Gym101128J

Gym101128J

---

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0Point 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\n",ans);return 0;
}