详解C#的排列组合
排列组合的概念
排列:从n个不同元素中取出m(m≤n)个元素,按照一定的顺序排成一列,叫做从n个元素中取出m个元素的一个排列(Arrangement)。
组合:从m个不同的元素中,任取n(n≤m)个元素为一组,叫作从m个不同元素中取出n个元素的一个组合。
排列组合实现代码
上一个项目做的一个水路的路径规划时,用到了排列的数据结构。求任意N个点里M个点的不同顺序的组合个数。
这样求最优路径。下面贴一段不知道哪里找的排列组合的算法。
public class PermutationAndCombination<T> { /// <summary> /// 交换两个变量 /// </summary> /// <param name="a">变量1</param> /// <param name="b">变量2</param> public static void Swap(ref T a, ref T b) { T temp = a; a = b; b = temp; } /// <summary> /// 递归算法求数组的组合(私有成员) /// </summary> /// <param name="list">返回的范型</param> /// <param name="t">所求数组</param> /// <param name="n">辅助变量</param> /// <param name="m">辅助变量</param> /// <param name="b">辅助数组</param> /// <param name="M">辅助变量M</param> private static void GetCombination(ref List<T[]> list, T[] t, int n, int m, int[] b, int M) { for (int i = n; i >= m; i--) { b[m - 1] = i - 1; if (m > 1) { GetCombination(ref list, t, i - 1, m - 1, b, M); } else { if (list == null) { list = new List<T[]>(); } T[] temp = new T[M]; for (int j = 0; j < b.Length; j++) { temp[j] = t[b[j]]; } list.Add(temp); } } } /// <summary> /// 递归算法求排列(私有成员) /// </summary> /// <param name="list">返回的列表</param> /// <param name="t">所求数组</param> /// <param name="startIndex">起始标号</param> /// <param name="endIndex">结束标号</param> private static void GetPermutation(ref List<T[]> list, T[] t, int startIndex, int endIndex) { if (startIndex == endIndex) { if (list == null) { list = new List<T[]>(); } T[] temp = new T[t.Length]; t.CopyTo(temp, 0); list.Add(temp); } else { for (int i = startIndex; i <= endIndex; i++) { Swap(ref t[startIndex], ref t[i]); GetPermutation(ref list, t, startIndex + 1, endIndex); Swap(ref t[startIndex], ref t[i]); } } } /// <summary> /// 求从起始标号到结束标号的排列,其余元素不变 /// </summary> /// <param name="t">所求数组</param> /// <param name="startIndex">起始标号</param> /// <param name="endIndex">结束标号</param> /// <returns>从起始标号到结束标号排列的范型</returns> public static List<T[]> GetPermutation(T[] t, int startIndex, int endIndex) { if (startIndex < 0 || endIndex > t.Length - 1) { return null; } List<T[]> list = new List<T[]>(); GetPermutation(ref list, t, startIndex, endIndex); return list; } /// <summary> /// 返回数组所有元素的全排列 /// </summary> /// <param name="t">所求数组</param> /// <returns>全排列的范型</returns> public static List<T[]> GetPermutation(T[] t) { return GetPermutation(t, 0, t.Length - 1); } /// <summary> /// 求数组中n个元素的排列 /// </summary> /// <param name="t">所求数组</param> /// <param name="n">元素个数</param> /// <returns>数组中n个元素的排列</returns> public static List<T[]> GetPermutation(T[] t, int n) { if (n > t.Length) { return null; } List<T[]> list = new List<T[]>(); List<T[]> c = GetCombination(t, n); for (int i = 0; i < c.Count; i++) { List<T[]> l = new List<T[]>(); GetPermutation(ref l, c[i], 0, n - 1); list.AddRange(l); } return list; } /// <summary> /// 求数组中n个元素的组合 /// </summary> /// <param name="t">所求数组</param> /// <param name="n">元素个数</param> /// <returns>数组中n个元素的组合的范型</returns> public static List<T[]> GetCombination(T[] t, int n) { if (t.Length < n) { return null; } int[] temp = new int[n]; List<T[]> list = new List<T[]>(); GetCombination(ref list, t, t.Length, n, temp, n); return list; } }
求组合:求5个数里任意3个数的组合
static void Main(string[] args) { int[] IntArr = new int[] { 1, 2, 3, 4, 5 }; //整型数组 List<int[]> ListCombination = PermutationAndCombination<int>.GetCombination(IntArr, 3); //求全部的3-3组合 foreach(int[] arr in ListCombination) { foreach(int item in arr) { Console.Write(item + " "); } Console.WriteLine(""); } Console.ReadKey(); }
求排列:5个数取3个的任意排列
int[] IntArr = new int[] { 1, 2, 3, 4, 5 }; //整型数组 List<int[]> ListCombination = PermutationAndCombination<int>.GetPermutation(IntArr, 3); //求全部的5取3排列 foreach(int[] arr in ListCombination) { foreach(int item in arr) { Console.Write(item + " "); } Console.WriteLine(""); }
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