bzoj2301: [HAOI2011]Problem b

Posted 2020-08-08 BBChq

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莫比乌斯反演学姿势

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define rep(i,s,t) for(int i=s;i<=t;i++)
#define dwn(i,s,t) for(int i=s;i>=t;i--)
#define clr(x,c) memset(x,c,sizeof(x))
#define ll long long
int read(){
    int x=0;char c=getchar();
    while(!isdigit(c)) c=getchar();
    while(isdigit(c)) x=x*10+c-‘0‘,c=getchar();
    return x;
}
const int nmax=50005;
int mo[nmax],prime[nmax],cnt=0;bool vis[nmax];
void init(){
    mo[1]=1;
    rep(i,2,nmax-1){
        if(!vis[i]) prime[++cnt]=i,mo[i]=-1;
        rep(j,1,cnt){
            if(i*prime[j]>=nmax) break;
            vis[i*prime[j]]=1;
            if(i%prime[j]==0){
                mo[i*prime[j]]=0;break;
            }
            mo[i*prime[j]]=-mo[i];
        }
    }
    rep(i,2,nmax-1) mo[i]+=mo[i-1];
}
/*void init(){
    mo[1]=1;
    rep(i,2,nmax-1){
        if(!vis[i]) prime[++cnt]=i,mo[i]=-1;
        rep(j,1,cnt){
            int tmp=prime[j];
            if(i*tmp>=nmax) break;
            vis[i*tmp]=1;
            if(i%tmp==0) {
                mo[i*tmp]=0;break;
            }
            mo[i*tmp]=-mo[i];
        }
    }
    rep(i,2,nmax-1) mo[i]+=mo[i-1];
}*/
ll cal(int n,int m,int k){
    ll ans=0;n/=k;m/=k;
    int last,t=min(n,m);
    for(int i=1;i<=t;i=last+1){
        last=min(n/(n/i),m/(m/i));
        ans+=(ll)(m/i)*(n/i)*(mo[last]-mo[i-1]);
    }
    return ans;
}
int main(){
    init();
    int n=read(),a,b,c,d,k;
    rep(i,1,n){
        a=read(),b=read(),c=read(),d=read();k=read();
        printf("%lld\n",cal(b,d,k)-cal(b,c-1,k)-cal(a-1,d,k)+cal(a-1,c-1,k));
    }
    return 0;
}