Submission #887839

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
887839	2023-12-15T09:55:25 Z	ad_red	Tri (CEOI09_tri)	C++17	0 / 100	1031 ms	7028 KB

#include <bits/stdc++.h>
#define endl "\n"
  
using namespace std;
using ll = long long;

  
struct Point{
  ll x, y;
};
  
ll vp(Point a, Point b) {
  return a.x * b.y - a.y * b.x;
}
  
ll sgn(Point a, Point b, Point c) {
  // -1 if the order is A-B-C from left to right if B is the bottom point
  // 1 or 0 otherwise
  
  ll q = vp(Point{a.x - b.x, a.y - b.y}, Point{c.x - b.x, c.y - b.y});
  return (q / abs(q));
}
  
bool operator<(Point a, Point b) {
  return sgn(a, Point{0LL, 0LL}, b) == -1;
}
  
bool in_triangle(Point a, Point b, Point c, Point p) {
  // assuming A-B-C
  
  return (sgn(a, b, p) == -1 && sgn(c, b, p) == 1 && sgn(p, c, a) == -1);
}
  
bool cmp_hull(Point a, Point b) {
  if (a.x == b.x) return a.y < b.y;
  return a.x < b.x;
}
  
/*
  Plan:
  0. Sort all points by angle
  1. Construct sqrt(n) convex hulls for all point sets
  2. For each triangle, consider all sqrt(n) ranges of points already present
  3. Check all points that are outside of the hulls manually
  3.5 On both sides
  4. For each complete range with a hull do a binary search on that hull:
  5. Start with the leftmost (by the angle) point, end with the point anticlockwise on the convex hull
  6. Check if the mid is in the triangle, if it is, then break. If we are moving further from the triangle by choosing a point to the right of the current one (cur_mid), then r = mid, else l = mid.
  
  Claim: the total thing takes no more than 200 lines.
*/
  
vector<Point> points;
const ll sqrt_size = 600;

signed main() {
  ll n, m;
  cin >> n >> m;
  
  for (ll i = 0; i < n; i++) {
    ll x, y;
    cin >> x >> y;
  
    points.push_back(Point{x, y});
  }
  
  sort(points.begin(), points.end()); // the comparator is there
  
  vector<vector<Point>> hulls(n);
  
  for (ll i = 0; i < n; i++) {
    hulls[i / sqrt_size].push_back(points[i]);
  }
  
  
  for (ll i = 0; i < n; i++) {
    if (hulls[i].empty()) continue;
    
    vector<Point> hull;
  
    sort(hulls[i].begin(), hulls[i].end(), cmp_hull);
  
    for (auto p : hulls[i]) {
      while (hull.size() > 1 && sgn(p, hull[(ll)hull.size() - 2], hull.back()) == -1) {
        hull.pop_back();
      }
      hull.push_back(p);
    }
  
    hulls[i] = hull;
    // top convex hull only!
  }
  
  // end of hull processing
  
  for (ll trn = 0; trn < m; trn++) {
    // current triangle
  
    Point a, b;
    cin >> a.x >> a.y >> b.x >> b.y;
  
    if (sgn(a, Point{0LL, 0LL}, b) >= 0) swap(a, b);
  
    ll left_start = n - 1, right_end = 0;
  
    // left_start - leftmost point that is in the angle
    // right_end - leftmost point after the angle
    {
      ll l = 0;
      ll r = n;
    
      while (r - l > 1) {
        ll mid = (l + r) / 2;
        if (sgn(a, Point{0, 0}, points[mid]) >= 0) {
          l = mid;
        } else {
          r = mid;
        }
      }
    
      left_start = l;
    }
  
    {
      ll l = 0;
      ll r = n;
    
      while (r - l > 1) {
        ll mid = (l + r) / 2;
        if (sgn(b, Point{0, 0}, points[mid]) >= 0) {
          l = mid;
        } else {
          r = mid;
        }
      }
    
      right_end = r;
    }
  
    if (left_start >= right_end) {
      cout << "N" << endl;
      continue;
    }
  
    bool flag = false;
  
