【POJ 3348】Cows（Andrew求凸包法）

最新推荐文章于 2022-07-04 22:04:47 发布

原创最新推荐文章于 2022-07-04 22:04:47 发布 · 140 阅读

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本文详细介绍了计算几何中的凸包算法，并通过C++代码实现。重点讲解了Andrew算法的原理，包括点的比较、向量操作如加法、减法、数乘、点积和叉积等。并通过实例演示了如何利用这些操作来确定凸包的顶点。

https://blog.youkuaiyun.com/linkfqy/article/details/72861176

#include<iostream>
#include<cmath>
#include<algorithm>
#define N 10005
#define eps 1e-6
using namespace std;
int n;
struct Point
{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
}p[N];
typedef Point Vector;
Vector operator +(Point a,Vector b)
{
    return Point(a.x+b.x,a.y+b.y);
}
Vector operator -(Point a,Point b)
{
    return Point(a.x-b.x,a.y-b.y);
}
Vector operator *(Vector a,double k)
{
    return Point(a.x*k,a.y*k);
}
double Dot(Vector a,Vector b)
{
    return (a.x*b.x)+(a.y*b.y);
}
double Cross(Vector a,Vector b)
{
    return (a.x*b.y)-(a.y*b.x);
}
double Len(Vector a)
{
    return sqrt(Dot(a,a));
}
inline bool cmp(const Point &a,const Point &b)
{
    if(fabs(a.x-b.x)>eps)   return a.x<b.x;
    else    return a.y<b.y;
}

int sta[N];
void Andrew()
{
    sta[1]=1;
    int top=1;
    for(int i=2;i<=n;i++)
    {
        while(top>1&&(Cross(p[i]-p[sta[top-1]],p[sta[top]]-p[sta[top-1]])<eps)) top--;
        sta[++top]=i;
    }
    int k=top;
    for(int i=n-1;i>=1;i--)
    {
        while(top>k&&(Cross(p[i]-p[sta[top-1]],p[sta[top]]-p[sta[top-1]])<eps)) top--;
        sta[++top]=i;
    }
    double ans=0;
    for(int i=1;i<top;i++)
    {
        ans+=Cross(p[sta[i]]-p[sta[1]],p[sta[i+1]]-p[1]);
    }
    cout<<abs(int(ans/100))<<endl;
}
int main()
{
    cin>>n;
    for(int i=1;i<=n;i++)
    {
        cin>>p[i].x>>p[i].y;        
    }
    sort(p+1,p+n+1,cmp);
    Andrew();
    return 0;
}