Submission #887661

#	Time	Username	Problem	Language	Result	Execution time	Memory
887661		ad_red	Tri (CEOI09_tri)	C++17	0 / 100	57 ms	13432 KiB

tri

#include <bits/stdc++.h>
#define endl "\n"

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")

using namespace std;
using ll = long long;
using ld = long double;

ll inf = 1e9;

struct Point{
  ll x, y;
};

void pv(vector<Point> s) {
  for (auto c : s) {
    cout << "{" << c.x << ", " << c.y << "} ";
  }
  cout << endl;
}

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;

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);

  ll n, m;
  cin >> n >> m;

  for (int 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 (int i = 0; i < n; i++) {
    hulls[i / sqrt_size].push_back(points[i]);
  }


  for (int 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[(int)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 (int 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) == 1) swap(a, b);

    ll left_start, right_end;

    // left_start - leftmost point that is in the angle
    // right_end - leftmost point after the angle

    ll l = -1;
    ll r = n - 1;

    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 = r;

    l = 0;
    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 (l >= r) {
      cout << "N" << endl;
      continue;
    }

    bool flag = false;

    if (right_end - left_start < sqrt_size) {
      for (int 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 < right_end && left_start % sqrt_size != 0) {
      if (in_triangle(a, Point{0, 0}, b, points[left_start])) {
        flag = true;
        break;
      }
      left_start++;
    }


    while (right_end > left_start && right_end % sqrt_size != 0) {
      right_end--;
      if (in_triangle(a, Point{0, 0}, b, points[right_end])) {
        flag = true;
        break;
      }
    }

    if (right_end <= left_start) {
      if (flag) {
        cout << "Y" << endl;
      } else {
        cout << "N" << endl;
      }
      continue;
    }

    assert(left_start % sqrt_size == 0);
    assert(right_end % sqrt_size == 0);

    if (flag) {
      cout << "Y" << endl;
      continue;
    }

    
    flag = false;

    for (int i = left_start / sqrt_size; i < right_end / sqrt_size; i++) {
      // convex hull processing

      ll l = 0;
      ll r = (int)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 (int 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 (stderr)

tri.cpp: In function 'int main()':
tri.cpp:230:21: 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]
  230 |         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:230:94: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
  230 |         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:237:67: warning: comparison of integer expressions of different signedness: 'int' and 'long long unsigned int' [-Wsign-compare]
  237 |       for (int j = (l - 3 + hulls[i].size()) % hulls[i].size(); j <= (r + 3 + hulls[i].size()) % hulls[i].size(); j++) {
      |                                                                 ~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 0 / 100