Z函数在C中的阶乘

Question

I came across a question online - to find the Z function of the factorial of t nos (no of zeroes at the lsb end of the factorial)

#include<stdio.h>
int fact(int x)
{
    if(x==1)
        return 1;
    else
    return (x*fact(x-1));
}
int main()
{
    int t,n,k,c;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        k=fact(n);
        c=0;
        while(k%10==0)
        {
            k/=10;
            c++;
        }
        printf("%d\n",c);
    }
    return 0;
}

This is the program I made, but it's too slow. How can I do this faster?

Answer 1

Looking at your code I can think of two possible solutions at the first glance.

• change the recursive loop into an iterative loop
• use memoization to speed up calculation of already known function values (basically it works like a cache)

Memoization technique can speed up the calculation significantly, though at the cost of usage of memory. If I were you I'd do the memoization. I am very confident your code will run faster, since it is a simple factorial function (actually a classic example for memoization, like the Fibonacci numbers).