POJ-2773 Happy 2006(容斥版)

题意：给出，m和k，求第k个与m互质的数。m (1 <= m <= 1000000), K (1 <= K <= 100000000).

思路：容斥+二分，很巧妙的方法。

View Code

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstdlib>
 4 #include <cmath>
 5 #include <cstring>
 6 #include <string>
 7 #include <algorithm>
 8 #include <vector>
 9 using namespace std;
10 #define LL long long
11 
12 LL m,k;
13 vector<LL>v;
14 
15 LL solve(LL x,LL n){
16     v.clear();
17     for(int i=2;i*i<=x;i++)
18         if(x%i==0){
19             v.push_back(i);
20             while(x%i==0) x/=i;
21         }
22     if(x>1) v.push_back(x);
23     LL sum=0;
24     for(LL i=1;i<1<<v.size();i++){
25         LL val=1,cnt=0;
26         for(LL j=0;j<v.size();j++){
27             if(i&1<<j){
28                 val*=v[j];
29                 cnt++;
30             }
31         }
32         if(cnt&1) sum+=n/val;
33         else sum-=n/val;
34     }
35     return n-sum;
36 }
37 
38 int main(){
39     
40 //    freopen("data.in","r",stdin);
41 //    freopen("data.out","w",stdout);
42     
43     while(scanf("%lld%lld",&m,&k)!=EOF){
44         LL l=1,r=1LL<<62;
45         LL ans;
46         while(l<=r){
47             LL mid=(l+r)>>1;
48             LL num=solve(m,mid);
49             if(num>=k){
50                 r=mid-1;
51                 if(num==k) ans=mid;
52             }
53             else l=mid+1;
54         }
55         printf("%lld\n",ans);
56     }
57     return 0;
58 }

posted @ 2012-10-11 19:20 Hug_Sea 阅读(197) 评论(0) 收藏举报

刷新页面返回顶部