USACO Section 3.2 Factorials（n！求最右边非零数）

Factorials

The factorial of an integer N, written N!, is the product of all the integers from 1 through N inclusive. The factorial quickly becomes very large: 13! is too large to store in a 32-bit integer on most computers, and 70! is too large for most floating-point variables. Your task is to find the rightmost non-zero digit of n!. For example, 5! = 1 * 2 * 3 * 4 * 5 = 120, so the rightmost non-zero digit of 5! is 2. Likewise, 7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040, so the rightmost non-zero digit of 7! is 4.

PROGRAM NAME: fact4

INPUT FORMAT

A single positive integer N no larger than 4,220.

SAMPLE INPUT (file fact4.in)

7

OUTPUT FORMAT

A single line containing but a single digit: the right most non-zero digit of N! .

SAMPLE OUTPUT (file fact4.out)

4
题意：求n！的最右边那个非0数字。

/*
  ID: dizzy_l1
  LANG: C++
  TASK: fact4
*/
#include<iostream>
#include<cstdio>

using namespace std;

int main()
{
    freopen("fact4.in","r",stdin);
    freopen("fact4.out","w",stdout);
    int n,i,ans,t;
    while(scanf("%d",&n)==1)
    {
        ans=1;
        for(i=2;i<=n;i++)
        {
            ans*=i;
            t=ans%10;
            while(t==0)
            {
                ans=ans/10;
                t=ans%10;
            }
            ans=ans%10000;//不能直接模10，n=15就过不了
        }
        ans=ans%10;
        printf("%d\n",ans);
    }
    return 0;
}