学步园

思路：用旋转卡壳求最远点对。

#include <iostream>
#include <cmath>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <vector>
#define next(i) ((i+1)%n)
using namespace std;
const double maxn = 401000;

const double eps = 1e-8;
int dcmp(double x) {
    if(fabs(x) < eps) return 0;
    if(x > 0) return 1;
    return -1;
}

struct point {
    double x, y;
    point() {}
    point(double a, double b) : x(a), y(b) {}
    friend point operator - (const point &a, const point &b) {
       return point(a.x-b.x, a.y-b.y);
    }
    friend point operator + (const point &a, const point &b) {
        return point(a.x+b.x, a.y+b.y);
    }
};

double det(const point &a, const point &b) {
   return a.x * b.y - a.y * b.x;
}

bool comp_less(const point &a, const point &b) {
    return dcmp(a.x-b.x)<0 || (dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)<0);
}

bool cmp(point &a, point &b) {
    if(a.x==b.x && a.y==b.y) return true;
    else return false;
}

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

struct polygon_convex {
    vector <point> P;
    polygon_convex(int Size = 0) {
        P.resize(Size);
    }
};

polygon_convex convex_hull(vector<point> a) {
    polygon_convex res(2*a.size()+5);
    sort(a.begin(), a.end(), comp_less);
    ///a.erase(unique(a.begin(), a.end()), a.end());
    a.erase(unique(a.begin(), a.end(), cmp), a.end());
    int m = 0;
    for(int i = 0; i < (int)a.size(); ++i) {
        while(m > 1 && dcmp(det(res.P[m-1]-res.P[m-2], a[i]-res.P[m-2]))<=0)
            --m;
        res.P[m++] = a[i];
    }
    int k = m;
    for(int i = int(a.size())-2; i >= 0; --i) {
        while(m > k && dcmp(det(res.P[m-1]-res.P[m-2], a[i]-res.P[m-2]))<=0)
            --m;
        res.P[m++] = a[i];
    }
    res.P.resize(m);
    if(a.size()>1) res.P.resize(m-1);
    return res;
}

double convex_diameter(polygon_convex &a) {
    vector<point> &p = a.P;
    int n = p.size();
    double maxd = 0.0;
    if(n==1) {
        return maxd;
    }
    int j = 1;
    for(int i = 0; i < n; ++i) {
        while(dcmp(det(p[next(i)]-p[i], p[j]-p[i])-det(p[next(i)]-p[i], p[next(j)]-p[i]))<0)
        {
            j = next(j);
        }
        double d = dist(p[i], p[j]);
        if(d > maxd) maxd = d;
        d = dist(p[next(i)], p[next(j)]);
        if(d>maxd)  maxd = d;
    }
    return maxd;
}

int main()
{
    int T;
    int n;
    point A, B, C, D;//正方形四个点。
    double x, y, w;
    vector <point> v;
    scanf("%d", &T);
    while(T--) {
        scanf("%d", &n);
        v.clear();
        for(int i = 0; i < n; i++) {
            scanf("%lf%lf%lf", &x, &y, &w);
            A = point(x, y);
            B = point(x+w, y);
            C = point(x, y+w);
            D = point(x+w, y+w);
            v.push_back(A);
            v.push_back(B);
            v.push_back(C);
            v.push_back(D);
        }
        double res = 0.0;
        polygon_convex result;
        result = convex_hull(v);
        res = convex_diameter(result);
        printf("%d\n", int(res));
    }
    return 0;
}
/**
input:
2
3
0 0 1
1 0 2
0 0 1
6
2 1 2
1 4 2
3 2 3
4 4 4
6 5 1
5 1 3
output:
13
85
**/