POJ 3525 Most Distant Point from the Sea 半平面交+二分

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/* ***********************************************
Author        :CKboss
Created Time  :2015年04月09日 星期四 19时43分00秒
File Name     :POJ1279.cpp
************************************************ */

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;

#define mp make_pair
#define pb push_back

const double eps = 1e-10;
const double pi = acos(-1.0);
const double inf = 1e9;
const int maxp = 2111;

int dcmp(double d) { if(fabs(d)<eps) return 0; return (d<0)?-1:1; }
inline double sqr(double x) { return x*x; }

struct point
{
double x,y;
point(double _x=0,double _y=0):x(_x),y(_y){}
void input() { scanf("%lf%lf",&x,&y); }
void output() { printf("%.2lf %.2lf\n",x,y); }
bool operator==(point a) const { return dcmp(a.x-x)==0&&dcmp(a.y-y)==0; }
bool operator<(point a) const { return dcmp(a.x-x)==0?dcmp(y-a.y)<0:x<a.x; }
double len() { return hypot(x,y); }
double len2() { return x*x+y*y; }
double distance(point p) { return hypot(x-p.x,y-p.y); }
point add(point p) { return point(x+p.x,y+p.y); }
point sub(point p) { return point(x-p.x,y-p.y); }
point mul(double b) { return point(x*b,y*b); }
point div(double b) { return point(x/b,y/b); }
double dot(point p) { return x*p.x+y*p.y; }
double det(point p) { return x*p.y-y*p.x; }
double rad(point a,point b)
{
point p=*this;
return fabs(atan2(fabs(a.sub(p).det(b.sub(p))),a.sub(p).dot(b.sub(p))));
}
//单位向量
point horunit(){return this->div(this->len());}
//左转的单位法向量
point verunit(){return point(-y,x).div(this->len());}
//向向量v的方向移动距离d
point todir(point v,double d)
{
return point(x+v.x*d,y+v.y*d);
}
};

struct line
{
point a,b;
line(){}
line(point _a,point _b) { a=_a; b=_b; }
bool operator==(const line v) const { return (a==v.a)&&(b==v.b); }
bool parallel(line v) { return dcmp(b.sub(a).det(v.b.sub(v.a)))==0; }
point crosspoint(line v)
{
double a1=v.b.sub(v.a).det(a.sub(v.a));
double a2=v.b.sub(v.a).det(b.sub(v.a));
return point((a.x*a2-b.x*a1)/(a2-a1),(a.y*a2-b.y*a1)/(a2-a1));
}

void adjust()
{
if (b<a)swap(a,b);
}

/// a-->b向左垂直方向平移距离d
line transhor(double d)
{
point v=b.sub(a);
point dir=v.verunit();
a=a.todir(dir,d);
b=b.todir(dir,d);
return *this;
}

void output()
{
printf("(%.2lf,%.2lf) --- (%.2lf,%.2lf)\n",a.x,a.y,b.x,b.y);
}
};

struct polygon
{
int n;
point p[maxp];
line l[maxp];

double getarea()
{
double sum=0;
int i;
for(i=0;i<n;i++)
{
sum+=p[i].det(p[(i+1)%n]);
}
return fabs(sum)/2;
}
};

struct halfplane:public line
{
double angle;
halfplane(){}
/// a-->b left
halfplane(point _a,point _b){ a=_a; b=_b;}
halfplane(line v) { a=v.a; b=v.b; }
void calcangle() { angle=atan2(b.y-a.y,b.x-a.x); }
bool operator<(const halfplane &b) const { return angle<b.angle; }
};

struct halfplanes
{
int n;
halfplane hp[maxp];
point p[maxp];
int que[maxp];
int st,ed;
void push(halfplane tmp)
{
hp[n++]=tmp;
}
void unique()
{
int m=1,i;
for(i=1;i<n;i++)
{
if(dcmp(hp[i].angle-hp[i-1].angle)) hp[m++]=hp[i];
else if(dcmp(hp[m-1].b.sub(hp[m-1].a).det(hp[i].a.sub(hp[m-1].a))>0))
hp[m-1]=hp[i];
}
n=m;
}
bool halfplaneinsert()
{
int i;
for(int i=0;i<n;i++) hp[i].calcangle();
sort(hp,hp+n);
unique();
que[st=0]=0; que[ed=1]=1;
p[1]=hp[0].crosspoint(hp[1]);
for(i=2;i<n;i++)
{
while(st<ed&&dcmp((hp[i].b.sub(hp[i].a).det(p[ed].sub(hp[i].a))))<0) ed--;
while(st<ed&&dcmp((hp[i].b.sub(hp[i].a).det(p[st+1].sub(hp[i].a))))<0) st++;
que[++ed]=i;
if(hp[i].parallel(hp[que[ed-1]])) return false;
p[ed]=hp[i].crosspoint(hp[que[ed-1]]);
}
while(st<ed&&dcmp((hp[st].b.sub(hp[que[st]].a).det(p[ed].sub(hp[que[st]].a))))<0) ed--;
while(st<ed&&dcmp((hp[que[ed]].b.sub(hp[que[ed]].a).det(p[st+1].sub(hp[que[ed]].a))))<0) st++;
if(st+1>=ed) return false;
return true;
}

void getconvex(polygon &con)
{
p[st]=hp[que[st]].crosspoint(hp[que[ed]]);
con.n=ed-st+1;
int j=st,i=0;
for(;j<=ed;i++,j++) con.p[i]=p[j];
}
};

int n;
vector<point> vp;

bool check(double d)
{
halfplanes hps ;
hps.n=0;
for(int i=0;i<n;i++)
{
/// i-->i+1
line l(vp[i],vp[(i+1)%n]);
l = l.transhor(d);
hps.push(halfplane(l));
}
return hps.halfplaneinsert();
}

int main()
{
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);

while(scanf("%d",&n)!=EOF&&n)
{
vp.clear();
for(int i=0;i<n;i++)
{
point tp; tp.input(); vp.pb(tp);
}

double low=0,high=inf,ans=inf;
while(low+eps<high)
{
double mid = (low+high)/2;
if(check(mid))
{
ans=mid; low = mid;
}
else high=mid;
}

printf("%.6f\n",ans);
}

return 0;
}