UVaLive4992:Jungle Outpost

传送门

半平面交。

首先，由显然成立法可以证明炸连续的几个总比分散火力效果更佳。

所以二分答案，转化为判定问题，即间隔$ans$个点的连线的半平面交是否为空。

半平面交判定即可。

时间复杂度：$O(Nlog^2N)$

//UVaLive4992
//by Cydiater
//2017.2.1
#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <cmath>
#include <ctime>
#include <cstdlib>
#include <queue>
#include <map>
#include <algorithm>
#include <iomanip>
#include <bitset>
#include <set>
#include <vector>
using namespace std;
#define ll 		long long
#define up(i,j,n)	for(int i=j;i<=n;i++)
#define down(i,j,n)	for(int i=j;i>=n;i--)
#define cmax(a,b)	a=max(a,b)
#define cmin(a,b)	a=min(a,b)
#define db		double
#define Vector 		Point
const int MAXN=1e5+5;
const int oo=0x3f3f3f3f;
const db eps=1e-10;
inline int read(){
	char ch=getchar();int x=0,f=1;
	while(ch>'9'||ch<'0'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
int dcmp(db x){if(fabs(x)<eps)return 0;else return x<0?-1:1;}
struct Point{
	db x,y;
	Point(db x=0,db y=0):x(x),y(y){}
};
Vector operator + (Point x,Point y){return Vector(x.x+y.x,x.y+y.y);}
Vector operator - (Point x,Point y){return Vector(x.x-y.x,x.y-y.y);}
Vector operator * (Vector x,db p){return Vector(x.x*p,x.y*p);}
Vector operator / (Vector x,db p){return Vector(x.x/p,x.y/p);}
bool operator < (const Vector &x,const Vector &y){return dcmp(x.x-y.x)==0?x.y<y.y:x.x<y.x;}
bool operator == (const Vector &x,const Vector &y){return dcmp(x.x-y.x)==0&&dcmp(x.y-y.y)==0;}
struct Line{
	Point P;
	Vector v;
	db ang;
	Line(){}
	Line(Point P,Vector v):P(P),v(v){ang=atan2(v.y,v.x);}
};
bool operator < (const Line &x,const Line &y){return x.ang<y.ang;}
Point V[MAXN],P[MAXN];
int N,top,head,tail;
Line L[MAXN],q[MAXN];
namespace solution{
	Point Write(){db x=read(),y=read();return Point(x,y);}
	db Cross(Vector x,Vector y){return x.x*y.y-x.y*y.x;}
	bool Onleft(Point P,Line Li){return dcmp(Cross(P-Li.P,Li.v))<0;}
	void Prepare(){
		V[0]=Write();
		down(i,N-1,1)V[i]=Write();
	}
	void Modify(int siz){
		up(i,0,N-1)L[i]=Line(V[i],V[(i+siz)%N]-V[i]);
	}
	Point LineMeet(Line x,Line y){
		db t=Cross(y.v,x.P-y.P)/Cross(x.v,y.v);
		return x.P+x.v*t;
	}
	bool check(){
		head=1;tail=0;q[++tail]=L[0];
		up(i,1,N-1){
			while(head<tail&&!Onleft(P[tail-1],L[i]))tail--;
			while(head<tail&&!Onleft(P[head],L[i]))head++;
			q[++tail]=L[i];
			if(dcmp(q[tail-1].ang-q[tail].ang)==0){
				tail--;
				if(Onleft(L[i].P,q[tail]))q[tail]=L[i];
			}
			if(head<tail)P[tail-1]=LineMeet(q[tail-1],q[tail]);
		}
		while(head<tail&&!Onleft(P[tail-1],q[head]))tail--;
		return tail-head>1;
	}
	void Solve(){
		int leftt=0,rightt=N-1,mid;
		while(leftt+1<rightt){
			mid=(leftt+rightt)>>1;
			Modify(mid);
			if(check())	leftt=mid;
			else		rightt=mid;
		}
		Modify(rightt);
		if(check())	cout<<rightt<<endl;
		else		cout<<leftt<<endl;
	}
}
int main(){
	//freopen("input.in","r",stdin);
	using namespace solution;
	while(scanf("%d",&N)!=EOF){
		Prepare();
		Solve();
	}
	return 0;
}