鏈接：http://acm.hdu.edu.cn/showproblem.php?pid=1392
題意：求凸包的周長。
思路：凸包裸題。
#include <cstdio>
#include <iostream>
#include <cmath>
#include <algorithm>
using namespace std;
const int N = 1e2+10;
const double eps = 1e-8;
int sgn(double x)
{
if(fabs(x)<eps) return 0;
else if(x<0) return -1;
else return 1;
}
struct Point
{
double x,y;
Point(){}
Point(double x,double y):x(x),y(y){}
Point operator -(const Point& b)const//相減
{
return Point(x-b.x,y-b.y);
}
double operator ^(const Point& b)const//叉乘
{
return x*b.y-y*b.x;
}
double operator *(const Point& b)const//點乘
{
return x*b.x+y*b.y;
}
}ps[N],st[N];
int n,pos,top;
double x;
bool cmp(const Point& a,const Point& b)
{
x=(a-ps[1])^(b-ps[1]);
if(sgn(x)==0)
{
if(a.y==b.y)
return a.x<b.x;
else return a.y<b.y;
}
else if(x>0) return 1;
else return 0;
}
bool check(Point a,Point b,Point c)
{
x=(b-a)^(c-a);
return x<0||sgn(x)==0;
}
double dist(Point a,Point b)
{
return sqrt((b-a)*(b-a));
}
double circum()
{
++top;
if(top==2)
{
return dist(st[0],st[1]);
}
double ans=0;
for(int i=0;i<top;i++)
{
ans+=dist(st[i],st[(i+1)%top]);
}
return ans;
}
int main(void)
{
while(~scanf("%d",&n)&&n)
{
pos=1;
for(int i=1;i<=n;i++)
{
scanf("%lf%lf",&ps[i].x,&ps[i].y);
if(ps[i].y<ps[pos].y || (ps[i].y==ps[pos].y&&ps[i].x<ps[pos].x))
pos=i;
}
if(n==1)
{
puts("0.00");
continue;
}
swap(ps[1],ps[pos]);
sort(ps+2,ps+n+1,cmp);
top=-1;
st[++top]=ps[1];
st[++top]=ps[2];
for(int i=3;i<=n;i++)
{
while(top>1&&check(st[top-1],st[top],ps[i]))
top--;
st[++top]=ps[i];
}
printf("%.2f\n",circum());
}
return 0;
}