Gym101128J

Gym101128J

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二分判断点是否在凸包内，模板更新

//Gym - 101128J
#include <bits/stdc++.h>
#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 = 10110;
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;}
    double length(){
        return s.distance(e);
    }
    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() );
    }
    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];
    void input(int _n) {
        n = _n;
        rep(i,0,n-1) p[i].input();
    }
    struct cmp{
        Point p;
        cmp(const Point &p0){p=p0;}
        bool operator ()(const Point &aa,const Point &bb) {
            Point a = aa, b = bb;
            int d = sgn((a-p)^(b-p));
            if(d == 0) {
                return sgn(a.distance(p)-b.distance(p)) < 0;
            }
            return d > 0;
        }
    };
    void norm() {
        Point mi = p[0];
        for(int i=1;i<n;++i) mi = min(mi,p[i]);
        sort(p,p+n,cmp(mi));
    }
    void Graham(polygon &convex) {
        norm();
        int &top = convex.n;
        top = 0;
        if(n == 1) {
            top = 1;
            convex.p[0] = p[0];
            return;
        }
        if(n == 2) {
            top = 2;
            convex.p[0] = p[0];
            convex.p[1] = p[1];
            if(convex.p[0] == convex.p[1]) --top;
            return;
        }
        convex.p[0] = p[0];
        convex.p[1] = p[1];
        top = 2;
        rep(i,2,n-1) {
            while(top > 1 && sgn((convex.p[top-1]-convex.p[top-2])^(p[i]-convex.p[top-2])) <= 0)
                --top;
            convex.p[top++] = p[i];
        }
        if(convex.n == 2 && (convex.p[0]==convex.p[1]))convex.n--;
    }
    double getarea() {
        double sum = 0;
        rep(i,0,n-1)
            sum += (p[i]^p[(i+1)%n]);
        return fabs(sum)*0.5;
    }
    int inconvex(Point s) { //update: 逆时针凸包 边界返回2， 内部返回1，外部返回0
        Point p0 = p[0];
        Line l1(p0,p[1]),l2(p0,p[n-1]);
        if(l1.pointseg(s) || l2.pointseg(s)) return 2;
        int l = 1, r = n - 2;
        while(l <= r) {
            int mid = (l+r)/2;
            int t1 = sgn((s-p0)^(p[mid]-p0));
            int t2 = sgn((s-p0)^(p[mid+1]-p0));
            if( t1 <= 0 && t2>=0 ) {
                int t3 = sgn((s-p[mid])^(p[mid+1]-p[mid]));
                if(t3 < 0) return 1; // 在内部
                else if(t3 == 0) return 2; //在边上
                return 0;
            }
            if(t1 > 0) r = mid-1;
            else l = mid+1;
        }
        return 0;
    }
};

int n,q,ans;
polygon P,T;
int main() {
    scanf("%d",&n);
    P.input(n);
    P.Graham(T);
    scanf("%d",&q);
    while(q--) {
        Point s;
        s.input();
        ans += !!(T.inconvex(s));
    }
    printf("%d
",ans);
    return 0;
}