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Submission #288869

# Submission time Handle Problem Language Result Execution time Memory
288869 2020-09-02T03:38:26 Z rama_pang Dragon 2 (JOI17_dragon2) C++14
100 / 100
 1004 ms 10872 KB 
#include <bits/stdc++.h>
using namespace std;

using Point = complex<long long>;

long long Dot(Point a, Point b) {
  return real(conj(a) * b);
}
long long Cross(Point a, Point b) {
  return imag(conj(a) * b);
}
bool Clockwise(Point a, Point b, Point c) {
  return Cross(b - a, c - a) > 0;
}
bool CounterClockwise(Point a, Point b, Point c) {
  return Cross(b - a, c - a) < 0;
}

namespace std {

template<class T>
istream& operator>>(istream &is, complex<T> &inp) {
  T a, b;
  is >> a >> b;
  inp = complex<T>(a, b);
  return is;
}

bool operator<(Point p, Point q) {
  return Cross(p, q) > 0;
}

}

class Fenwick {
 public:
  int sz;
  vector<int> tree;

  Fenwick() {}
  Fenwick(int sz) : sz(sz), tree(sz) {}

  void Update(int p, int x) {
    for (int i = p; i < sz; i |= i + 1) {
      tree[i] += x;
    }
  }
  int Sum(int p) {
    int res = 0;
    for (int i = p + 1; i > 0; i &= i - 1) {
      res += tree[i - 1];
    }
    return res;
  }
  int Sum(int l, int r) {
    return Sum(r) - Sum(l - 1);
  }
};

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

  int N, M;
  cin >> N >> M;

  vector<int> C(N);
  vector<Point> P(N);
  for (int i = 0; i < N; i++) {
    cin >> P[i] >> C[i];
    C[i]--;
  }

  Point X, Y;
  cin >> X >> Y;

  vector<bool> side(N);
  for (int i = 0; i < N; i++) {
    side[i] = Clockwise(X, Y, P[i]);
  }

  vector<Point> angle_x(N), angle_y(N);
  vector<pair<Point, int>> sorted_x(N);
  vector<pair<int, Point>> sorted_y(N);
  for (int i = 0; i < N; i++) {
    angle_x[i] = (side[i] ? P[i] - X : X - P[i]);
    sorted_x[i] = make_pair(angle_x[i], i);
    
    angle_y[i] = (side[i] ? P[i] - Y : Y - P[i]);
    sorted_y[i] = make_pair(C[i], angle_y[i]);
  }
  sort(begin(sorted_x), end(sorted_x));
  sort(begin(sorted_y), end(sorted_y));

  vector<int> pos_in_sorted(N), color_pos(M + 1);
  for (int i = 0; i < N; i++) {
    pos_in_sorted[i] = lower_bound(begin(sorted_y), end(sorted_y), make_pair(C[i], angle_y[i])) - begin(sorted_y);
  }
  for (int i = 0; i <= M; i++) {
    color_pos[i] = lower_bound(begin(sorted_y), end(sorted_y), make_pair(i, Y - X)) - begin(sorted_y);;
  }

  int Q;
  cin >> Q;
  vector<int> A(Q), B(Q);
  vector<long long> ans(Q);
  vector<vector<pair<int, int>>> query_a(M);
  vector<vector<pair<int, int>>> query_b(M);
  for (int i = 0; i < Q; i++) {
    cin >> A[i] >> B[i];
    A[i]--, B[i]--;
    query_a[A[i]].emplace_back(B[i], i);
  }

  // O(N sqrt Q log N)
  const int SQRT = round(sqrt(Q));
  for (int i = 0; i < M; i++) {
    if (query_a[i].size() >= SQRT) {
      for (auto j : query_a[i]) {
        query_b[j.first].emplace_back(i, j.second);
      }
      query_a[i].clear();
    }
  }

  { // Solve query_a
    Fenwick f0(N); // side[i] = true
    Fenwick f1(N); // side[i] = false
    for (int i = 0; i < N; i++) {
      if (!side[i]) {
        f1.Update(pos_in_sorted[i], +1);
      }
    }
    for (int t = 0; t < N; t++) {
      int i = sorted_x[t].second;
      int c = C[i];
      for (auto q : query_a[c]) {
        int pos = lower_bound(begin(sorted_y), end(sorted_y), make_pair(q.first, angle_y[i])) - begin(sorted_y);
        ans[q.second] += f0.Sum(pos, color_pos[q.first + 1] - 1);
        ans[q.second] += f1.Sum(color_pos[q.first], pos - 1);
      }
      if (side[i]) {
        f0.Update(pos_in_sorted[i], +1);
      } else {
        f1.Update(pos_in_sorted[i], -1);
      }
    }
  }

