Luogu 1452 Beauty Contest

• 求平面最远点对,先求出凸包,再找凸包的直径.
• 使用旋转卡壳,直径一定出现在对踵点对间.比较不同点到同一直线距离可以用叉积算三角形面积来比较.
• 实现时注意关于栈的 \(top\) 的细节.

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define mp make_pair
#define pii pair<int,int>
inline int read()
{
    int x=0;
    bool pos=1;
    char ch=getchar();
    for(;!isdigit(ch);ch=getchar())
        if(ch=='-')
            pos=0;
    for(;isdigit(ch);ch=getchar())
        x=x*10+ch-'0';
    return pos?x:-x;
}
const int MAXN=5e4+10;
const double eps=1e-9;
struct v2{
    ll x,y;
    v2(ll x=0,ll y=0):x(x),y(y) {}
    v2 operator + (const v2 &rhs) const
        {
            return v2(x+rhs.x,y+rhs.y);
        }
    v2 operator / (const double &rhs) const
        {
            return v2(x/rhs,y/rhs);
        }
    v2 operator - (const v2 &rhs) const
        {
            return v2(x-rhs.x,y-rhs.y);
        }
    ll operator * (const v2 &rhs) const
        {
            return x*rhs.y-y*rhs.x;
        }
    ll modulus2()
        {
            return x*x+y*y;
        }
    bool operator < (const v2 &rhs) const
        {
            return x==rhs.x?y<rhs.y:x<rhs.x;
        }
};
v2 origin;
bool cmp(const v2 &a,const v2 &b)
{
    double A=atan2(a.y-origin.y,a.x-origin.x),B=atan2(b.y-origin.y,b.x-origin.x);
    return A==B?a.x<b.x:A<B;
}
v2 stk[MAXN];
int tp;
void ConvexHull(v2 *p,int n)
{
    for(int i=2;i<=n;++i)
        if(p[i]<p[1])
            swap(p[i],p[1]);//p1为左下角的点
    origin=p[1];
    sort(p+2,p+n+1,cmp);
    stk[tp]=p[1];//从0开始存 
    for(int i=2;i<=n;++i)
        {
            while(tp>=2 && (stk[tp]-stk[tp-1])*(p[i]-stk[tp])<=0)
                --tp;
            stk[++tp]=p[i];
        }
}
ll RotatingCaliper()
{
    if(tp==1)
        return (stk[0]-stk[1]).modulus2();
    stk[++tp]=stk[0];
    ll ans=0;
    int j=2;
    for(int i=0;i<tp;++i)
        {
            while(abs((stk[i]-stk[j])*(stk[i+1]-stk[j]))<abs((stk[i]-stk[j+1])*(stk[i+1]-stk[j+1])))
                j=(j+1)%tp;
            ans=max(ans,(stk[i]-stk[j]).modulus2());
            ans=max(ans,(stk[i+1]-stk[j]).modulus2());
        }
    return ans;
}
int n;
v2 p[MAXN];
int main()
{
//  freopen("testdata.in","r",stdin);
    n=read();
    for(int i=1;i<=n;++i)
        scanf("%lld%lld",&p[i].x,&p[i].y);
    ConvexHull(p,n);
    ll ans=RotatingCaliper();
    printf("%lld\n",ans);
    return 0;
}
//785190749