int[,] reslut, ArrayList elements, int m, int x, int y) { ArrayList tmpElements = new ArrayList(); //所有本循环使用的元素都将暂时存放在这个数组 int elementsCount = elements.Count; //先记录可选元素个数 int sub; for (int i = elementsCount - 1; i &gt;= m - 1; i--, y += sub) //从elementsCount-1(即n-1)到m-1的循环,每次循环后移动行指针 { sub = CombinationCount(m - 1, i); //求取当前子组合的个数 int val = RemoveAndWrite(elements, 0, ref reslut, x, y, sub); tmpElements.Add(val); //把这个可选元素存放到临时数组,循环结束后一并恢复到elements数组中 if (sub &gt; 1 || (elements.Count + 1 == m &amp;&amp; elements.Count &gt; 0)) //递归条件为 子组合数大于1 或 可选元素个数+1等于当前目标选择元素个数且可选元素个数大于1 Combination(ref reslut, elements, m - 1, x + 1, y); } elements.InsertRange(0, tmpElements); //一次性把上述循环删除的可选元素恢复到可选元素数组中 } /// &lt;summary&gt; /// 返回由Index指定的可选元素值,并在数组中删除之,再从y行开始在x列中连续写入subComb个值 /// &lt;/summary&gt; 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 &lt; count; i++) reslut[x, y + i] = val; return val; } #endregion } </textarea>
测试代码：

using System;
using System.Drawing;
using System.Collections;
using System.ComponentModel;
using System.Windows.Forms;
using System.Data;
namespace CombinatoricsLib
{
    /// <summary>
    /// Form1 的摘要说明。
    /// </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>
        /// 必需的设计器变量。
        /// </summary>
        private System.ComponentModel.Container components = null;
        public frmTest()
        {
            //
            // Windows 窗体设计器支持所必需的
            //
            InitializeComponent();
            //
            // TODO: 在 InitializeComponent 调用后添加任何构造函数代码
            //
        }
        /// <summary>
        /// 清理所有正在使用的资源。
        /// </summary>
        protected override void Dispose(bool disposing)
        {
            if (disposing)
            {
                if (components != null)
                {
                    components.Dispose();
                }
            }
            base.Dispose(disposing);
        }
        #region Windows 窗体设计器生成的代码
        /// <summary>
        /// 设计器支持所需的方法 - 不要使用代码编辑器修改
        /// 此方法的内容。
        /// </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("宋体", 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("宋体", 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,
                                                                            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("宋体", 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,
                                                                            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.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>
        /// 应用程序的主入口点。
        /// </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);
                reslut = Combinatorics.Combination(m, n);
                panelErrMsg.Text = "Showing...";
                gridShow.DataSource = Combinatorics.TwoDemisionIntArrayToDataTable(reslut);
                panelErrMsg.Text = "Idle";
            }
            else
                panelErrMsg.Text = "Input number is invalid";
        }
    }
}