LA 4728 Squares 凸包 .

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题目地址：https://vjudge.net/problem/UVALive-4728

最远的两点肯定是凸包上的点，所以先求凸包

再枚举凸包上的两个点，更新最远的距离，这里用滑动窗口算法优化

也按照旋转卡壳方法写了一遍

#include <bits/stdc++.h>using namespace std;#define REP(i,a,b)  for(int i=a;i<=(int)(b);++i)#define REPD(i,a,b) for(int i=a;i>=(int)(b);--i)const double PI=acos(-1);const double EPS=1e-6;int dcmp(double x){if(fabs(x)<EPS) return 0;return x > 0 ? 1 : -1;}struct Point{double x,y;};typedef Point Vector;bool operator < (const Point& p1, const Point& p2){return p1.x<p2.x || (p1.x==p2.x && p1.y<p2.y) ;}Vector operator / (const Point& A, double x){return Vector{A.x/x, A.y/x};}Vector operator * (const Vector& A, double x){return Vector{A.x*x, A.y*x};}Vector operator - (const Vector& A, const Vector& B){return Vector{A.x-B.x,A.y-B.y};}Vector operator + (const Point& A, const Vector& v){return Point{A.x+v.x,A.y+v.y};}Vector Rotate(const Point& p,double ang){return Vector{p.x*cos(ang)-p.y*sin(ang),p.x*sin(ang)+p.y*cos(ang)};}double Cross(const Vector& A, const Vector& B){return A.x*B.y-A.y*B.x;}double Dot(Vector A, Vector B){return A.x*B.x+A.y*B.y;}double LengthSquare(Vector v){return fabs(Dot(v,v));}const int maxn=100000+5;Point s[maxn*4],sol[maxn];double w[maxn];int convexHull(Point* A, int n, Point* sol){sort(A,A+n);int m=0;REP(i,0,n-1){while(m>1 && dcmp( Cross(sol[m-1]-sol[m-2], A[i]-sol[m-1])) <= 0) m--;sol[m++]=A[i];}int k=m;REPD(i,n-2,0){while(m>k && dcmp( Cross(sol[m-1]-sol[m-2], A[i]-sol[m-1])) <= 0) m--;sol[m++]=A[i];}if(n>1) m--;return m;}double RotateCaliper(Point* A, int n){  //旋转卡壳A[n]=A[0];double ans=0.;for(int u=0,v=1;u<n;u++){for(;;){int sign=dcmp( Cross(A[u+1]-A[u], A[v+1]-A[v]));if(sign<=0){ans=max(ans, LengthSquare(A[v]-A[u]));if(sign==0) ans=max(ans, LengthSquare(A[v+1]-A[u]));break;}v=(v+1)%n;}}return ans;}int main(int argc, char const *argv[]){// freopen("input.in","r",stdin);int T,n; scanf("%d",&T);while(T--&&scanf("%d",&n)==1){int pCnt=0;REP(i,0,n-1) {double x,y,w;scanf("%lf%lf%lf",&x,&y,&w);s[pCnt++]=Point{x+w,y};s[pCnt++]=Point{x,y+w};s[pCnt++]=Point{x+w,y+w};s[pCnt++]=Point{x,y};}int cnt=convexHull(s,pCnt,sol);/*int i=0,j=0; double D=0.;while(i<cnt&&j<cnt){while(j<cnt-1 && dcmp(LengthSquare(sol[j+1]-sol[i])-LengthSquare(sol[j]-sol[i])) >0 ) j++;D=max(D,LengthSquare(sol[j]-sol[i]));i++;}printf("%.0lf\n", D);*/printf("%.0lf\n", RotateCaliper(sol,cnt));}return 0;}

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