poj 3336 计算几何 + bfs

求出所有的交点，去重，如果是警察点，就不放入点集

再把不在线段交点上的警察点加入点集，排序

由于一个点只能和同一线段上相邻的点连边，所以枚举每条直线，相邻的点如果不是警察，建边

最后bfs判断能否搜到即可

View Code

#include <math.h>
#include <cstdio>
#include <vector>
#include <queue>
#include<algorithm>
using namespace std;
const  int maxn = 10001;
const double eps = 1e-8;
inline double sgn(double x) {return fabs(x)<eps?0:(x>0?1:-1);}
struct Point{
    double x,y;
    bool flag;
    bool operator < (const Point &p) const {
        return sgn(x-p.x)<0 || sgn(x-p.x)==0 && sgn(y-p.y)<0; 
    }
    bool operator == (const Point& t) const {
        return sgn(x-t.x)==0 && sgn(y-t.y)==0;
    }
}Po[maxn],set[maxn];
struct Seg{Point s,e;}seg[110];
struct Line {  double a, b, c;};
inline double cross(Point a,Point b,Point c){return (b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x);}
bool dotOnSeg(Point p, Point s, Point e) {                
    if ( p == s || p == e )     return true;
    return sgn(cross(s,e,p))==0 && sgn((p.x-s.x)*(p.x-e.x))<=0 && sgn((p.y-s.y)*(p.y-e.y))<=0;
} 
Line Turn(Point s, Point e) {                                    
    Line ln;
    ln.a =s.y - e.y ;
    ln.b =e.x - s.x;
    ln.c =s.x*e.y - e.x*s.y;
    return ln;
}
bool Seg_Inst(Seg s1, Seg s2, Point &p) {
    Line l1=Turn(s1.s,s1.e),l2=Turn(s2.s,s2.e);    
    double d = l1.a*l2.b - l2.a*l1.b;
    if ( sgn(d) ==0 )     return false;
    p.x = (-l1.c*l2.b + l2.c*l1.b) / d;
    p.y = (-l1.a*l2.c + l2.a*l1.c) / d;
    return dotOnSeg(p,s1.s,s1.e) && dotOnSeg(p,s2.s,s2.e);
}
bool bin(Point p[],int n,Point x){
    int l=0,r=n-1,mid;
    while(l<=r){
        mid=(l+r)>>1;
        if(p[mid]==x) return true;
        if(p[mid]<x) l=mid+1;
        else r=mid-1;
    }
    return false;
}
int t,n,m,tot;
Point from,to;
void init(){
    int i,j,k;
    scanf("%d%d",&n,&m);
    scanf("%lf%lf%lf%lf",&from.x,&from.y,&to.x,&to.y);
    for(i=0;i<n;i++)
        scanf("%lf%lf%lf%lf",&seg[i].s.x,&seg[i].s.y,&seg[i].e.x,&seg[i].e.y);
    for(i=0;i<m;i++){
        scanf("%lf%lf",&Po[i].x,&Po[i].y);
        Po[i].flag=true;
    }
    sort(Po,Po+m);
    tot=0;set[tot++]=from;set[tot++]=to;
    for(i=0;i<n;i++){
        for(j=i+1;j<n;j++){
            Point tmp;
            if(Seg_Inst(seg[i],seg[j],tmp))    set[tot++]=tmp;
        }
    }
    sort(set,set+tot);
    for(i=j=0;i<tot;i++){    
        if(!bin(Po,m,set[i]))
    if(i==0||!(set[i]==set[i-1]))
        set[j++]=set[i];
    }
    tot=j;
    for(i=0;i<tot;i++)set[i].flag=false;
    for(i=0;i<m;i++){
        int cnt=0;
        for(j=0;j<n;j++)
            if(dotOnSeg(Po[i],seg[j].s,seg[j].e))    cnt++;
        if(cnt==1)  set[tot++]=Po[i];
    }
    sort(set,set+tot);
}
vector<int> edge[maxn];
vector<int> dot_set_onseg[maxn];
void build(){
    int i,j,k;
    for(i=0;i<=n;i++) dot_set_onseg[i].clear();
    for(i=0;i<=tot;i++) edge[i].clear();
    for(i=0;i<n;i++)
        for(j=0;j<tot;j++)
            if(dotOnSeg(set[j],seg[i].s,seg[i].e))
                dot_set_onseg[i].push_back(j);
    for(i=0;i<n;i++){
        int SIZE=dot_set_onseg[i].size();
        for(j=0;j<SIZE-1;j++){
            while(j<SIZE-1&&set[dot_set_onseg[i][j]].flag) j++;
            if(j==SIZE-1) break;
            if(!set[dot_set_onseg[i][j+1]].flag){
                int a=dot_set_onseg[i][j];
                int b=dot_set_onseg[i][j+1];
                edge[a].push_back(b);
                edge[b].push_back(a);
            }
        }
    }
}
int vis[maxn];
bool bfs(){
    memset(vis,0,sizeof(vis));
    int st=lower_bound(set,set+tot,from)-set;
    int ed=lower_bound(set,set+tot,to)-set;
    queue<int> Q;
    Q.push(st);vis[st]=1;
    while(!Q.empty()){
        int fr=Q.front();Q.pop();
        for(int i=0;i<edge[fr].size();i++){
            if(vis[edge[fr][i]]) continue;
            if(edge[fr][i]==ed) return true;
            Q.push(edge[fr][i]);
            vis[edge[fr][i]]=1;
        }
    }
    return false;
}
int main(){
    scanf("%d",&t);
    while(t--){
        init();
        build();
        if(bfs()) printf("YES\n");
        else printf("NO\n");
    }
    return 0;
}