先求凸包，答案是凸包周长 + 2πl。因为简单多边形的转角是360度，所以加上一个圆的周长。
/**//*************************************************************************
Author: WHU_GCC
Created Time: 2007-8-21 15:02:36
File Name: pku1113.cpp
Description:
************************************************************************/
#include <iostream>
#include <cmath>
using namespace std;
#define out(x) (cout << #x << ": " << x << endl)
typedef long long int64;
const int maxint = 0x7FFFFFFF;
const int64 maxint64 = 0x7FFFFFFFFFFFFFFFLL;
template <class T> void show(T a, int n) 
{ for (int i = 0; i < n; ++i) cout << a[i] << ' '; cout << endl; }
template <class T> void show(T a, int r, int l) { for (int i = 0; i < r; ++i) show(a[i], l); cout << endl; }
const int maxn = 1001;
typedef struct point_t
{
int x, y;
};
typedef struct polygon_t
{
int n;
point_t p[maxn];
};
int operator <(const point_t &a, const point_t &b)
{
return a.y < b.y || a.y == b.y && a.x < b.x;
}
point_t operator -(const point_t &a, const point_t &b)
{
point_t ret;
ret.x = a.x - b.x;
ret.y = a.y - b.y;
return ret;
}
double dist(const point_t &a, const point_t &b)
{
return sqrt(double((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y)));
}
int cross(const point_t &a, const point_t &b)
{
return a.x * b.y - a.y * b.x;
}
int turn_left(const point_t &a, const point_t &b, const point_t &c)
{
return cross(b - a, c - b) > 0;
}
class point_set_c
{
public:
void init(int _n, point_t _p[]);
polygon_t convex_hull();
private:
int n;
point_t p[maxn];
};
void point_set_c::init(int _n, point_t _p[maxn])
{
n = _n;
for (int i = 0; i < n; i++)
p[i] = _p[i];
}
polygon_t point_set_c::convex_hull()
{
int stack[maxn];
int top = 1;
stack[0] = 0;
sort(p, p + n);
for (int i = 1; i < n;)
{
if (top == 1 || turn_left(p[stack[top - 2]], p[stack[top - 1]], p[i]))
stack[top++] = i++;
else top--;
}
int t_top = top;
for (int i = n - 2; i >= 0;)
{
if (top == t_top || turn_left(p[stack[top - 2]], p[stack[top - 1]], p[i]))
stack[top++] = i--;
else top--;
}
polygon_t ret;
ret.n = 0;
for (int i = 0; i < top - 1; i++)
ret.p[ret.n++] = p[stack[i]];
return ret;
}
point_t p[maxn];
int n;
point_set_c ps;
polygon_t poly;
int main()
{
int l;
while (scanf("%d%d", &n, &l) != EOF)
{
for (int i = 0; i < n; i++)
scanf("%d%d", &p[i].x, &p[i].y);
ps.init(n, p);
poly = ps.convex_hull();
double ans = 0.0;
for (int i = 0; i < poly.n; i++)
ans += dist(poly.p[i], poly.p[(i + 1) % poly.n]);
ans += 2 * l * acos(-1.0);
printf("%.0lf\n", ans);
}
return 0;
}