递归大约是2001年时候用VS7 beta写的一点东西了，现在回看起来不是一般的幼稚。。。好处是还能运行：）,看到CSDN上有朋友要C# 的代码，我也不揣简陋，献丑了。(转换成VS03的工程了）
Combinatorics.cs代码清单
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
}
测试窗体frmTest.cs代码清单:
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,
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,
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>
/// 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);
else
reslut = Combinatorics.Combination(m, n);
panelErrMsg.Text = "Showing...";
gridShow.DataSource = Combinatorics.TwoDemisionIntArrayToDataTable(reslut);
panelErrMsg.Text = "Idle";
}
else
panelErrMsg.Text = "Input number is invalid";
}
}
}
运行效果如图：
感觉没什么好废话的，用DataTable输出就是为了方便绑定实体值（比如做攻击字典）的枚举。各路高人见笑了。
递归枚举排列、组合的C#源码
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