poj 1113

凸包

至今还不知道这道题为什么凸包就是解，在网上搜结题报告也都是说求凸包，没告诉深层原因，求大神解答

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <math.h>
using namespace std;
const int maxn=1000+10;
struct node
{
	int x,y;
};
node point[maxn];
int ch[maxn];
int n,l;
bool cmp(node a,node b)
{
	if(a.x<b.x) return true;
	else if(a.x==b.x) return a.y<b.y?true:false;
	else return false;
}
int cross(node a,node b,node c)
{
	return (b.x-a.x)*(c.y-b.y)-(b.y-a.y)*(c.x-b.x);
}
int  Andrew()
{
	sort(point,point+n,cmp);
	int m=0;
	int i;
	for(i=0;i<n;i++)
	{
		while(m>1&&cross(point[ch[m-1]],point[ch[m-2]],point[i])<=0) m--;
		ch[m++]=i;
	}
	int k=m;
	for(i=n-2;i>=0;i--)
	{
		while(m>k&&cross(point[ch[m-1]],point[ch[m-2]],point[i])<=0) m--;
		ch[m++]=i;
	}
	return m;
}
double dis(node a,node b)
{
	return sqrt(double((b.x-a.x)*(b.x-a.x)+(b.y-a.y)*(b.y-a.y)));
}
int main()
{
	while(~scanf("%d%d",&n,&l))
	{
		int i;
		for(i=0;i<n;i++) scanf("%d%d",&point[i].x,&point[i].y);
		int tot=Andrew();
		double out=2*acos(-1.0)*l;
		for(i=0;i<tot-1;i++)
		{
			out+=dis(point[ch[i]],point[ch[i+1]]);
		}
		printf("%.lf\n",out);
	}
	return 0;
}