Submission #1348633

#TimeUsernameProblemLanguageResultExecution timeMemory
1348633avighnaTeam Contest (JOI22_team)C++20
55 / 100
2096 ms5432 KiB
#include <bits/stdc++.h>

using namespace std;

struct triplet {
  int x, y, z;
  triplet() : x(0), y(0), z(0) {}
  auto operator<=>(const triplet &r) const = default;
};

const int inf = 1e9;

class segment_tree {
  int n;
  vector<int> seg;

public:
  segment_tree(int n) : n(n), seg(2 * n, -inf) {}

  void apply(int i, int x) {
    i += n;
    for (seg[i] = max(seg[i], x), i >>= 1; i > 0; i >>= 1) {
      seg[i] = max(seg[2 * i], seg[2 * i + 1]);
    }
  }

  int query(int l, int r) {
    int ans = -inf;
    for (l += n, r += n + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1)
        ans = max(ans, seg[l++]);
      if (r & 1)
        ans = max(ans, seg[--r]);
    }
    return ans;
  }
};

int main() {
  cin.tie(nullptr)->sync_with_stdio(false);

  int n;
  cin >> n;
  vector<triplet> a(n);
  vector<int> buff_y, buff_z;
  for (auto &[x, y, z] : a) {
    cin >> x >> y >> z;
    buff_y.push_back(y), buff_y.push_back(y - 1);
    buff_z.push_back(z), buff_z.push_back(z - 1);
  }
  sort(a.begin(), a.end());
  a.erase(unique(a.begin(), a.end()), a.end());
  n = a.size();

  sort(buff_y.begin(), buff_y.end());
  sort(buff_z.begin(), buff_z.end());
  buff_y.erase(unique(buff_y.begin(), buff_y.end()), buff_y.end());
  buff_z.erase(unique(buff_z.begin(), buff_z.end()), buff_z.end());
  auto compr_y = [&](int i) { return lower_bound(buff_y.begin(), buff_y.end(), i) - buff_y.begin(); };
  auto compr_z = [&](int i) { return lower_bound(buff_z.begin(), buff_z.end(), i) - buff_z.begin(); };

  segment_tree st_y(buff_y.size()), st_z(buff_z.size());
  auto add = [&](int y, int z) {
    st_y.apply(compr_y(y), z);
    st_z.apply(compr_z(z), y);
    // best_pair = max(best_pair, y + st_y.query(0, compr_y(y - 1))); // we dominate someone on y
    // // but what if someone else dominates us on y and we dominate z?
    // best_pair = max(best_pair, z + st_z.query(0, compr_z(z - 1)));
  };

  int ans = -1;
  queue<triplet> q;
  for (int i = 0; i < n; ++i) {
    q.push(a[i]);
    while (!q.empty() && q.front().x < a[i].x) {
      triplet t = q.front();
      q.pop();
      add(t.y, t.z);
    }
    for (int j = 0; j < i && a[j].x < a[i].x; ++j) { // x is satisfied
      // either j dominates y or j dominates z
      // if j dominates y
      if (a[j].y > a[i].y) {
        int z = st_y.query(0, compr_y(a[j].y - 1));
        if (z > a[i].z && z > a[j].z) {
          ans = max(ans, a[i].x + a[j].y + z);
        }
      }
      // if j dominates z
      if (a[j].z > a[i].z) {
        int y = st_z.query(0, compr_z(a[j].z - 1));
        if (y > a[i].y && y > a[j].y) {
          ans = max(ans, a[i].x + y + a[j].z);
        }
      }
    }
  }

  cout << ans << '\n';
}
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