    if (right_end - left_start <= sqrt_size) {
      for (ll i = left_start; i < right_end; i++) {
        if (in_triangle(a, Point{0, 0}, b, points[i])) {
          flag = true;
          break;
        }
      }
  
      if (flag) {
        cout << "Y" << endl;
      } else {
        cout << "N" << endl;
      }
  
      continue;
    }
  
    flag = false;
  
    while (left_start % sqrt_size != 0) {
      if (in_triangle(a, Point{0, 0}, b, points[left_start])) {
        flag = true;
      }
      left_start++;
    }
  
    while (right_end - 1 > left_start && right_end % sqrt_size != 0) {
      right_end--;
      if (in_triangle(a, Point{0, 0}, b, points[right_end])) {
        flag = true;
      }
    }
  
    flag = false;
  
    for (ll i = left_start / sqrt_size; i < right_end / sqrt_size; i++) {
      // convex hull processing
  
      ll l = 0;
      ll r = (ll)hulls[i].size();
  
      while (r - l > 1) {
        ll mid = (r + l) / 2;
  
        if (in_triangle(a, Point{0, 0}, b, hulls[i][mid])) {
          flag = true;
          break;
        }
  
        if (mid + 1 == hulls[i].size() || !in_triangle(a, Point{0, 0}, b, hulls[i][mid + 1]) && sgn(hulls[i][mid + 1], a, hulls[i][mid]) == -1) {
          r = mid;
        } else {
          l = mid;
        }
      }
  
      for (ll j = (l - 3 + hulls[i].size()) % hulls[i].size(); j <= (r + 3 + hulls[i].size()) % hulls[i].size(); j++) {
        if (in_triangle(a, Point{0, 0}, b, hulls[i][j])) {
          flag = true;
          break;
        }
      }
  
      if (flag) break;
    }
  
    if (flag) {
      cout << "Y" << endl;
    } else {
      cout << "N" << endl;
    }
  }
  
  return 0;
}

Compilation message

tri.cpp: In function 'int main()':
tri.cpp:196:21: warning: comparison of integer expressions of different signedness: 'll' {aka 'long long int'} and 'std::vector<Point>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  196 |         if (mid + 1 == hulls[i].size() || !in_triangle(a, Point{0, 0}, b, hulls[i][mid + 1]) && sgn(hulls[i][mid + 1], a, hulls[i][mid]) == -1) {
      |             ~~~~~~~~^~~~~~~~~~~~~~~~~~
tri.cpp:196:94: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
  196 |         if (mid + 1 == hulls[i].size() || !in_triangle(a, Point{0, 0}, b, hulls[i][mid + 1]) && sgn(hulls[i][mid + 1], a, hulls[i][mid]) == -1) {
      |                                           ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
tri.cpp:203:66: warning: comparison of integer expressions of different signedness: 'll' {aka 'long long int'} and 'long long unsigned int' [-Wsign-compare]
  203 |       for (ll j = (l - 3 + hulls[i].size()) % hulls[i].size(); j <= (r + 3 + hulls[i].size()) % hulls[i].size(); j++) {
      |                                                                ~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
0 / 100.0

#	Verdict	Execution time	Memory	Grader output
1	Incorrect	3 ms	348 KB	Output isn't correct
2	Incorrect	3 ms	504 KB	Output isn't correct
3	Incorrect	117 ms	2340 KB	Output isn't correct
4	Incorrect	330 ms	3620 KB	Output isn't correct
5	Incorrect	1031 ms	6980 KB	Output isn't correct
6	Incorrect	678 ms	5688 KB	Output isn't correct
7	Incorrect	863 ms	6788 KB	Output isn't correct
8	Incorrect	325 ms	6080 KB	Output isn't correct
9	Incorrect	358 ms	6332 KB	Output isn't correct
10	Incorrect	402 ms	7028 KB	Output isn't correct

Submission #887839

Compilation message

Subtask #1 0 / 100.0

Subtask #1
0 / 100.0