bzoj3051: [wc2013]平面图

Description

 

Input

Output

扫描线求出平面图的对偶图然后求最小生成树，用并查集按秩合并，以便查询两点间路径最大权

#include<stdio.h>
#include<algorithm>
#include<vector>
#include<set>
#include<cmath>
int f[200007],f2[200007],h2[200007];
int get(int*f,int x){
    int a=x,c;
    while(x!=f[x])x=f[x];
    while(x!=f[a])c=f[a],f[a]=x,a=c;
    return x;
}
int get2(int x){
    while(x!=f2[x])x=f2[x];
    return x;
}
void merge(int a,int b){
    a=get(f,a);b=get(f,b);
    if(a<b)f[b]=a;
    else f[a]=b;
}
double X;
struct ln{
    double k,b;int id;
    double operator()(double x)const{return k*x+b;}
    bool operator<(ln w)const{return operator()(X)+1e-8<w(X);}
};
std::set<ln>line;
struct pos{
    double x,y;
    void R(){
        scanf("%lf%lf",&x,&y);
    }
}ps[100007],qs[100007][2];
struct dir{
    double d;
    int i1,i2;
    bool operator<(dir w)const{return d<w.d;}
};
std::vector<dir>vs[100007];
struct ev{
    int t;
    double x;
    int w;
    bool operator<(ev a)const{return x!=a.x?x<a.x:t<a.t;}
}e[500007];
int ep=0,ee[200007];
int n,m,q;
struct edge{
    int a,b,c,ID;
    ln l;
    void R(int I){
        ID=I;
        scanf("%d%d%d",&a,&b,&c);
        if(ps[a].x>ps[b].x)std::swap(a,b);
        if(ps[a].x!=ps[b].x){
            e[ep++]=(ev){1,ps[a].x,I};
            e[ep++]=(ev){0,ps[b].x,I};
            double k=(ps[b].y-ps[a].y)/(ps[b].x-ps[a].x);
            l=(ln){k,ps[a].y-ps[a].x*k,I};
        }
        vs[a].push_back((dir){atan2(ps[b].y-ps[a].y,ps[b].x-ps[a].x),I,I+m});
        vs[b].push_back((dir){atan2(ps[a].y-ps[b].y,ps[a].x-ps[b].x),I+m,I});
    }
    bool operator<(const edge&w)const{return c<w.c;}
}es[100007];
int ws[100007][2];
void maxs(int&a,int b){if(a<b)a=b;}
int main(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m*2;++i)f[i]=f2[i]=i;
    for(int i=1;i<=n;++i)ps[i].R();
    for(int i=1;i<=m;++i)es[i].R(i);
    scanf("%d",&q);
    for(int i=1;i<=q;++i){
        qs[i][0].R();
        qs[i][1].R();
        e[ep++]=(ev){2,qs[i][0].x,i};
        e[ep++]=(ev){3,qs[i][1].x,i};
    }
    std::sort(e,e+ep);
    e[ep].x=e[ep-1].x+10000;
    double x0=e[0].x-10000,x1;
    for(int i=0,j=0;i<ep;){
        x1=e[i].x;
        for(;j<ep&&e[j].x==x1;++j);
        X=(x0+x1)/2.;
        for(;i<j&&e[i].t==0;++i){
            std::set<ln>::iterator it=line.find(es[e[i].w].l);
            line.erase(it);
        }
        X=(x1+e[j].x)/2.;
        for(int k=i;k<j&&e[k].t==1;++k){
            ln w=es[e[k].w].l;
            line.insert(w);
        }
        for(;i<j&&e[i].t==1;++i){
            ln w=es[e[i].w].l;
            std::set<ln>::iterator it=line.find(w);
            ++it;
            if(it==line.end())merge(0,e[i].w+m);
            else merge(e[i].w+m,it->id);
            --it;
            if(it==line.begin())merge(0,e[i].w);
            else --it,merge(e[i].w,it->id+m);
        }
        X=x1;
        for(;i<j;++i){
            ln w=(ln){0,qs[e[i].w][e[i].t-2].y,0};
            std::set<ln>::iterator it=line.lower_bound(w);
            if(it!=line.end())ws[e[i].w][e[i].t-2]=it->id;
        }
        x0=x1;
    }
    for(int i=1;i<=n;++i)if(!vs[i].empty()){
        std::sort(vs[i].begin(),vs[i].end());
        vs[i].push_back(vs[i][0]);
        for(int j=1;j<vs[i].size();++j){
            merge(vs[i][j-1].i2,vs[i][j].i1);
        }
    }
    std::sort(es+1,es+m+1);
    for(int i=1;i<=m;++i){
        int x=get2(get(f,es[i].ID));
        int y=get2(get(f,es[i].ID+m));
        if(x&&y&&x!=y){
            if(h2[x]<h2[y])f2[x]=y,ee[x]=es[i].c;
            else{
                if(h2[x]==h2[y])++h2[x];
                f2[y]=x;ee[y]=es[i].c;
            }
        }
    }
    for(int i=1;i<=q;++i){
        int x=get(f,ws[i][0]),y=get(f,ws[i][1]);
        if(!x||!y)puts("-1");
        else{
            int v=0;
            while(x!=y){
                if(h2[x]>h2[y])std::swap(x,y);
                maxs(v,ee[x]);
                x=f2[x];
            }
            printf("%d\n",v);
        }
    }
    return 0;
}