oj.uz

Submission #643497

# Submission time Handle Problem Language Result Execution time Memory
643497 2022-09-22T07:53:50 Z lunchbox1 Dragon 2 (JOI17_dragon2) C++17
100 / 100
 1230 ms 17140 KB 
/*
JOI17_dragon2 - Dragon 2

assume that |i|<|j| in the queries. notice that if you spend |i| per query,
then you get a O(n sqrt n) complexity
- if |i| less than sqrt n, then it's ok
- otherwise we have that both |i| (and |j|) are greater than sqrt n. there are
at most sqrt(n) j that are possible due to |j| so this amortizes to O(n sqrt n)

so for the geo part, we can write that the line crosses the village as a form 
of two inequalities (one for p and one for q).

you can use a 2d segtree (pst + binary search) to deal with this.

complexity is O(n sqrt n log n).
*/
#include <bits/stdc++.h>
using namespace std;

template<class T>
pair<T, T> _minmax(const T& a, const T& b) {
  if (a < b)
    return make_pair(a, b);
  else
    return make_pair(b, a);
}

typedef __int128 i128;

const int N = 30000, Q = 100000;
const i128 PI = (i128) 1e36 * acosl(-1);

i128 acos2_128(int x, int y) {
  return (i128) 1e36 * atan2l(y, x);
}
i128 opposite(const i128& x) {
  return x < 0 ? x + PI : x - PI;
}

struct point {
  int x, y;
  i128 ang_a, ang_b;

  point() {}
  point(int x, int y) : x(x), y(y) {}
  i128 angle(const point& p) const {
    return acos2_128(p.x - x, p.y - y);
  }
} A, B;

int ans[Q];

namespace pst {
  const int M = N * 15 * 2;
  int sum[M], ll[M], rr[M], _;
 
  void clear() {
    _ = 0;
  }
  int node(int k = 0) {
    ++_;
    sum[_] = sum[k];
    ll[_] = ll[k], rr[_] = rr[k];
    return _;
  }
  int build(int l, int r) {
    int v = node(), m;
   
    if (l < r) {
      m = (l + r) / 2;
      ll[v] = build(l, m);
      rr[v] = build(m + 1, r);
    }
    return v;
  }
  int update(int v, int l, int r, int i, int x) {
    int v_ = node(v), m;
   
    sum[v_] += x;
    if (l < r) {
      m = (l + r) / 2;
      if (i <= m)
        ll[v_] = update(ll[v_], l, m, i, x);
      else
        rr[v_] = update(rr[v_], m + 1, r, i, x);
    }
    return v_;
  }
  int query(int v, int l, int r, int ql, int qr) {
    int m;
   
    if (qr < l || ql > r)
      return 0;
    if (ql <= l && qr >= r)
      return sum[v];
    m = (l + r) / 2;
    return query(ll[v], l, m, ql, qr) + query(rr[v], m + 1, r, ql, qr);
  }
}

struct group {
  vector<int> vv;
  vector<i128> xx, yy;
  vector<point> pp;
  int n;

  int size() {
    return n;
  }
  void add(const point& p) {
    pp.push_back(p), n++;
  }
  void add_query(const i128& lx, const i128& rx, const i128& ly, const i128& ry, int h) {
    short l = lower_bound(yy.begin(), yy.end(), ly) - yy.begin();
    short r = upper_bound(yy.begin(), yy.end(), ry) - yy.begin() - 1;
    short l_ = lower_bound(xx.begin(), xx.end(), lx - 1) - xx.begin();
    short r_ = upper_bound(xx.begin(), xx.end(), rx) - xx.begin() - 1;

    ans[h] += pst::query(vv[r_ + 1], 0, yy.size() - 1, l, r) - pst::query(vv[l_], 0, yy.size() - 1, l, r);
  }
  void add1(const point& q, int h) {
    auto [l_a, r_a] = _minmax(q.ang_a, opposite(q.ang_a));
    bool side_a = l_a <= B.ang_a && B.ang_a <= r_a;
    auto [l_b, r_b] = _minmax(q.ang_b, opposite(q.ang_b));
    bool side_b = l_b <= A.ang_b && A.ang_b <= r_b;

