【计算几何】【凸包】【极角排序】【二分】Gym - 101128J - Saint John Festival

#include<cstdio>
#include<algorithm>
#include<cmath>
using namespace std;
typedef long long ll;
int n,m,K,O;
struct Point{
	ll x,y;
	double jiao;
	Point(){}
	Point(const ll &x,const ll &y){
		this->x=x;
		this->y=y;
	}
	void Read(){
		scanf("%lld%lld",&x,&y);
	}
};
typedef Point Vector;
Point p0,p;
Vector operator - (const Point &a,const Point &b){
	return Vector(a.x-b.x,a.y-b.y);
}
ll Cross(const Vector &a,const Vector &b){
	return a.x*b.y-a.y*b.x;
}
bool cmp(const Point &a,const Point &b){
	return a.x!=b.x ? a.x<b.x : a.y<b.y;
}
bool cm2(const Point &a,const Point &b){
	return a.jiao<b.jiao;
}
Point ps[10010],qs[10010];
bool check(int mid){
	return Cross(qs[mid]-p0,p-p0)<=0;
}
int main(){
//	freopen("j.in","r",stdin);
	scanf("%d",&n);
	for(int i=0;i<n;++i){
		ps[i].Read();
	}
	sort(ps,ps+n,cmp);
	for(int i=0;i<n;++i){
		while(K>1 && Cross(qs[K-1]-qs[K-2],ps[i]-qs[K-1])<=0){
			--K;
		}
		qs[K++]=ps[i];
	}
	for(int i=n-2,t=K;i>=0;--i){
		while(K>t && Cross(qs[K-1]-qs[K-2],ps[i]-qs[K-1])<=0){
			--K;
		}
		qs[K++]=ps[i];
	}
	--K;
	for(int i=1;i<K;++i){
		if(qs[i].y<qs[O].y || (qs[i].y==qs[O].y && qs[i].x<qs[O].x)){
			O=i;
		}
	}
	p0=qs[O];
	for(int i=0;i<K;++i){
		qs[i].jiao=atan2((double)(qs[i].y-qs[O].y),(double)(qs[i].x-qs[O].x));
	}
	for(int i=O;i<K-1;++i){
		qs[i]=qs[i+1];
	}
	--K;
	sort(qs,qs+K,cm2);
	scanf("%d",&m);
	int ans=0;
	for(int i=1;i<=m;++i){
		p.Read();
		if(Cross(p-p0,qs[0]-p0)<=0 && Cross(p-p0,qs[K-1]-p0)>=0){
			int l=1,r=K-1;
			while(l<r){
				int mid=(l+r>>1);
				if(check(mid)){
					r=mid;
				}
				else{
					l=mid+1;
				}
			}
			if(Cross(p-qs[l-1],qs[l]-qs[l-1])<=0){
				++ans;
			}
		}
	}
	printf("%d\n",ans);
	return 0;
}