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POJ 1912 A highway and the seven dwarfs (凸包)

 

【题目链接】 http://poj.org/problem?id=1912

 

【题目大意】

  给出一些点,表示一些屋子,这些屋子共同组成了村庄,现在要建一些高速公路
  问是否经过了村庄。

 

【题解】

  这些屋子的关键点一定在凸包上,所以我们只要求出凸包,判断是否和线相交即可
  我们求出与高速公路相近和近似相反的向量,判断连线是否与这条公路相交即可。

 

【代码】

#include <cstdio>#include <algorithm>#include <cmath>#include <vector>using namespace std;double EPS=1e-10;const double PI=acos(-1.0);double add(double a,double b){    if(abs(a+b)<EPS*(abs(a)+abs(b)))return 0;    return a+b;}struct P{    double x,y;    P(){}    P(double x,double y):x(x),y(y){}    P operator + (P p){return P(add(x,p.x),add(y,p.y));}    P operator - (P p){return P(add(x,-p.x),add(y,-p.y));}    P operator * (double d){return P(x*d,y*d);}    double dot(P p){return add(x*p.x,y*p.y);} //点积    double det(P p){return add(x*p.y,-y*p.x);}  //叉积};bool cmp_x(const P& p,const P& q){    if(p.x!=q.x)return p.x<q.x;    return p.y<q.y;  }vector<P> convex_hull(P* ps,int n){    sort(ps,ps+n,cmp_x);    int k=0;    vector<P> qs(n*2);    for(int i=0;i<n;i++){        while((k>1)&&(qs[k-1]-qs[k-2]).det(ps[i]-qs[k-1])<=0)k--;        qs[k++]=ps[i];    }    for(int i=n-2,t=k;i>=0;i--){        while(k>t&&(qs[k-1]-qs[k-2]).det(ps[i]-qs[k-1])<=0)k--;        qs[k++]=ps[i];    }qs.resize(k-1);    return qs;}double dist(P p,P q){return sqrt((p-q).dot(p-q));}double normalize(double r){	  if(r<-PI/2.0+EPS)r+=PI*2;	  return r;}double atan2(const P& p){    return normalize(atan2(p.y, p.x));}bool double_cmp(double a,double b){    return a+EPS<b;}const int MAX_N=100010;int N,n;P ps[MAX_N];double as[MAX_N];void solve(){    for(int i=0;i<N;i++)scanf("%lf%lf",&ps[i].x,&ps[i].y);    vector<P> chs;    if(N>1){        chs=convex_hull(ps,N);        n=chs.size();        chs.push_back(chs[0]);    }    for(int i=0;i<n;i++)as[i]=atan2(chs[i+1]-chs[i]);    sort(as,as+n,double_cmp);    P p1,p2;    while(~scanf("%lf%lf%lf%lf",&p1.x,&p1.y,&p2.x,&p2.y)){        if(N<2){puts("GOOD");continue;}        int x=upper_bound(as,as+n,atan2(p2-p1),double_cmp)-as;        int y=upper_bound(as,as+n,atan2(p1-p2),double_cmp)-as;        puts((((p2-p1).det(chs[x]-p1)*(p2-p1).det(chs[y]-p1)>-EPS))?"GOOD":"BAD");    }}int main(){    while(~scanf("%d",&N))solve();    return 0;}

POJ 1912 A highway and the seven dwarfs (凸包)