    if (side_a == 1) {
      if (side_b == 1)
        add_query(l_a, r_a, l_b, r_b, h);
      else {
        add_query(l_a, r_a, -PI, l_b - 1, h);
        add_query(l_a, r_a, r_b + 1, PI, h);
      }
    } else {
      if (side_b == 1) {
        add_query(-PI, l_a - 1, l_b, r_b, h);
        add_query(r_a + 1, PI, l_b, r_b, h);
      } else {
        add_query(-PI, l_a - 1, -PI, l_b - 1, h);
        add_query(r_a + 1, PI, -PI, l_b - 1, h);
        add_query(-PI, l_a - 1, r_b + 1, PI, h);
        add_query(r_a + 1, PI, r_b + 1, PI, h);
      }
    }
  }
  void add2(const point& q, int h) {
    auto [l_a, r_a] = _minmax(q.ang_a, opposite(q.ang_a));
    bool side_a = !(l_a <= B.ang_a && B.ang_a <= r_a);
    auto [l_b, r_b] = _minmax(q.ang_b, opposite(q.ang_b));
    bool side_b = !(l_b <= A.ang_b && A.ang_b <= r_b);

    if (side_a == 1) {
      if (side_b == 1)
        add_query(l_a, r_a, l_b, r_b, h);
      else {
        add_query(l_a, r_a, -PI, l_b - 1, h);
        add_query(l_a, r_a, r_b + 1, PI, h);
      }
    } else {
      if (side_b == 1) {
        add_query(-PI, l_a - 1, l_b, r_b, h);
        add_query(r_a + 1, PI, l_b, r_b, h);
      } else {
        add_query(-PI, l_a - 1, -PI, l_b - 1, h);
        add_query(r_a + 1, PI, -PI, l_b - 1, h);
        add_query(-PI, l_a - 1, r_b + 1, PI, h);
        add_query(r_a + 1, PI, r_b + 1, PI, h);
      }
    }
    tie(l_a, r_a) = _minmax(opposite(q.ang_a), B.ang_a);
    side_a = !(l_a <= q.ang_a && q.ang_a <= r_a);
    tie(l_b, r_b) = _minmax(opposite(q.ang_b), A.ang_b);
    side_b = !(l_b <= q.ang_b && q.ang_b <= r_b);
    if (side_a == 1) {
      if (side_b == 1)
        add_query(l_a, r_a, l_b, r_b, h);
      else {
        add_query(l_a, r_a, -PI, l_b - 1, h);
        add_query(l_a, r_a, r_b + 1, PI, h);
      }
    } else {
      if (side_b == 1) {
        add_query(-PI, l_a - 1, l_b, r_b, h);
        add_query(r_a + 1, PI, l_b, r_b, h);
      } else {
        add_query(-PI, l_a - 1, -PI, l_b - 1, h);
        add_query(r_a + 1, PI, -PI, l_b - 1, h);
        add_query(-PI, l_a - 1, r_b + 1, PI, h);
        add_query(r_a + 1, PI, r_b + 1, PI, h);
      }
    }
  }
  void build() {
    for (const point& p : pp) {
      xx.push_back(p.ang_a);
      yy.push_back(p.ang_b);
    }
    sort(xx.begin(), xx.end());
    sort(yy.begin(), yy.end());
    sort(pp.begin(), pp.end(), [&](const point& p, const point& q) {
      return p.ang_a < q.ang_a;
    });
    pst::clear();
    vv.push_back(pst::build(0, yy.size() - 1));
    for (const point& p : pp) {
      int i = lower_bound(yy.begin(), yy.end(), p.ang_b) - yy.begin();

      vv.push_back(pst::update(vv.back(), 0, yy.size() - 1, i, +1));
    }
  }
  void clear() {
    xx.clear();
    yy.clear();
  }
} gr[N];

int main() {
#ifndef LOCAL
  ios::sync_with_stdio(false);
  cin.tie(NULL);
#endif
  static vector<tuple<int, int, bool>> todo[N];
  vector<pair<point, int>> pp;
  int n, m, q;

  cin >> n >> m;
  pp.resize(n);
  for (auto &[p, c] : pp)
    cin >> p.x >> p.y >> c, c--;
  cin >> A.x >> A.y >> B.x >> B.y;
  A.ang_a = A.angle(A);
  A.ang_b = B.angle(A);
  B.ang_a = A.angle(B);
  B.ang_b = B.angle(B);
  for (auto &[p, c] : pp) {
    p.ang_a = A.angle(p);
    p.ang_b = B.angle(p);
    gr[c].add(p);
  }
  pp.clear();
  cin >> q;
  for (int h = 0; h < q; h++) {
    int c1, c2;

    cin >> c1 >> c2, c1--, c2--;
    if (gr[c1].size() < gr[c2].size())
      todo[c2].push_back({c1, h, 0});
    else
      todo[c1].push_back({c2, h, 1});
  }
  for (int c = 0; c < m; c++) {
    gr[c].build();
    for (auto [c_, h, t] : todo[c])
      for (const point& p : gr[c_].pp)
        if (t == 0)
          gr[c].add1(p, h);
        else
          gr[c].add2(p, h);
    gr[c].clear();
    todo[c].clear();
  }
  for (int h = 0; h < q; h++)
    cout << ans[h] << '\n';
  return 0;
}

