admin管理员组

文章数量:1594236

H - Interesting Numbers

  URAL - 2070 

Nikolay and Asya investigate integers together in their spare time. Nikolay thinks an integer is interesting if it is a prime number. However, Asya thinks an integer is interesting if the amount of its positive divisors is a prime number (e.g., number 1 has one divisor and number 10 has four divisors). Nikolay and Asya are happy when their tastes about some integer are common. On the other hand, they are really upset when their tastes differ. They call an integer satisfying if they both consider or do not consider this integer to be interesting. Nikolay and Asya are going to investigate numbers from segment [  L;  R] this weekend. So they ask you to calculate the number of satisfying integers from this segment.
Input
In the only line there are two integers  L and  R (2 ≤  L ≤  R ≤ 10  12).
Output
In the only line output one integer — the number of satisfying integers from segment [  L;  R].
Example
input output
3 7

4

2 2

1

77 1010

924

题目链接：https://cn.vjudge/contest/160744#problem/H


不难的一个数论题，题目的意思是说让你求在L,R区间里，同时满足或者同事不满足素数和这个数的约数个数是素数的要求的数的个数。。有点绕。

我们先用素数筛求出1e6以内的素数，然后我们用唯一分解定理来求约数个数

代码：

#include <cstdio>
#include <cstring>
#include <iostream>
#define LL long long
using namespace std;
const int maxn=1000010;
LL vis[maxn];
LL p[maxn];
int sum;
void getprime(){
    sum=1;
    for(LL i=2;i<=maxn;i++){
        if(vis[i]==0){
            p[sum++]=i;
            for(LL j=i*2;j<=maxn;j+=i){
                vis[j]=1;
            }
        }
    }
}
LL solve(LL x){
    LL ret=x;
    for(int i=1;i<sum;i++){
        LL t=(LL)p[i]*p[i];
        int k=2;
        for(;t<=x;k++,t=t*p[i]){
            if(!vis[k+1]){//判断2条件是不是满足
                ret--;//只满足一个条件
            }
        }
    }
    return ret;
}
int main(){
    getprime();
    LL L,R;
    while(~scanf("%lld%lld",&L,&R)){
        LL ans=solve(R)-solve(L-1);
        cout<<ans<<endl;
    }
    return 0;
}


本文标签： 素数定理分解NUMBERSInteresting

版权声明：本文标题：H - Interesting Numbers URAL - 2070 ----素数筛+唯一分解定理 内容由热心网友自发贡献，该文观点仅代表作者本人， 转载请联系作者并注明出处：https://www.elefans.com/dianzi/1728179885a1148290.html， 本站仅提供信息存储空间服务，不拥有所有权，不承担相关法律责任。如发现本站有涉嫌抄袭侵权/违法违规的内容，一经查实，本站将立刻删除。