C#實現排列組合演算法

數學中排列組合,排列P（N，R）

其實排列實現了，組合也就實現了組合C(N,R)就是P(N,R)/P(R,R) ，比較簡單的是遞迴演算法，但考慮到遞迴的效能，下面採用了2種非遞迴的方法，代碼如下

using System;using System.Collections.Generic;namespace Test{    class Program     {        static void Main(string[] args)        {            Console.WriteLine(P1(6, 3));            Console.WriteLine(P2(6, 3));            Console.WriteLine(C(6, 2));        }        /// <summary>        /// 排列迴圈方法        /// </summary>        /// <param name="N"></param>        /// <param name="R"></param>        /// <returns></returns>        static long P1(int N, int R)        {            if (R > N || R <= 0 || N <= 0 ) throw new ArgumentException("params invalid!");            long t = 1;            int i = N;                        while (i!=N-R)            {                try                {                    checked                    {                        t *= i;                    }                }                catch                {                    throw new OverflowException("overflow happens!");                }                --i;            }            return t;        }        /// <summary>        /// 排列堆棧方法        /// </summary>        /// <param name="N"></param>        /// <param name="R"></param>        /// <returns></returns>        static long P2(int N, int R)        {            if (R > N || R <= 0 || N <= 0 ) throw new ArgumentException("arguments invalid!");            Stack<int> s = new Stack<int>();            long iRlt = 1;            int t;            s.Push(N);            while ((t = s.Peek()) != N - R)            {                try                {                    checked                    {                        iRlt *= t;                    }                }                catch                {                    throw new OverflowException("overflow happens!");                }                s.Pop();                s.Push(t - 1);            }            return iRlt;        }        /// <summary>        /// 組合        /// </summary>        /// <param name="N"></param>        /// <param name="R"></param>        /// <returns></returns>        static long C(int N, int R)        {            return P1(N, R) / P1(R, R);        }    }    }