# codeforces #339 div 2 C. Peter and Snow Blower

Posted by 111qqz on Wednesday, February 17, 2016

## TOC

### http://codeforces.com/contest/614/problem/C

``````/* ***********************************************
Author :111qqz
Created Time :2016年02月16日 星期二 16时58分59秒
File Name :code/cf/problem/614C.cpp
************************************************ */

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <cstdlib>
#include <ctime>
#define fst first
#define sec second
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define ms(a,x) memset(a,x,sizeof(a))
typedef long long LL;
#define pi pair < int ,int >
#define MP make_pair

using namespace std;
const double eps = 1E-8;
const int dx4[4]={1,0,0,-1};
const int dy4[4]={0,-1,1,0};
const int inf = 0x3f3f3f3f;
const int N = 1E5+7;
const double PI = acos(-1.0);

int dblcmp(double d)
{
return d<-eps?-1:d>eps;
}
struct point
{
double x,y;
point (){}
point (double _x,double _y):
x(_x),y(_y){};
void input()
{
cin>>x>>y;
}
point sub(point p)
{
return point (x-p.x,y-p.y);
}
double dot(point p)
{
return x*p.x+y*p.y;
}
double distance2(point p)
{
return (x-p.x)*(x-p.x)+(y-p.y)*(y-p.y);
}
double distance(point p)
{
return hypot(x-p.x,y-p.y);
}
double det(point p)
{
return x*p.y-y*p.x;
}
}p[N],q;
double sqr(double x)
{
return x*x;
}
struct line
{
point a,b;
line(){}
line (point _a,point _b)
{
a = _a;
b = _b;
}
double length()
{
return a.distance(b);
}

double dispointtoline2(point p)
{
double res = sqr(fabs(p.sub(a).det(b.sub(a)))/length());
//	cout<<"res:"<<res<<endl;
return res;
}
double dispointtoseg2(point p)
{
if (dblcmp(p.sub(b).dot(a.sub(b)))<0||dblcmp(p.sub(a).dot(b.sub(a)))<0)
return min(p.distance2(a),p.distance2(b));

return dispointtoline2(p);
}
}li[N];

int n;
int main()
{
#ifndef  ONLINE_JUDGE
freopen("code/in.txt","r",stdin);
#endif

cin>>n;
q.input();
double MIN = 99999999999999999;
double MAX = -1;
for ( int i = 1 ; i <= n ; i++)
{
p[i].input();
double d= p[i].distance2(q);
MAX = max(MAX,d);
}

for ( int i = 1 ; i <= n-1 ; i++)
{
li[i] = line(p[i],p[i+1]);
}
li[n]=line(p[n],p[1]);
for ( int i = 1 ; i <= n ; i++)
{
double d = li[i].dispointtoseg2(q);
//	    cout<<li[i].a.x<<" "<<li[i].a.y<<"   "<<li[i].b.x<<" "<<li[i].b.y<<endl;
//    cout<<"d:"<<d<<endl;
MIN = min(MIN,d);
}
//	cout<<"MAX:"<<MAX<<"  MIN:"<<MIN<<endl;
double ans = (MAX-MIN)*PI;
printf("%.18f\n",ans);

#ifndef ONLINE_JUDGE
fclose(stdin);
#endif
return 0;
}
``````

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