USACO 3.2 Factorials

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

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以为一个个把个位乘起来%10就好了，然并不，有些时候
例如75*4和74*14的最右非零位是不一样的，其实我们只需要手动去除2和5这两个质因子剩下的乘起来%10就可以了
纪念我的智障……

 /*
 ID: ivorysi
 PROG: fact4
 LANG: C++
 */
 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <queue>
 #include <set>
 #include <vector>
 #define siji(i,x,y) for(int i=(x);i<=(y);++i)
 #define gongzi(j,x,y) for(int j=(x);j>=(y);--j)
 #define xiaosiji(i,x,y) for(int i=(x);i<(y);++i)
 #define sigongzi(j,x,y) for(int j=(x);j>(y);--j)
 #define inf 0x7fffffff
 #define MAXN 400005
 #define ivorysi
 #define mo 97797977
 #define ha 974711
 #define ba 47
 #define fi first
 #define se second
 //#define pis pair<int,string>
 using namespace std;
 typedef long long ll;
 int two,five;
 int n;
 int ans=;
 void divide(int &u) {
     while(u%==) {++five;u/=;}
     while(u%==) {++two;u/=;}
 }
 void solve() {
     scanf("%d",&n);
     siji(i,,n) {
         int tmp=i;
         divide(tmp);
         ans=(ans*tmp+)%;
     }
     two-=five;
     siji(i,,two) ans=ans*%;
     printf("%d\n",ans);
 }
 int main(int argc, char const *argv[])
 {
 #ifdef ivorysi
     freopen("fact4.in","r",stdin);
     freopen("fact4.out","w",stdout);
 #else
     //freopen("f1.in","r",stdin);
 #endif
     solve();
 }