2013
12-09

# Surround the Trees

There are a lot of trees in an area. A peasant wants to buy a rope to surround all these trees. So at first he must know the minimal required length of the rope. However, he does not know how to calculate it. Can you help him?
The diameter and length of the trees are omitted, which means a tree can be seen as a point. The thickness of the rope is also omitted which means a rope can be seen as a line.

There are no more than 100 trees.

The input contains one or more data sets. At first line of each input data set is number of trees in this data set, it is followed by series of coordinates of the trees. Each coordinate is a positive integer pair, and each integer is less than 32767. Each pair is separated by blank.

Zero at line for number of trees terminates the input for your program.

The minimal length of the rope. The precision should be 10^-2.

9
12 7
24 9
30 5
41 9
80 7
50 87
22 9
45 1
50 7
0 

243.06

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <cmath>
using namespace std;
#define eps 1e-6
#define PI 3.14159265
struct point
{
double x;
double y;
}po[1500],temp;
int n,l,pos;
bool zero(double a)
{
return fabs(a) < eps;
}
double dis(point &a,point &b)//返回两点之间距离的平方
{
return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y));
}
double across(point &a,point &b,point &c)//求a b and a c 的X积
{
return (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x);
}
int cmp(const void *a,const void *b)
{
return across(po[0],*(point*)a,*(point*)b) > 1e-8 ? -1 : 1;
}
int select()
{
int i,j,k=1;
for(i=2;i<n;i++)
{
if(zero(across(po[0],po[k],po[i])))
{
if(dis(po[0],po[k]) < dis(po[0],po[i]))
po[k]=po[i];
}
else
po[++k]=po[i];
}
return k+1;
}
int graham(int num)
{
double ans=0;
int i,j,k=2;
po[num]=po[0];//fangbian
num++;
for(i=3;i<num;i++)
{
while(across(po[k-1],po[k],po[i]) < -eps)
{k--;}
po[++k]=po[i];//就这个循环结束，不需要了！
}
for(i=1;i<=k;i++)
{
ans+=dis(po[i-1],po[i]);
}
printf("%.2lf\n",ans);

return 0;
}
int main()
{
int i,j,k;
point my_temp;
while(scanf("%d",&n),n)
{
scanf("%lf%lf",&po[0].x,&po[0].y);
temp=po[0];
pos=0;
for(i=1;i<n;i++)
{
scanf("%lf%lf",&po[i].x,&po[i].y);
if(po[i].y < temp.y)
temp=po[i],pos=i;
}
if(n==2)
{
printf("%.2lf\n",dis(po[0],po[1]));
continue;
}
my_temp=po[0];
po[0]=po[pos];
po[pos]=my_temp;
qsort(po+1,n-1,sizeof(po[0]),cmp);
graham(select());
}
return 0;
}

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