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| #include <bits/stdc++.h>
#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")
#define MAX_N 505
#define INF 987654321
#define ll long long
#define pll pair<ll, ll>
#define vpll vector<pll>
#define vall3 vector<array<ll,3>>
#define all5 array<ll,5>
#define vall5 vector<all5>
#define vll vector<ll>
#define vs vector<string>
#define usll unordered_set<ll>
#define vvs vector<vs>
#define vvll vector<vll>
#define all(a) begin(a), end(a)
using namespace std;
const double pi=3.1415926535;
struct Point {
ll x, y;
bool operator ==(const Point& other) const {
return x == other.x and y == other.y;
}
Point operator -(const Point& other) const {
return {x - other.x, y - other.y};
}
bool operator <(const Point& other) const {
if(x == other.x) return y < other.y;
return x < other.x;
}
ll norm() { return x * x + y * y; }
};
ll dot(Point a, Point b) {
return a.x * b.x + a.y * b.y;
}
double abs(Point a) {
return sqrt(a.norm());
}
double angle(Point a, Point b) {
return acos(dot(a, b) / abs(a) / abs(b));
}
ll dist(Point& a, Point& b) {
return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
}
vector<Point> p;
ll ccw(Point &a, Point &b, Point &c) {
ll res = a.x * b.y + b.x * c.y + c.x * a.y;
res -= (a.x * c.y + b.x * a.y + c.x * b.y);
return res;
}
bool cmp(Point& a, Point& b) {
ll c=ccw(p[0], a, b);
if(c) return c > 0;
return dist(p[0], a) < dist(p[0], b);
}
vector<Point> convexHull() {
swap(p[0], *min_element(all(p)));
sort(begin(p) + 1, end(p), cmp);
vector<Point> st;
for(auto& pt: p) {
while(st.size() >= 2 and ccw(pt, st[st.size() - 2], st[st.size() - 1]) <= 0)
st.pop_back();
st.push_back(pt);
}
return st;
}
bool inside(vector<Point>& hull, Point& o) {
auto CCW = [&](Point& a, Point& b, Point& o) {
ll cw = ccw(a, b, o);
if(cw > 0) return 1;
if(cw == 0) return 0;
return -1;
};
ll cw = CCW(hull[0], hull[1], o), n = hull.size();
for(ll i = 1; i < n; i++) {
if(cw != CCW(hull[i], hull[(i + 1) % n], o))
return false;
}
return true;
}
ll solve() {
auto hull = convexHull();
ll res = 0, n = hull.size();
ll l = 0, r = 0;
for(ll i = 0; i < n; i++) {
if(hull[i].x < hull[l].x) l = i;
if(hull[i].x > hull[r].x) r = i;
}
res = max(res, dist(hull[l], hull[r]));
Point o{0,0};
for(ll i = 0; i < n; i++) {
auto R = hull[r] - hull[(r + 1) % n];
auto L = hull[(l + 1) % n] - hull[l];
if(ccw(o, L, R) > 0) {
l = (l + 1) % n;
} else {
r = (r + 1) % n;
}
res = max(res, dist(hull[l], hull[r]));
}
return res;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.setf(ios::fixed);
cout.precision(8);
ll tc;
cin>>tc;
while(tc--) {
ll n, x, y, w;
p.clear();
cin>>n;
for(ll i = 0; i < n; i++) {
cin>>x>>y>>w;
p.push_back({x,y});
p.push_back({x + w, y});
p.push_back({x, y + w});
p.push_back({x + w, y + w});
}
cout<<solve()<<'\n';
}
return 0;
}
|
