POJ3335(半平面交)

Posted 2020-12-26 rrrr-wys

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)
",s.x,s.y);
        printf("e: (%f,%f)
",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;
}