UVaLive4992:Jungle Outpost
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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; }
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