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=,int y=):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=;
     vector<Pt> ch(n+);
     for(int i=;i<n;i++) {
         while(m> && cross(ch[m-]-ch[m-],p[i]-ch[m-])<=) m--;
         ch[m++]=p[i];
     }
     int k=m;
     for(int i=n-;i>=;i--) {
         while(m>k && cross(ch[m-]-ch[m-],p[i]-ch[m-])<=) m--;
         ch[m++]=p[i];
     }
     if(n>) 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==) return ;                                        //特殊情况处理
     if(n==) return dist(p[],p[]);
     p.push_back(p[]);                                        //for u
     int ans=;
     for(int u=,v=;u<n;u++) {
         for(;;) {
             int diff=cross(p[u+]-p[u],p[v+]-p[v]);
             if(diff<=) {                                    //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+]));     //平行
                 break;
             }
             v=(v+)%n;
         }
     }
     return ans;
 }
 void read(int& x) {
     char c=getchar();
     while(!isdigit(c)) c=getchar();
     x=;
     while(isdigit(c))
         x=x*+c-'' , c=getchar();
 }
 int main() {
     int T;
     read(T);
     while(T--) {
         int n; read(n);
         vector<Pt> ps;
         for(int i=;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\n",diameter(ps));
     }
     return ;
 }