  { // Solve query_b
    Fenwick f0(N); // side[i] = true
    Fenwick f1(N); // side[i] = false
    for (int i = 0; i < N; i++) {
      f0.Update(pos_in_sorted[i], +1);
    }
    for (int t = 0; t < N; t++) {
      int i = sorted_x[t].second;
      int c = C[i];
      for (auto q : query_b[c]) {
        int pos = lower_bound(begin(sorted_y), end(sorted_y), make_pair(q.first, angle_y[i])) - begin(sorted_y);
        if (side[i]) {
          ans[q.second] += f0.Sum(color_pos[q.first], pos - 1);
        } else {
          ans[q.second] += f1.Sum(pos, color_pos[q.first + 1] - 1);
        }
      }
      f0.Update(pos_in_sorted[i], -1);
      f1.Update(pos_in_sorted[i], +1);
    }
  }

  for (int i = 0; i < Q; i++) {
    cout << ans[i] << '\n';
  }
  return 0;
}

Compilation message

dragon2.cpp: In function 'int main()':
dragon2.cpp:118:27: warning: comparison of integer expressions of different signedness: 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} and 'const int' [-Wsign-compare]
  118 |     if (query_a[i].size() >= SQRT) {
      |         ~~~~~~~~~~~~~~~~~~^~~~~~~

Subtask #1
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 640 KB Output is correct
2 Correct 5 ms 640 KB Output is correct
3 Correct 25 ms 768 KB Output is correct
4 Correct 75 ms 3576 KB Output is correct
5 Correct 49 ms 3960 KB Output is correct
6 Correct 3 ms 896 KB Output is correct
7 Correct 3 ms 896 KB Output is correct
8 Correct 3 ms 640 KB Output is correct
9 Correct 2 ms 640 KB Output is correct
10 Correct 2 ms 640 KB Output is correct

Subtask #2
45.0 / 45.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 3600 KB Output is correct
2 Correct 57 ms 3612 KB Output is correct
3 Correct 34 ms 3600 KB Output is correct
4 Correct 28 ms 3732 KB Output is correct
5 Correct 31 ms 5232 KB Output is correct
6 Correct 27 ms 3600 KB Output is correct
7 Correct 28 ms 3600 KB Output is correct
8 Correct 28 ms 3600 KB Output is correct
9 Correct 20 ms 3600 KB Output is correct
10 Correct 22 ms 3712 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 640 KB Output is correct
2 Correct 5 ms 640 KB Output is correct
3 Correct 25 ms 768 KB Output is correct
4 Correct 75 ms 3576 KB Output is correct
5 Correct 49 ms 3960 KB Output is correct
6 Correct 3 ms 896 KB Output is correct
7 Correct 3 ms 896 KB Output is correct
8 Correct 3 ms 640 KB Output is correct
9 Correct 2 ms 640 KB Output is correct
10 Correct 2 ms 640 KB Output is correct
11 Correct 30 ms 3600 KB Output is correct
12 Correct 57 ms 3612 KB Output is correct
13 Correct 34 ms 3600 KB Output is correct
14 Correct 28 ms 3732 KB Output is correct
15 Correct 31 ms 5232 KB Output is correct
16 Correct 27 ms 3600 KB Output is correct
17 Correct 28 ms 3600 KB Output is correct
18 Correct 28 ms 3600 KB Output is correct
19 Correct 20 ms 3600 KB Output is correct
20 Correct 22 ms 3712 KB Output is correct
21 Correct 30 ms 3600 KB Output is correct
22 Correct 56 ms 3596 KB Output is correct
23 Correct 342 ms 3960 KB Output is correct
24 Correct 726 ms 6740 KB Output is correct
25 Correct 135 ms 7328 KB Output is correct
26 Correct 102 ms 8616 KB Output is correct
27 Correct 34 ms 5904 KB Output is correct
28 Correct 33 ms 5912 KB Output is correct
29 Correct 82 ms 9204 KB Output is correct
30 Correct 524 ms 9896 KB Output is correct
31 Correct 85 ms 10272 KB Output is correct
32 Correct 89 ms 10868 KB Output is correct
33 Correct 875 ms 10024 KB Output is correct
34 Correct 92 ms 10280 KB Output is correct
35 Correct 89 ms 10872 KB Output is correct
36 Correct 93 ms 9888 KB Output is correct
37 Correct 94 ms 10404 KB Output is correct
38 Correct 280 ms 10792 KB Output is correct
39 Correct 1004 ms 10448 KB Output is correct
40 Correct 867 ms 10028 KB Output is correct
41 Correct 87 ms 10664 KB Output is correct
42 Correct 94 ms 10528 KB Output is correct
43 Correct 105 ms 10656 KB Output is correct
44 Correct 38 ms 6048 KB Output is correct
45 Correct 38 ms 6164 KB Output is correct
46 Correct 38 ms 6144 KB Output is correct
47 Correct 36 ms 5920 KB Output is correct
48 Correct 37 ms 6016 KB Output is correct
49 Correct 39 ms 5920 KB Output is correct