bzoj 1670 [Usaco2006 Oct]Building the Moat护城河的挖掘——凸包

题目：https://www.lydsy.com/JudgeOnline/problem.php?id=1670

用叉积判断。注意两端的平行于 y 轴的。

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define ll long long
#define db double
using namespace std;
const int N=,INF=1e7;
int n,sta[N],top;db ans;
struct Node{
  int x,y;
  Node(int x=,int y=):x(x),y(y) {}
  bool operator< (const Node &b)const
  {return x<b.x||(x==b.x&&y<b.y);}
  Node operator- (const Node &b)const
  {return Node(b.x-x,b.y-y);}
}a[N];
ll Sqr(int x){return (ll)x*x;}
ll Cross(Node a,Node b){return (ll)a.x*b.y-(ll)a.y*b.x;}
db dist(Node a,Node b){return sqrt(Sqr(a.x-b.x)+Sqr(a.y-b.y));}
int main()
{
  scanf("%d",&n);
  for(int i=;i<=n;i++)scanf("%d%d",&a[i].x,&a[i].y);
  sort(a+,a+n+);
  for(int i=;i<=n;i++)
    {
      while(top>&&Cross(a[i]-a[sta[top]],a[i]-a[sta[top-]])>=)top--;
      sta[++top]=i;
    }
  for(int i=;i<=top;i++)ans+=dist(a[sta[i-]],a[sta[i]]);
  for(int i=;i<=n;i++)a[i].y=INF-a[i].y+;
  sort(a+,a+n+);
  top=;
  for(int i=;i<=n;i++)
    {
      while(top>&&Cross(a[i]-a[sta[top]],a[i]-a[sta[top-]])>=)top--;
      sta[++top]=i;
    }
  for(int i=;i<top;i++)ans+=dist(a[sta[i-]],a[sta[i]]);
  if(top>&&a[sta[top]].x!=a[sta[top-]].x)ans+=dist(a[sta[top-]],a[sta[top]]);
  if(a[].x==a[].x)ans+=abs(a[].y-a[].y);
  printf("%.2f\n",ans);
  return ;
}