排列与组合在C＃ [英] Permutation and Combination in C#

问题描述

请告诉我怎样可以申请排列组合在C＃控制台应用程序，并采取N个值和R，并计算排列组合。

Please tell me how can I apply permutation and combination in C# console application and take values of N and r and calculate permutation and combination.

推荐答案

我刚刚有了一个去这样做为了好玩，它实际上是一个小的挑战，一个天真的执行溢出长非常快。我已经包括那些评论。

I just had a go doing this for fun, it's actually a little challenge as a naive implementation overflows long very quickly. I've included those in comments.

nPr = n! / (n - r)!
nCr = n! / r! (n - r)!

Implementaion

Implementaion

public static class PermutationsAndCombinations
{
    public static long nCr(int n, int r)
    {
        // naive: return Factorial(n) / Factorial(r) * Factorial(n - r);
        return nPr(n, r) / Factorial(r);
    }

    public static long nPr(int n, int r)
    {
        // naive: return Factorial(n) / Factorial(n - r);
        return FactorialDivision(n, n - r);
    }

    private static long FactorialDivision(int topFactorial, int divisorFactorial)
    {
        long result = 1;
        for (int i = topFactorial; i > divisorFactorial; i--)
            result *= i;
        return result;
    }

    private static long Factorial(int i)
    {
        if (i <= 1)
            return 1;
        return i * Factorial(i - 1);
    }
}

用法

Usage

Console.WriteLine(PermutationsAndCombinations.nPr(10, 3));
Console.WriteLine(PermutationsAndCombinations.nCr(10, 3));

打印：

Prints:

720
120

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