POJ3335(半平面交)

POJ3335

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半平面交裸题

//poj3335
#include <cstdio>
#include <cmath>
#include <algorithm>
#define rep(i,a,b) for(int i=a;i<=b;++i)
const double eps = 1e-8;
const double inf = 1e20;
const double pi = acos(-1.0);
const int maxp = 50110;using namespace std;int sgn(double x) {if(fabs(x) < eps) return 0;if(x < 0) return -1;else return 1;
}struct Point {double x,y;Point(){}Point(double _x,double _y){x=_x;y=_y;}void input() {scanf("%lf%lf",&x,&y);}bool operator == (Point b) const{return sgn(x-b.x) == 0 && sgn(y-b.y) == 0;}bool operator < (Point b) const{return sgn(x-b.x)==0?sgn(y-b.y)<0:x<b.x;}Point operator - (const Point &b) const {return Point(x-b.x,y-b.y);}double operator ^ (const Point &b) const {return x*b.y - y*b.x;}double operator * (const Point &b) const {return x*b.x + y*b.y;}Point operator * (const double &k) const {return Point(x*k,y*k);}Point operator / (const double &k) const {return Point(x/k,y/k);}Point operator + (const Point &b) const {return Point(x+b.x,y+b.y);}double len() {return hypot(x,y);}double len2() {return x*x+y*y;}double distance(Point p) {return hypot(x-p.x,y-p.y);}
};struct Line {Point s,e;Line(){}Line(Point _s,Point _e){s=_s;e=_e;}Line(double a ,double b ,double c) {if(sgn(a)==0) {s = Point(0,-c/b);e = Point(1,-c/b);}else if(sgn(b)==0) {s = Point(-c/a,0);e = Point(-c/a,1);}else {s = Point(0,-c/b);e = Point(1,(-c-a)/b);}}double length(){return s.distance(e);}bool parallel(Line v) {return sgn((e-s)^(v.e-v.s))==0;}double dispointtoline(Point p) {return fabs((p-s)^(e-s))/length();}Point lineprog(Point p) {return s + ( ((e-s)*((e-s)*(p-s)))/(e-s).len2() );}Point crosspoint(Line v) {double a1 = (v.e-v.s)^(s-v.s);double a2 = (v.e-v.s)^(e-v.s);return Point((s.x*a2-e.x*a1)/(a2-a1),(s.y*a2-e.y*a1)/(a2-a1));}int pointseg(Point p) { // update: 点在线段上return sgn((p-s)^(e-s)) == 0 && min(s.x,e.x) <= p.x && p.x <= max(s.x,e.x) && min(s.y,e.y) <= p.y && p.y <= max(s.y,e.y);}
};struct polygon {int n;Point p[maxp];Line l[maxp];void getline() {for(int i=0;i<n;++i)l[i] = Line(p[i],p[(i+1)%n]);}void input(int _n) {n = _n;rep(i,0,n-1) p[i].input();}
};struct halfplane: public Line {double angle;halfplane(){}halfplane(Point _s,Point _e) {s = _s; e = _e;}halfplane(Line v) {s = v.s; e = v.e;}void output() {printf("s: (%f,%f)\n",s.x,s.y);printf("e: (%f,%f)\n",e.x,e.y);}void calcangle() {angle = atan2(e.y-s.y,e.x-s.x);}bool operator < (const halfplane &b)const {return angle < b.angle;}
};
struct halfplanes {int n;halfplane hp[maxp];Point p[maxp];int que[maxp];int st,ed;void push(halfplane tmp) {hp[n++] = tmp;}void unique() {int m = 1;for(int i=1;i<n;++i) {if(sgn(hp[i].angle-hp[i-1].angle)!=0)hp[m++] = hp[i];else if(sgn( (hp[m-1].e-hp[m-1].s)^(hp[i].s-hp[m-1].s) ) > 0)hp[m-1] = hp[i];}n = m;}bool halfplaneinsert() {for(int i=0;i<n;++i) hp[i].calcangle();sort(hp,hp+n);unique();que[st=0] = 0;que[ed=1] = 1;p[1] = hp[0].crosspoint(hp[1]);for(int i=2;i<n;++i) {while(st<ed && sgn((hp[i].e-hp[i].s)^(p[ed]-hp[i].s))<0)ed--;while(st<ed && sgn((hp[i].e-hp[i].s)^(p[st+1]-hp[i].s))<0)st++;que[++ed] = i;if(hp[i].parallel(hp[que[ed-1]])) return false;p[ed]=hp[i].crosspoint(hp[que[ed-1]]);}while(st<ed && sgn((hp[que[st]].e-hp[que[st]].s)^(p[ed]-hp[que[st]].s))<0)ed--;while(st<ed && sgn((hp[que[ed]].e-hp[que[ed]].s)^(p[st+1]-hp[que[ed]].s))<0)st++;if(st+1>=ed) return false;return true;}void getconvex(polygon &con) {p[st] = hp[que[st]].crosspoint(hp[que[ed]]);con.n = ed-st+1;for(int j=st,i=0;j<=ed;++i,++j)con.p[i] = p[j];}
}A;
polygon P;
int n,T;
bool usd[maxp];
int main() {scanf("%d",&T);while(T--) {scanf("%d",&n);P.input(n);P.getline();A.n = 0;rep(i,0,n-1) {Line tl = P.l[i];swap(tl.s,tl.e);A.push(halfplane(tl));}if(A.halfplaneinsert()) puts("YES");else puts("NO");}return 0;
}