C ++程序计算大阶乘的商 [英] C++ program to calculate quotients of large factorials

问题描述

我如何编写一个c ++程序来计算大阶乘。

How can I write a c++ program to calculate large factorials.

例如，如果我想计算（100！）/答案是100，但如果我分别计算分子和分母的阶乘，这两个数字是巨大的。

Example, if I want to calculate (100!) / (99!), we know the answer is 100, but if i calculate the factorials of the numerator and denominator individually, both the numbers are gigantically large.

推荐答案

Dirk的答案（其中imo是正确的答案）：

expanding on Dirk's answer (which imo is the correct one):

#include "math.h"
#include "stdio.h"
int main(){
  printf("%lf\n", (100.0/99.0) * exp(lgamma(100)-lgamma(99)) );
}

尝试，它真的做你想要的，即使它看起来有点疯狂，如果你不熟悉它。使用bigint库将是非常低效的。拍摄日志的速度是超快的。这运行瞬间。

try it, it really does what you want even though it looks a little crazy if you are not familiar with it. Using a bigint library is going to be wildly inefficient. Taking exps of logs of gammas is super fast. This runs instantly.

您需要乘以100/99的原因是gamma等于n-1！不是n！所以是的，你可以只做exp（lgamma（101）-lgamma（100））。此外，gamma定义的不仅仅是整数。

The reason you need to multiply by 100/99 is that gamma is equivalent to n-1! not n!. So yeah, you could just do exp(lgamma(101)-lgamma(100)) instead. Also, gamma is defined for more than just integers.

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