POJ 3525 Most Distant Point from the Sea

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector>
#include<deque>
#include<queue>

using namespace std;
#define FOR(i,a,b) for(int (i)=(a);(i)<=(b);(i)++)
#define DOR(i,a,b) for(int (i)=(a);(i)>=(b);(i)--)

#define oo 1e6
#define eps 1e-6
#define nMax 100000
#define pb push_back
#define pf push_front

#define F first
#define S second

#define bug puts("OOOOh.....");
#define zero(x) (((x)>0?(x):-(x))<eps)

#define LL long long
#define DB double

int dcmp(double x){
if(fabs(x)<eps) return 0;
return x>0?1:-1;
}
class point {
public:
double x,y;
point (double x=0,double y=0):x(x),y(y) {}
void make(double _x,double _y) {x=_x;y=_y;}
void read() { scanf("%lf%lf",&x,&y); }
void out() { printf("%.2lf %.2lf\n",x,y);}
double len() { return sqrt(x*x+y*y); }
point friend operator - (point const& u,point const& v) {
return point(u.x-v.x,u.y-v.y);
}
point friend operator + (point const& u,point const& v) {
return point(u.x+v.x,u.y+v.y);
}
double friend operator * (point const& u,point const& v) {
return u.x*v.y-u.y*v.x;
}
double friend operator ^ (point const& u,point const& v) {
return u.x*v.x+u.y*v.y;
}
point friend operator * (point const& u,double const& k) {
return point(u.x*k,u.y*k);
}
friend bool operator < (point const& u,point const& v){
if(dcmp(v.x-u.x)==0) return dcmp(u.y-v.y)<0;
return dcmp(u.x-v.x)<0;
}
friend bool operator != (point const& u,point const& v){
return dcmp(u.x-v.x) || dcmp(u.y-v.y);
}
};
double const pi = acos(-1.0);
typedef point vec;

typedef class HalfPlane{
public:
point P,a;
vec V;
double arg,len;
HalfPlane(){};
HalfPlane(point a,point b):a(a){
V = b-a;
arg = atan2(V.y,V.x);
len = V.len();
}
void forward(double l){
P = point(-V.y,V.x)*(l/len) + a;
}
} HP;

double const inf = 1e5;
deque<HP> que;
deque<point> ans;
vector<HP> init() {                                  // Init
while(!que.empty()) que.pop_back();
while(!ans.empty()) ans.pop_back();
vector<HP> ret;ret.clear();
ret.pb(HP(point(-inf,-inf),point(inf,-inf)));
ret.pb(HP(point(inf,-inf),point(inf,inf)));
ret.pb(HP(point(inf,inf),point(-inf,inf)));
ret.pb(HP(point(-inf,inf),point(-inf,-inf)));
return ret;
}
int  satisfy(HP u, point a){
return dcmp(u.V*(a-u.P)) >= 0;
}
int cmp(HP a,HP b){
int ret = dcmp(a.arg-b.arg);
if(ret == 0) return satisfy(b,a.P);
return ret < 0;
}
int parrell(HP a,HP b){
return dcmp(a.V*b.V) == 0;
}
int same_dir(HP a,HP b){
return dcmp(a.V ^ b.V) >= 0;
}
int Same(HP a,HP b){
return (dcmp((a.P-b.P)*a.V)==0);
}
point Intersection(HP a,HP b){
point u = a.P-b.P;
double t = (b.V*u)/(a.V*b.V);
return a.P + a.V*t;
}
int erase_back(HP v){
while(ans.size() && !satisfy(v,ans.back())) {
if(parrell(v,que.back())) return 0;
ans.pop_back();
que.pop_back();
}
return 1;
}
int erase_front(HP v){
while(ans.size() && !satisfy(v,ans.front())) {
if(parrell(v,que.front())) return 0;
ans.pop_front();
que.pop_front();
}
return 1;
}
int add(HP v){
if(parrell(v,que.back())) return 0;                        // Can't Be such kind
ans.push_back(Intersection(v,que.back()));
que.pb(v);
return 1;
}
void build(vector<HP>& hp){
vector<HP> Add =init();
for(int i=0;i<4;i++) hp.pb(Add[i]);
}
int HP_insection(vector<HP> hp,double l){
for(int i=0;i<(int)hp.size();i++) hp[i].forward(l);
while(!que.empty()) que.pop_back();
while(!ans.empty()) ans.pop_back();
sort(hp.begin(),hp.end(),cmp);
que.pb(hp[0]);
for(int i=1;i<hp.size();i++) {
if(dcmp(hp[i].arg - hp[i-1].arg)==0) continue;
if(!erase_back(hp[i])) return 0;
if(!erase_front(hp[i])) return 0;;
if(!add(hp[i]))  return 0;
}
while(ans.size() && !satisfy(que.front(),ans.back())){
ans.pop_back();
que.pop_back();
}
while(ans.size() && !satisfy(que.back(),ans.front())) {
ans.pop_front();
que.pop_front();
}
if(!add(que.front())) return 0;
return (int) ans.size() > 2;
// return vector<point> (ans.begin(),ans.end());   // if you need; you would better use unique
}

vector<HP> v;
int n;
void sovle(){
double l=0.0,r=10000.0;
double mid;
double ret = 0.0;
while(r-l>1e-7){
mid = (l+r)/2.0;
if(HP_insection(v,mid)) {
ret = max(ret,mid);
l = mid;
}else r=mid;
}
printf("%.6f\n",ret);
}
point p[nMax];

int main(){
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
//	freopen("D1.sol","w",stdout);
#endif
while(scanf("%d",&n),n){
//		printf("n=%d\n",n);
FOR(i,0,n-1) p[i].read();
v.clear();
p
=p[0];
for(int i=0;i<n;i++) v.pb(HP(p[i],p[i+1]));
//	printf("%d\n",HP_insection(v,0.0));
//	build(v);//printf("%d\n",v.size());
sovle();
}
return 0;
}