UVA 4728 Squares（凸包+旋转卡壳）

题目链接：http://acm.hust.edu.cn/vjudge/problem/viewProblem.action?id=17267

【思路】

       凸包+旋转卡壳

       求出凸包，用旋转卡壳算出凸包的直径即可。

【代码】

#include<cstdio>
#include<vector>
#include<iostream>
#include<algorithm>
using namespace std;

struct Pt {
    int x,y;
    Pt(int x=0,int y=0):x(x),y(y) {};
};
typedef Pt vec;

vec operator - (Pt A,Pt B) { return vec(A.x-B.x,A.y-B.y); }
bool operator < (const Pt& a,const Pt& b) {
    return a.x<b.x || (a.x==b.x && a.y<b.y);
}
bool operator == (const Pt& a,const Pt& b) {
    return a.x==b.x && a.y==b.y;
}

int Dot(vec A,vec B) { return A.x*B.x+A.y+B.y; }
int cross(vec A,vec B) { return A.x*B.y-A.y*B.x; }
int dist(Pt A,Pt B) {
    return (A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y);
}

int n;
vector<Pt> ConvexHull(vector<Pt> p) {
    sort(p.begin(),p.end());
    p.erase(unique(p.begin(),p.end()),p.end());
    int n=p.size();
    int m=0;
    vector<Pt> ch(n+1);
    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--;
    ch.resize(m);
    return ch;
}

int diameter(vector<Pt> ps) {                                //旋转卡壳 
    vector<Pt> p=ConvexHull(ps);
    int n=p.size();
    if(n==1) return 0;                                        //特殊情况处理 
    if(n==2) return dist(p[0],p[1]);
    p.push_back(p[0]);                                        //for u 
    int ans=0;
    for(int u=0,v=1;u<n;u++) {                
        for(;;) {            
            int diff=cross(p[u+1]-p[u],p[v+1]-p[v]);
            if(diff<=0) {                                    //此时uv为对踵点 
                ans=max(ans,dist(p[u],p[v]));
                if(!diff) ans=max(ans,dist(p[u],p[v+1]));     //平行 
                break;
            }
            v=(v+1)%n;
        }
    }
    return ans;
}
void read(int& x) {
    char c=getchar();
    while(!isdigit(c)) c=getchar();
    x=0;
    while(isdigit(c))
        x=x*10+c-'0' , c=getchar();
} 
int main() {
    int T;
    read(T);
    while(T--) {
        int n; read(n);
        vector<Pt> ps;
        for(int i=0;i<n;i++) {
            int x,y,w;
            read(x),read(y),read(w);
            ps.push_back(Pt(x,y));
            ps.push_back(Pt(x+w,y));
            ps.push_back(Pt(x,y+w));
            ps.push_back(Pt(x+w,y+w));
        }
        printf("%d
",diameter(ps));
    }
    return 0;
}