【USACO 3.2.1】阶乘

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cmath>
 4 #include <cstring>
 5 #include <algorithm>
 6 const int maxn=4220;
 7 using namespace std; 
 8 int cnt[maxn],vis[maxn];
 9 int prime[maxn];
10 void built_prime();//打表 
11 void check(int n);
12 int pow_mod(int num,int t);
13 int main()
14 {
15     int n,i,temp,ans=1;
16     //文件操作
17     freopen("fact4.in","r",stdin);
18     freopen("fact4.out","w",stdout);
19     built_prime();
20     //printf("1");
21     scanf("%d",&n);
22     for (i=1;i<=n;i++) check(i);//分解质因数 
23     temp=min(cnt[2],cnt[5]);
24     cnt[2]-=temp;cnt[5]-=temp;
25     for (i=1;i<=prime[0];i++)
26     {
27         if (cnt[prime[i]]!=0)
28         ans=(ans*pow_mod(prime[i],cnt[prime[i]]))%10;//快速幂取模 
29     }
30     printf("%d",ans%10);
31     return 0;
32 }
33 int pow_mod(int num,int t)
34 {
35     if (t==1) return num%10;
36     if (t==2) return (num*num)%10;
37     int temp=pow_mod(num,t/2);
38     if (t%2==0) return (temp*temp)%10;
39     else return (temp*temp*num)%10;
40 }
41 void built_prime()
42 {
43      int i,j;
44      memset(cnt,0,sizeof(cnt));
45      prime[0]=0;
46      for (i=2;i<=maxn;i++)
47      {
48          if (vis[i]==0)
49          {
50              prime[++prime[0]]=i;
51              for (j=i;j<=maxn;j+=i) vis[j]=1;
52          }
53      }
54 }
55 void check(int n)
56 {
57      int i;
58      while (n!=1)
59      {
60            for (i=1;i<=prime[0];i++)
61            if (n%prime[i]==0) {cnt[prime[i]]++;n=n/prime[i];break;}
62      }
63 }