洛谷 P1452 Beauty Contest 解题报告

P1452 Beauty Contest

题意

求平面\(n(\le 50000)\)个点的最远点对

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收获了一堆计算几何的卡点..

凸包如果不保留共线的点，在加入上凸壳时搞一个相对栈顶，以免把\(n\)号点删走了

旋转卡壳和凸包都想一下更新的时候带不带等于号阿

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Code:

#include <cstdio>
#include <algorithm>
using std::max;
const int N=5e4+10;
int s[N],tot,n,p;
struct Vector
{
    int x,y;
    bool friend operator <(Vector a,Vector b){return a.x==b.x?a.y<b.y:a.x<b.x;}
    Vector friend operator -(Vector a,Vector b){return Vector{a.x-b.x,a.y-b.y};}
}bee[N];
int Cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}
int cal(int a,int b,int c){return Cross(bee[c]-bee[a],bee[c]-bee[b]);}
int Dis(int a,int b){return (bee[a].x-bee[b].x)*(bee[a].x-bee[b].x)+(bee[a].y-bee[b].y)*(bee[a].y-bee[b].y);}
void ins(int i)
{
    while(tot>p&&Cross(bee[i]-bee[s[tot]],bee[s[tot]]-bee[s[tot-1]])>=0) --tot;
    s[++tot]=i;
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d%d",&bee[i].x,&bee[i].y);
    std::sort(bee+1,bee+1+n);
    int ans=Dis(1,n);p=1;
    for(int i=1;i<=n;i++) ins(i);
    p=tot;
    for(int i=n-1;i;i--) ins(i);
    for(int p=2,i=1;i<tot;i++)
    {
        while(cal(s[i],s[i+1],s[p])<cal(s[i],s[i+1],s[p+1])) p=p==tot-1?1:p+1;
        ans=max(ans,max(Dis(s[i],s[p]),Dis(s[i+1],s[p])));
    }
    printf("%d\n",ans);
    return 0;
}

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2019.2.15