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("");
    }