C# 排列组合

排列组合的概念

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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

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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

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    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

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    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("");    }