This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <cstdio>
#include <iostream>
#include <fstream>
#include <deque>
#include <algorithm>
#include <utility>
#include <vector>
#include <cmath>
#include <queue>
using namespace std;
#define in cin
#define out cout
#define PII pair<int, int>
#define x first
#define y second
#define pi 3.14159265358979323846
struct p
{
double x, y;
bool operator <(const p &pa) const {
return (x < pa.x) || (x == pa.x && y < pa.y);
}
};
double cross(const p &O, const p &A, const p &B)
{
return (A.x - O.x) * (B.y - O.y) - (A.y - O.y) * (B.x - O.x);
}
vector<p> ch(vector<p> P)
{
int n = P.size(), k = 0;
vector<p> H(2*n);
sort(P.begin(), P.end());
for(int i=0; i<n; i++)
{
while( k>= 2 && cross(H[k-2], H[k-1], P[i]) <= 0) k--;
H[k++] = P[i];
}
for(int i=n-2, t=k+1; i>=0; i--) {
while( k >= t && cross(H[k-2], H[k-1], P[i]) <= 0) k--;
H[k++] = P[i];
}
H.resize(k);
return H;
}
double getdistance(const p &a, const p &b)
{
return sqrt( (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y) );
}
int main()
{
//freopen("in.txt", "r+", stdin);
int n; in >> n;
double radi; in >> radi;
out << fixed;
out.precision(15);
vector<p> pts;
for(int i=0; i<n; i++)
{
p t; in >> t.x >> t.y;
pts.push_back(t);
}
pts = ch(pts);
if(n == 2)
{
out << getdistance(pts[0], pts[1]) * 2 + radi*2*pi;
return 0;
}
double res = 0;
int lenp = pts.size()-1;
for(int i=0; i<lenp; i++)
{
int a = i-1; if(a < 0) a = lenp-1;
int b = i;
int c = i+1; if(b >= lenp) c = 0;
p pa = pts[a];
p pb = pts[b];
p pc = pts[c];
res += getdistance(pa, pb);
double tan_ab = atan2(pb.y-pa.y, pb.x-pa.x);
double tan_bc = atan2(pc.y-pb.y, pc.x-pb.x);
if(tan_ab < 0) tan_ab += 2*pi;
if(tan_bc < 0) tan_bc += 2*pi;
double angle = abs(tan_ab - tan_bc);
if(angle > pi) angle = 2*pi - angle;
//out << radi*(pi-angle) << endl;
res += radi*(pi-angle);
}
out << res << endl;
return 0;
}
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