C#实现排列组合算法

数学中排列组合,排列P（N，R）

其实排列实现了，组合也就实现了组合C(N,R)就是P(N,R)/P(R,R) ，比较简单的是递归算法，但考虑到递归的性能，下面采用了2种非递归的方法，代码如下

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>
        /// 排列循环方法
        /// </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>
        /// 排列堆栈方法
        /// </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>
        /// 组合
        /// </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);
        }
    }
    
}