【二分】【半平面交】Gym

发现炸毁的瞭望塔必然是连续的，其余下的部分是一个半平面。

二分答案，枚举所有可能的炸毁情况，做个半平面交，如果交出来面积是0，就可以保证不存在安全区域。

#include<cstdio>
#include<cmath>
#include<algorithm>
#include<cstring>
using namespace std;
#define EPS 0.0000001
#define N 50010
typedef double db;
const db PI=acos(-1.0);
struct Point{db x,y;};
typedef Point Vector;
Vector operator - (const Point &a,const Point &b){return (Vector){a.x-b.x,a.y-b.y};}
Vector operator * (const Vector &a,const db &k){return (Vector){a.x*k,a.y*k};}
Vector operator + (const Vector &a,const Vector &b){return (Vector){a.x+b.x,a.y+b.y};}
db Cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}
struct Line
{
    Point p; Vector v; db ang;
    Line(){}
    Line(const Point &a,const Point &b)
      {
        v=b-a;
        p=a;
        ang=atan2(v.y,v.x);
        if(ang<0) ang+=2.0*PI;
      }
};
bool operator < (const Line &a,const Line &b){return a.ang<b.ang;}
bool OnLeft(Line l,Point a){return Cross(l.v,a-l.p)>0;}
Point GetJiaodian(Line a,Line b){return a.p+a.v*(Cross(b.v,a.p-b.p)/Cross(a.v,b.v));}
int n;
Point ps[N];
Line q[N];
Line ls[N];
int nn;
Point a[N];
#define INF 10000000000.0
bool BPMJ(int x)
{
	int head=1,tail=1;
	n=0;
	memset(q,0,sizeof(q));
	memset(ps,0,sizeof(ps));
	for(int i=nn;i>=x+2;--i){
		ls[++n]=Line(a[i],a[i-x-1]);
	}
	for(int i=x+1,j=0;i>=1;++j,--i){
		ls[++n]=Line(a[i],a[nn-j]);
	}
//    ls[++n]=Line((Point){INF,INF},(Point){-INF,INF});
//    ls[++n]=Line((Point){-INF,INF},(Point){-INF,-INF});
//    ls[++n]=Line((Point){-INF,-INF},(Point){INF,-INF});
//    ls[++n]=Line((Point){INF,-INF},(Point){INF,INF});
    sort(ls+1,ls+n+1);
    q[1]=ls[1];
    for(int i=2;i<=n;++i)
      {
        while(head<tail&&(!OnLeft(ls[i],ps[tail-1]))) --tail;
        while(head<tail&&(!OnLeft(ls[i],ps[head]))) ++head;
        q[++tail]=ls[i];
        if(fabs(Cross(q[tail].v,q[tail-1].v))<EPS)
          {
            --tail;
            if(OnLeft(q[tail],ls[i].p))
              q[tail]=ls[i];
          }
        if(head<tail)
          ps[tail-1]=GetJiaodian(q[tail-1],q[tail]);
      }
    while(head<tail&&(!OnLeft(q[head],ps[tail-1]))) --tail;
    if(tail-head<=1){
    	return 1;
    }
    ps[tail]=GetJiaodian(q[tail],q[head]);
    return head>tail;
}
int main()
{
	freopen("jungle.in","r",stdin);
	freopen("jungle.out","w",stdout);
    scanf("%d",&nn);
    for(int i=1;i<=nn;++i) scanf("%lf%lf",&a[i].x,&a[i].y);
    int l=1,r=nn-2;
    while(l<r){
    	int mid=(l+r>>1);
    	if(BPMJ(mid)){
    		r=mid;
    	}
    	else{
    		l=mid+1;
    	}
    }
    printf("%d
",l);
    return 0;
}