[POJ2187]Beauty Contest（凸包+旋转卡壳）

题目描述

传送门

题解

凸包+旋转卡壳裸题

代码

#include
#include
#include
#include
#include
using namespace std;
#define N 100005

const double eps=1e-7;
int dcmp(double x)
{
    if (x<=eps&&x>=-eps) return 0;
    return (x>0)?1:-1;
}
struct Vector
{
    double x,y;
    Vector(double X=0,double Y=0)
    {
        x=X,y=Y;
    }
    bool operator < (const Vector &a) const
    {
        return xtypedef Vector Point;
Vector operator - (Vector a,Vector b) {return Vector(a.x-b.x,a.y-b.y);}

int n,top;
double ans;
Point p[N],stack[N];

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));
}
double DisTL(Point P,Point A,Point B)
{
    Vector v=B-A,w=P-A;
    return fabs(Cross(v,w)/Len(v));
}
void graham()
{
    sort(p+1,p+n+1);
    top=0;
    for (int i=1;i<=n;++i)
    {
        while (top>1&&dcmp(Cross(stack[top]-stack[top-1],p[i]-stack[top-1]))<=0)
            --top;
        stack[++top]=p[i];
    }
    int k=top;
    for (int i=n-1;i>=1;--i)
    {
        while (top>k&&dcmp(Cross(stack[top]-stack[top-1],p[i]-stack[top-1]))<=0)
            --top;
        stack[++top]=p[i];
    }
    if (n>1) --top;
}
double rotating()
{
    if (top==1) return 0;
    if (top==2) return Len(stack[2]-stack[1]);
    int now=1;
    double ans=0;
    for (int i=1;i<=top;++i)
    {
        while (dcmp(DisTL(stack[now],stack[i],stack[i%top+1])-DisTL(stack[now%top+1],stack[i],stack[i%top+1]))<=0)
            now=now%top+1;
        ans=max(ans,Len(stack[now]-stack[i]));
        ans=max(ans,Len(stack[now]-stack[i%top+1]));
    }
    return ans;
}
int main()
{
    scanf("%d",&n);
    for (int i=1;i<=n;++i) scanf("%lf%lf",&p[i].x,&p[i].y);
    graham();
    ans=rotating();
    printf("%.0lf\n",ans*ans);
}