BZOJ 2820: YY的GCD 莫比乌斯反演_数学推导_线性筛

Code:

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <vector> 
#define maxn 10000009
const long long N = 10000009 ; 
#define ll long long 
#define setIO(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)  
using namespace std; 
int vis[maxn],prime[maxn],mu[maxn],g[maxn],tot; 
long long sumv[maxn]; 
void init(){
    mu[1]=1; 
    for(int i=2;i<maxn;++i) {
        if(!vis[i]) { prime[++tot]=i,mu[i]=-1; }
        for(int j=1;j<=tot && (ll)prime[j]*i < (ll)maxn;++j) 
        {
            vis[prime[j]*i]=1; 
            if(i % prime[j]==0) {
                mu[i * prime[j]]=0; 
                break; 
            }
            mu[i * prime[j]]=-mu[i]; 
        }
    } 
    for(int i=1;i<=tot;++i)
        for(ll j=1;(ll)j*prime[i]<N;++j) 
            g[prime[i]*j]+=mu[j];
    for(int i=1;i<=10000000;++i) sumv[i] = (long long)sumv[i-1]+g[i]; 
}
ll work(int n,int m) {
    if(n>m) swap(n,m); 
    long long ans=0; 
    for(ll i=1,j;i<=n;i=j+1) {
        j = min(n/(n/i),m/(m/i)); 
        ans += (n/i) * (m/i) * (sumv[j] - sumv[i-1]); 
    }
    return ans; 
}
int main(){
    //setIO("input");
    init();  
    int T,x,y; scanf("%d",&T);
    while(T--) scanf("%d%d",&x,&y),printf("%lld\n",work(x,y));  
    return 0; 
}