tests/Count_Points_in_Triangle.test.cpp

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

Depends on

• geometry/Point.h
• geometry/TrianglePointCount.h
• misc/macros.h

Code

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

#include "../misc/macros.h"
#include "../geometry/TrianglePointCount.h"

using P = Point<i64>;

void solve() {
  vector<P> A, B;
  int n, m;
  cin >> n;
  A.resize(n);
  for (auto& [x, y] : A) cin >> x >> y;
  cin >> m;
  B.resize(m);
  for (auto& [x, y] : B) cin >> x >> y;
  TrianglePointCount<P, 500, 500> tpc(A, B);
  int q;
  cin >> q;
  while (q--) {
    int a, b, c;
    cin >> a >> b >> c;
    cout << tpc.query(a, b, c) << '\n';
  }
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tc = 1;
  // cin >> tc;
  while (tc--) solve();
}

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

#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/TrianglePointCount.h"

template <class P, int MAXN, int MAXM>
struct TrianglePointCount {
  // Bảng lưu trạng thái: side[i][j] = bitset các điểm B nằm bên trái vector A[i]->A[j]
  bitset<MAXM> side[MAXN][MAXN];
  const vector<P>& A;  // Tham chiếu tới mảng A để kiểm tra hướng khi truy vấn
  // Constructor: Thực hiện Precomputation O(N^2 * M)
  TrianglePointCount(const vector<P>& A, const vector<P>& B)
      : A(A) {
    int n = sz(A), m = sz(B);
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        if (i == j) continue;
        P vecIJ = A[j] - A[i]; // Vector A[i] -> A[j]
        for (int k = 0; k < m; ++k) {
          P vecIK = B[k] - A[i]; // Vector A[i] -> B[k]
          // Nếu B[k] nằm thực sự bên trái A[i]->A[j] (cross product > 0)
          if (vecIJ.cross(vecIK) > 0) side[i][j][k] = 1;
        }
      }
    }
  }
  // Truy vấn: Đếm số điểm B nằm trong tam giác A[a], A[b], A[c]
  // Độ phức tạp: O(M/64) ~ O(1)
  int query(int a, int b, int c) {
    // Kiểm tra hướng của tam giác
    auto area = A[a].cross(A[b], A[c]);
    if (area == 0) return 0;  // Tam giác suy biến (thẳng hàng)
    if (area > 0) {
      // Ngược chiều kim đồng hồ (CCW): A->B->C
      // Điểm trong tam giác phải nằm trái AB, trái BC, VÀ trái CA
      return (side[a][b] & side[b][c] & side[c][a]).count();
    } else {
      // Cùng chiều kim đồng hồ (CW): A->C->B là CCW
      return (side[a][c] & side[c][b] & side[b][a]).count();
    }
  }
};
#line 5 "tests/Count_Points_in_Triangle.test.cpp"

using P = Point<i64>;

void solve() {
  vector<P> A, B;
  int n, m;
  cin >> n;
  A.resize(n);
  for (auto& [x, y] : A) cin >> x >> y;
  cin >> m;
  B.resize(m);
  for (auto& [x, y] : B) cin >> x >> y;
  TrianglePointCount<P, 500, 500> tpc(A, B);
  int q;
  cin >> q;
  while (q--) {
    int a, b, c;
    cin >> a >> b >> c;
    cout << tpc.query(a, b, c) << '\n';
  }
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tc = 1;
  // cin >> tc;
  while (tc--) solve();
}

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