[POJ 2187]Beauty Contest(旋转卡壳)

题目链接

http://poj.org/problem?id=2187

题目大意

求平面上最远的两个点的距离的平方。

思路

裸凸包+旋转卡壳求凸包上最远点对。。。
注意旋转卡壳的很多细节，不然会WA。。。
其实这个题也是可以用 O(n2) 暴力水过的，因为数据太弱。。。

代码

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <algorithm>
#include <cmath>

#define MAXN 51000
#define EPS 1e-6

using namespace std;

int n;

int dcmp(double x)
{
    if(fabs(x)<EPS) return 0;
    if(x>EPS) return 1;
    return -1;
}

struct Point
{
    double x,y;
    Point(){}
    Point(double _x,double _y):x(_x),y(_y){}
}points[MAXN],stack[MAXN];

Point operator-(Point a,Point b)
{
    return Point(a.x-b.x,a.y-b.y);
}

double operator*(Point a,Point b)
{
    return a.x*b.x+a.y*b.y;
}

double dist(Point a,Point b)
{
    return ((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}

int top=0;

bool cmp(Point a,Point b)
{
    if(!dcmp(a.x-b.x)) return a.y<b.y;
    return a.x<b.x;
}

double cross(Point a,Point b) //a->b X a->c
{
    return a.x*b.y-b.x*a.y;
}

void Graham()
{
    sort(points+1,points+n+1,cmp);
    for(int i=1;i<=n;i++)
    {
        while(top>=2&&dcmp(cross(stack[top]-stack[top-1],points[i]-stack[top-1])<=0)) top--; //!!!!
        stack[++top]=points[i];
    }
    int tmp=top;
    for(int i=n-1;i>=1;i--)
    {
        while(top>=tmp+1&&dcmp(cross(stack[top]-stack[top-1],points[i]-stack[top-1])<=0)) top--;
        stack[++top]=points[i];
    }
}

double rotcalip()
{
    double ans=0;
    int p=2;
    for(int i=1;i<=top;i++)
    {
        while(dcmp(cross(stack[i+1]-stack[i],stack[p]-stack[i])-cross(stack[i+1]-stack[i],stack[p+1]-stack[i]))<0) p=p%top+1; //!!!!!!我顶你个肺
        ans=max(ans,max(dist(stack[p],stack[i]),dist(stack[p],stack[i+1])));
    }
    return ans;
}

int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%lf%lf",&points[i].x,&points[i].y);
    Graham();
    printf("%d\n",(int)rotcalip());
    return 0;
}