Codeforces 776E The Holmes Children

题目链接：http://codeforces.com/problemset/problem/776/E

${\because gcd(i,n-i)=1\Leftrightarrow gcd(i,n)=1}$

${\therefore f(x)=\phi (x)}$

${\because \sum_{d|x}\phi(d)=x}$

${\therefore g(x)=x}$

问题转换为求${\phi(\phi(\phi(...)))}$嵌套${\left \lfloor \frac{k}{2} \right \rfloor}$层。

考虑这样的嵌套至多${log}$次就会到$1$，所以直接暴力做就可以了。

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<algorithm>
 4 #include<vector>
 5 #include<cstdlib>
 6 #include<cmath>
 7 #include<cstring>
 8 using namespace std;
 9 #define maxn 10010
10 #define llg long long 
11 #define md 1000000007
12 #define yyj(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout);
13 
14 
15 llg phi(llg x)
16 {
17     llg m=sqrt(x+0.5);
18     llg ans=x;
19     for (llg i=2;i<=m;i++)
20         if (x%i==0)
21         {
22             ans=ans/i*(i-1);
23             while (x%i==0) x/=i;
24         }
25     if (x>1) ans=ans/x*(x-1);
26     return ans;
27 }
28 llg n,m,k;
29 
30 int main()
31 {
32     yyj("E");
33     cin>>n>>k;
34     llg ans=phi(n);
35     for (llg i=2;i<=k;i++)
36     {
37         if (i%2) ans=phi(ans);
38         if (ans==phi(ans)) break;
39     }
40     cout<<ans%md;
41     return 0;
42 }

 

posted @ 2017-02-24 10:28  №〓→龙光←  阅读(417)  评论(0)  编辑  收藏  举报