tests/Furthest_Pair_of_Points.test.cpp

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Last update: 2025-11-28 02:09:51+07:00
Problem: https://judge.yosupo.jp/problem/furthest_pair

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/furthest_pair"

#include "../misc/macros.h"
#include "../geometry/ConvexHull.h"
#include "../geometry/HullDiameter.h"

using P = Point<ld>;

void solve() {
  int n;
  cin >> n;
  vector<P> pts(n);
  for (auto& [x, y] : pts) cin >> x >> y;
  auto cvh = convexHull(pts);
  auto [pi, pj] = hullDiameter(cvh);
  int i, j;
  for (i = 0; i < n; ++i) {
    if (pts[i] == pi) {
      cout << i << ' ';
      break;
    }
  }
  for (j = 0; j < n; ++j) {
    if (pts[j] == pj && j != i) {
      cout << j << '\n';
      break;
    }
  }
}

int main() {
  int tc;
  cin >> tc;
  while (tc--) solve();
}

#line 1 "tests/Furthest_Pair_of_Points.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/furthest_pair"

#line 1 "misc/macros.h"
// #pragma GCC optimize("Ofast,unroll-loops")       // unroll long, simple loops
// #pragma GCC target("avx2,fma")                   // vectorizing code
// #pragma GCC target("lzcnt,popcnt,abm,bmi,bmi2")  // for fast bitset operation

#include <bits/extc++.h>
#include <tr2/dynamic_bitset>

using namespace std;
using namespace __gnu_pbds;  // ordered_set, gp_hash_table
// using namespace __gnu_cxx; // rope

// for templates to work
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#define pb push_back
#define eb emplace_back
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using pii = pair<i32, i32>;
using vi = vector<i32>;

// fast map
const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash {  // customize hash function for gp_hash_table
  int operator()(int x) const { return x ^ RANDOM; }
};
gp_hash_table<int, int, chash> table;

/* ordered set
    find_by_order(k): returns an iterator to the k-th element (0-based)
    order_of_key(k): returns the number of elements in the set that are strictly less than k
*/
template <class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

/*  rope
    rope <int> cur = v.substr(l, r - l + 1);
    v.erase(l, r - l + 1);
    v.insert(v.mutable_begin(), cur);
*/
#line 2 "geometry/Point.h"

template <class T>
int sgn(T x) { return (x > 0) - (x < 0); }
template <class T>
struct Point {
  typedef Point P;
  T x, y;
  explicit Point(T x = 0, T y = 0) : x(x), y(y) {}
  bool operator<(P p) const { return tie(x, y) < tie(p.x, p.y); }
  bool operator==(P p) const { return tie(x, y) == tie(p.x, p.y); }
  P operator+(P p) const { return P(x + p.x, y + p.y); }
  P operator-(P p) const { return P(x - p.x, y - p.y); }
  P operator*(T d) const { return P(x * d, y * d); }
  P operator/(T d) const { return P(x / d, y / d); }
  T dot(P p) const { return x * p.x + y * p.y; }
  T cross(P p) const { return x * p.y - y * p.x; }
  T cross(P a, P b) const { return (a - *this).cross(b - *this); }
  T dist2() const { return x * x + y * y; }
  T dist() const { return sqrt(dist2()); }
  // angle to x-axis in interval [-pi, pi]
  T angle() const { return atan2l(y, x); }
  P unit() const { return *this / dist(); }  // makes dist()=1
  P perp() const { return P(-y, x); }        // rotates +90 degrees
  P normal() const { return perp().unit(); }
  // returns point rotated 'a' radians ccw around the origin
  P rotate(ld a) const {
    return P(x * cos(a) - y * sin(a), x * sin(a) + y * cos(a));
  }
  friend ostream& operator<<(ostream& os, P p) {
    return os << "(" << p.x << "," << p.y << ")";
  }
};
#line 2 "geometry/ConvexHull.h"

template <class P>
vector<P> convexHull(vector<P> pts) {
  if (sz(pts) <= 1) return pts;
  sort(all(pts));
  vector<P> h(2 * sz(pts) + 2);
  int s = 0, t = 0;
  for (int it = 2; it--; s = --t, reverse(all(pts))) {
    for (P p : pts) {
      while (t >= s + 2 && h[t - 2].cross(h[t - 1], p) <= 0) t--;
      h[t++] = p;
    }
  }
  return {h.begin(), h.begin() + t - (t == 2 && h[0] == h[1])};
}
#line 2 "geometry/HullDiameter.h"

// S must already be a convex hull
template<class P>
array<P, 2> hullDiameter(vector<P> S) {
  int n = sz(S), j = n < 2 ? 0 : 1;
  pair<i64, array<P, 2>> res({0, {S[0], S[0]}});
  for (int i = 0; i < j; ++i) {
    for (;; j = (j + 1) % n) {
      res = max(res, {(S[i] - S[j]).dist2(), {S[i], S[j]}});
      if ((S[(j + 1) % n] - S[j]).cross(S[i + 1] - S[i]) >= 0) break;
    }
  }
  return res.second;
}
#line 6 "tests/Furthest_Pair_of_Points.test.cpp"

using P = Point<ld>;

void solve() {
  int n;
  cin >> n;
  vector<P> pts(n);
  for (auto& [x, y] : pts) cin >> x >> y;
  auto cvh = convexHull(pts);
  auto [pi, pj] = hullDiameter(cvh);
  int i, j;
  for (i = 0; i < n; ++i) {
    if (pts[i] == pi) {
      cout << i << ' ';
      break;
    }
  }
  for (j = 0; j < n; ++j) {
    if (pts[j] == pj && j != i) {
      cout << j << '\n';
      break;
    }
  }
}

int main() {
  int tc;
  cin >> tc;
  while (tc--) solve();
}