bzoj2820 分类： bzoj 2015-06-02 14:02 26人阅读 评论(0) 收藏

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http://blog.csdn.net/weixinding/article/details/7621103
http://blog.csdn.net/z690933166/article/category/1349672

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莫比乌斯反演+容斥原理，好神奇！

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#include<map>
#include<stack>
#include<queue>
#include<ctime>
#include<cmath>
#include<string>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<utility>
#include<iostream>
#include<algorithm>

const int SIZE = 1e7+5;

int mu[SIZE], g[SIZE], prime[SIZE>>4], tot;
bool check[SIZE];  int sum[SIZE];

void PreWork()
{
    sum[1] = g[1] = 0, mu[1] = 1;

    for(int i = 2; i < SIZE; i++)   
    {
        if(!check[i]) prime[++tot] = i, mu[i] = -1, g[i] = 1;

        sum[i] = sum[i-1] + g[i];

        for(int j = 1, t; j <= tot && (t = prime[j]*i) < SIZE; j++)
        {
            check[t] = true;

            if(i%prime[j]) mu[t] = -mu[i], g[t] = mu[i] - g[i];
            else {mu[t] = 0, g[t] = mu[i]; break;}
        }
    }   
}

long long Count(int p,int q)
{
    long long ret = 0;

    if(p > q) std::swap(p,q);

    for(int i = 1, next = 0; i <= p; i = next+1)
    {
        next = std::min(p/(p/i), q/(q/i));
        ret += (long long)(sum[next]-sum[i-1])*(p/i)*(q/i);
    }
    return ret;
}

int main()
{
    int T;

#ifndef ONLINE_JUDGE
    freopen("bzoj2820.in","r",stdin);
    freopen("bzoj2820.out","w",stdout);
#endif

    scanf("%d",&T);

    PreWork();

    while(T--)
    {
        int m, n;long long ans;

        scanf("%d%d",&m,&n);

        printf("%lld\n",Count(m,n)); 
    }

#ifndef ONLINE_JUDGE
    fclose(stdin);
    fclose(stdout);
    return 0;
#endif
}

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