Question

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

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.

Answer 1

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)) );
}

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.

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.