BZOJ1038: [ZJOI2008]瞭望塔

//BZOJ1038
//by Cydiater
//2017.2.1
#include <iostream>
#include <map>
#include <ctime>
#include <cmath>
#include <queue>
#include <cstdlib>
#include <cstdio>
#include <iomanip>
#include <cstring>
#include <string>
#include <algorithm>
#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=1e3+5;
const db oo=1e15;
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;}
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;}
int N,head,tail,top1,top2,pos;
Point P[MAXN],ch1[MAXN],ch2[MAXN];
db ans=oo;
Line L[MAXN],q[MAXN],lh1[MAXN],lh2[MAXN];
namespace solution{
db Cross(Vector x,Vector y){return x.x*y.y-x.y*y.x;}
bool Onleft(Point p,Line l){return dcmp(Cross(p-l.P,l.v))<=0;}
db Dot(Vector x,Vector y){return x.x*y.x+x.y*y.y;}
db Len(Vector x){return sqrt(Dot(x,x));}
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;
}
void Prepare(){
N=read();
up(i,1,N)P[i].x=read();
up(i,1,N)P[i].y=read();
memcpy(ch1,P,sizeof(ch1));
top1=N;
up(i,1,N-1)L[i]=Line(P[i],P[i+1]-P[i]);
memcpy(lh1,L,sizeof(lh1));
}
db walk1(db x){
db y=-oo;
up(i,1,top2)if(dcmp(lh2[i].v.x)!=0){
db k=lh2[i].v.y/lh2[i].v.x;
db b=lh2[i].P.y-k*lh2[i].P.x;
cmax(y,k*x+b);
}
return y;
}
db walk2(db x){
if(x>ch1[top1-1].x)return -oo;
down(i,top1-1,1)if(lh1[i].P.x<=x){
db k=lh1[i].v.y/lh1[i].v.x;
db b=lh1[i].P.y-k*lh1[i].P.x;
return k*x+b;
}
return -oo;
}
void Solve(){
sort(L+1,L+N);
head=1;tail=0;q[++tail]=L[1];
up(i,2,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].ang-q[tail-1].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--;
top2=tail-head+1;
up(i,head,tail){
ch2[i-head+1]=P[i];
lh2[i-head+1]=q[i];
}
/*up(i,1,top1-1){
printf("%lf %lf\n",ch1[i].x,ch1[i].y);
}*/
up(i,1,top1)cmin(ans,walk1(ch1[i].x)-ch1[i].y);
up(i,1,top2-1)cmin(ans,ch2[i].y-walk2(ch2[i].x));
if(dcmp(ans-oo)==0)ans=0;
printf("%.3lf\n",dcmp(ans)==0?0:ans);
}
}
int main(){
//freopen("input.in","r",stdin);
//freopen("out1.out","w",stdout);
using namespace solution;
Prepare();
Solve();
return 0;
}