Subtask #1
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 4948 KB Output is correct
2 Correct 18 ms 4776 KB Output is correct
3 Correct 61 ms 4892 KB Output is correct
4 Correct 66 ms 7756 KB Output is correct
5 Correct 46 ms 7900 KB Output is correct
6 Correct 6 ms 4820 KB Output is correct
7 Correct 8 ms 4892 KB Output is correct
8 Correct 6 ms 4948 KB Output is correct
9 Correct 6 ms 4820 KB Output is correct
10 Correct 5 ms 4820 KB Output is correct

Subtask #2
45.0 / 45.0

# Verdict Execution time Memory Grader output
1 Correct 59 ms 12548 KB Output is correct
2 Correct 198 ms 10124 KB Output is correct
3 Correct 52 ms 10820 KB Output is correct
4 Correct 29 ms 10236 KB Output is correct
5 Correct 29 ms 11084 KB Output is correct
6 Correct 53 ms 12592 KB Output is correct
7 Correct 45 ms 12604 KB Output is correct
8 Correct 39 ms 12772 KB Output is correct
9 Correct 32 ms 12336 KB Output is correct
10 Correct 30 ms 12300 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 4948 KB Output is correct
2 Correct 18 ms 4776 KB Output is correct
3 Correct 61 ms 4892 KB Output is correct
4 Correct 66 ms 7756 KB Output is correct
5 Correct 46 ms 7900 KB Output is correct
6 Correct 6 ms 4820 KB Output is correct
7 Correct 8 ms 4892 KB Output is correct
8 Correct 6 ms 4948 KB Output is correct
9 Correct 6 ms 4820 KB Output is correct
10 Correct 5 ms 4820 KB Output is correct
11 Correct 59 ms 12548 KB Output is correct
12 Correct 198 ms 10124 KB Output is correct
13 Correct 52 ms 10820 KB Output is correct
14 Correct 29 ms 10236 KB Output is correct
15 Correct 29 ms 11084 KB Output is correct
16 Correct 53 ms 12592 KB Output is correct
17 Correct 45 ms 12604 KB Output is correct
18 Correct 39 ms 12772 KB Output is correct
19 Correct 32 ms 12336 KB Output is correct
20 Correct 30 ms 12300 KB Output is correct
21 Correct 74 ms 12524 KB Output is correct
22 Correct 197 ms 10196 KB Output is correct
23 Correct 1230 ms 10736 KB Output is correct
24 Correct 1183 ms 13472 KB Output is correct
25 Correct 124 ms 13748 KB Output is correct
26 Correct 87 ms 14676 KB Output is correct
27 Correct 32 ms 12144 KB Output is correct
28 Correct 31 ms 12104 KB Output is correct
29 Correct 124 ms 16752 KB Output is correct
30 Correct 77 ms 17020 KB Output is correct
31 Correct 79 ms 17140 KB Output is correct
32 Correct 94 ms 14472 KB Output is correct
33 Correct 728 ms 14836 KB Output is correct
34 Correct 73 ms 15000 KB Output is correct
35 Correct 74 ms 14444 KB Output is correct
36 Correct 78 ms 14388 KB Output is correct
37 Correct 101 ms 14668 KB Output is correct
38 Correct 765 ms 15072 KB Output is correct
39 Correct 985 ms 14616 KB Output is correct
40 Correct 883 ms 14864 KB Output is correct
41 Correct 140 ms 15220 KB Output is correct
42 Correct 188 ms 14348 KB Output is correct
43 Correct 269 ms 14264 KB Output is correct
44 Correct 73 ms 13484 KB Output is correct
45 Correct 67 ms 11852 KB Output is correct
46 Correct 69 ms 11548 KB Output is correct
47 Correct 67 ms 13440 KB Output is correct
48 Correct 62 ms 11972 KB Output is correct
49 Correct 52 ms 11520 KB Output is correct