uva1453 旋转卡壳算法

链接：http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=4199

题意：给出若干个正方形，求出他们的顶点中距离最大的两个点间的距离的平方。

思路：很直接的求点集的直径，采用旋转卡壳算法。算法参考：http://www.cppblog.com/staryjy/archive/2010/09/25/101412.html

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn=1000000;
const double eps=1e-8;
struct Point
{
    int x,y;
    Point(int x=0,int y=0):x(x),y(y) {}
}p[maxn],ch[maxn];

typedef Point Vector;

Vector operator + (Vector A,Vector B)
{
    return Vector(A.x+B.x,A.y+B.y);
}

Vector operator - (Vector A,Vector B)
{
    return Vector(A.x-B.x,A.y-B.y);
}
int dcmp(double x)
{
    if(fabs(x)<eps) return 0;
    else return x<0?-1:1;
}
bool operator == (const Point& a,const Point& b)//两点相等
{
    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)==0;
}
double Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;
}
int dist2(Point a,Point b)
{
    return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);
}
int cmp(const Point &a,const Point &b)
{
    if(a.x<b.x) return 1;
    else if(a.x==b.x)
    {
        if(a.y<b.y) return 1;
        else return 0;
    }
    else return 0;
}
int ConvexHull(Point *p,int n,Point *ch)
{
    sort(p,p+n,cmp);
    n=unique(p,p+n)-p;//去重
    int m=0;
    for(int i=0;i<n;i++)
    {
        while(m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]) <= 0)
            m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;i--)
    {
        while(m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]) <= 0)
            m--;
        ch[m++]=p[i];
    }
    if(n>1) m--;
    return m;
}

int RotatingCalipers(Point *ch,int n)//计算凸包直径，凸包顶点数组ch，顶点个数n，按逆时针排列，输出直径的平方
{
    int q=1;
    int ans=0;
    ch[n]=ch[0];
    for(int p=0;p<n;p++)
    {
        while(Cross(ch[p+1]-ch[p],ch[q+1]-ch[p])>Cross(ch[p+1]-ch[p],ch[q]-ch[p]))
            q=(q+1)%n;
        ans=max(ans,max(dist2(ch[p],ch[q]),dist2(ch[p+1],ch[q+1])));
    }
    return ans;
}
int main()
{
    //freopen("ine.cpp","r",stdin);
    int t;
    scanf("%d",&t);
    while(t--)
    {
        int n,k=0;
        scanf("%d",&n);
        while(n--)
        {
            int x,y,w;
            scanf("%d%d%d",&x,&y,&w);
            p[k++]=Point(x,y);
            p[k++]=Point(x+w,y);
            p[k++]=Point(x,y+w);
            p[k++]=Point(x+w,y+w);
        }
        int m=ConvexHull(p,k,ch);
        int ans=RotatingCalipers(ch,m);
        printf("%d
",ans);
    }
    return 0;
}