记忆体ncr递归阶乘问题不适用于大输入

我在计算 nck公司 使用递归和记忆的组合问题。它在小投入下运行良好。然而,对于大投入来说,这是失败的。

对于8C3,答案是56。[工作]

[10115692输出无效]

http://cpp.sh/9ijiy

#include <iostream>
#include <map>
using namespace std;

long long int calls=0; // I know global vars are bad, but, i'm only using it for checking number of recursive calls

long long int fact(int n)
{
    calls++;
    static map<int, long long int> cache = {{0,1},{1,1}}; // factorial of 0 and 1 is 1

    if(cache.find(n) == cache.end()) // if n is NOT found
    {
        long long int ans = (long long int)n*fact(n-1);
        cache.insert(pair<int, long long int>(n,ans));
    }

    return cache[n];

}
long long int combin(int n, int k)
{
    return fact(n)/(fact(n-k)*fact(k));
}
int main()
{
    calls=0; cout << "8C3 is " << combin(8,6) << endl;
    cout << "Number of calls is " << calls << endl;

    calls=0; cout << "156C12 is " << combin(156,12) << endl;
    cout << "Number of calls is " << calls << endl;

    return 0;
}