递归枚举排列、组合的C#源码

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"; } } }