oj.uz

Submission #404810

# Submission time Handle Problem Language Result Execution time Memory
404810 2021-05-15T04:21:37 Z rama_pang Friends (BOI17_friends) C++17
100 / 100
 337 ms 25228 KB 
#include <bits/stdc++.h>
using namespace std;

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

  int N, P, Q;
  cin >> N >> P >> Q;

  const auto Impossible = [&]() {
    cout << "detention\n";
    exit(0);
  };

  vector<vector<int>> adj(N);
  vector<vector<int>> mat(N, vector<int>(N));
  for (int i = 0; i < N; i++) {
    int p;
    cin >> p;
    while (p--) {
      int j;
      cin >> j;
      mat[i][j] = 1;
      adj[i].emplace_back(j);
    }
  }

  for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++) {
      if (mat[i][j] != mat[j][i]) {
        Impossible();
      }
    }
  }

  // Solution:
  // Consider finding a group for a node u. For every node v
  // not adjacent to u, we don't need to consider them (since
  // it will only increase Q unnecessarily). For every node v
  // adjacent to u, either we pick v (and increase current p)
  // or we don't pick v (and increase current q). This way,
  // we have around 2^{P + Q} total options.
  //
  // We find a group for every node u. This runs in O(N (P + Q) 2^{P + Q}).
  // Then, for every pair of nodes, consider the 2 groups of these
  // nodes. If they arent' disjoint, we want to split them so they
  // are. We can note that:
  //
  // p1, p2 <= P, q1, q2 <= Q
  // Let p3 = intersection of (p1, p2).
  // Then:
  // q1 + edges[p1][p3] <= Q
  // q2 + edges[p3][p2] <= Q.
  // So, min(q1 + edges[p3][p2], q2 + edges[p1][p3]) <= Q.
  //
  // So, we can always split them into disjoint groups. We repair
  // all groups this way in O(N^2 * (P + Q)).
  //
  // Time complexity: O(N * (P + Q) * (N + 2^{P + Q})).

  vector<int> cur;
  vector<int> state;

  const auto GetGroup = [&](const auto &self, int cur_head, int ptr, int p, int q, vector<int> &res) {
    if (!res.empty()) return;
    if (p > P || q > Q) return;
    if (cur_head == p) { // found group
      res = cur;
      return;
    }

    int u = cur[cur_head];
    if (adj[u].size() == ptr) {
      return self(self, cur_head + 1, 0, p, q, res);
    }

    int v = adj[u][ptr];
    if (state[v] == 0) { // v is undecided
      state[v] = -1;
      self(self, cur_head, ptr + 1, p, q + 1, res);
      state[v] = +1;
      cur.emplace_back(v);
      self(self, cur_head, ptr + 1, p + 1, q, res);
      cur.pop_back();
      state[v] = 0;
    } else if (state[v] == -1) { // we already decided not to pick this node
      return self(self, cur_head, ptr + 1, p, q + 1, res);
    } else if (state[v] == +1) { // we already picked this node in group
      return self(self, cur_head, ptr + 1, p, q, res);
    }
  };

  vector<vector<int>> inGroup(N);
  for (int u = 0; u < N; u++) {
    state.assign(N, 0);
    cur = {u};
    state[u] = 1;
    GetGroup(GetGroup, 0, 0, 1, 0, inGroup[u]);
    if (inGroup[u].empty()) {
      Impossible();
    }
  }

  const auto IsValid = [&](const vector<int> &A) {
    if (A.size() > P) return false;
    int q = 0;
    static vector<int> in(N);
    for (auto i : A) in[i] = 1;
    for (auto i : A) for (auto j : adj[i]) if (!in[j]) q++;
    for (auto i : A) in[i] = 0;
    return q <= Q;
  };

  const auto FixGroup = [&](int x, int y) {
    static vector<int> who(N);
    for (auto i : inGroup[x]) who[i] = 0;
    for (auto i : inGroup[y]) who[i] = 0;
    for (auto i : inGroup[x]) who[i] |= 1;
    for (auto i : inGroup[y]) who[i] |= 2;

    bool intersect = false;
    for (auto i : inGroup[x]) if (who[i] == 3) intersect = true;
    for (auto i : inGroup[y]) if (who[i] == 3) intersect = true;

    if (!intersect) return true;

    static vector<int> xA, yA; xA.clear(); yA.clear();
    static vector<int> xB, yB; xB.clear(); yB.clear();

    for (auto i : inGroup[x]) {
      if (who[i] == 1) {
        xA.emplace_back(i);
        xB.emplace_back(i);
      } else {
        xA.emplace_back(i);
      }
    }

    for (auto i : inGroup[y]) {
      if (who[i] == 2) {
        yA.emplace_back(i);
        yB.emplace_back(i);
      } else {
        yA.emplace_back(i);
      }
    }

    if (IsValid(xA) && IsValid(yB)) {
      inGroup[x] = xA;
      inGroup[y] = yB;
    } else if (IsValid(xB) && IsValid(yA)) {
      inGroup[x] = xB;
      inGroup[y] = yA;
    } else {
      return false;
    }
    return true;
  };

  state.assign(N, 0);
  for (int i = 0; i < N; i++) {
    for (int j = i + 1; j < N; j++) {
      assert(FixGroup(i, j));
    }
  }

  vector<vector<int>> answer;
  for (int i = 0; i < N; i++) {
    if (!inGroup[i].empty()) {
      answer.emplace_back(inGroup[i]);
    }
  }

  cout << "home\n";
  cout << answer.size() << '\n';
  for (auto &a : answer) {
    sort(begin(a), end(a));
    cout << a.size();
    for (auto i : a) cout << ' ' << i;
    cout << '\n';
  }
  return 0;
}

Compilation message

friends.cpp: In instantiation of 'main()::<lambda(const auto:23&, int, int, int, int, std::vector<int>&)> [with auto:23 = main()::<lambda(const auto:23&, int, int, int, int, std::vector<int>&)>]':
friends.cpp:99:46:   required from here
friends.cpp:74:23: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
   74 |     if (adj[u].size() == ptr) {
      |         ~~~~~~~~~~~~~~^~~~~~
friends.cpp: In lambda function:
friends.cpp:106:18: warning: comparison of integer expressions of different signedness: 'std::vector<int>::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  106 |     if (A.size() > P) return false;
      |         ~~~~~~~~~^~~

Subtask #1
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct

Subtask #2
37.0 / 37.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 4 ms 460 KB Output is correct
3 Correct 2 ms 332 KB Output is correct
4 Correct 1 ms 588 KB Output is correct
5 Correct 2 ms 588 KB Output is correct
6 Correct 1 ms 460 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 4 ms 588 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 4 ms 460 KB Output is correct
3 Correct 2 ms 332 KB Output is correct
4 Correct 1 ms 588 KB Output is correct
5 Correct 2 ms 588 KB Output is correct
6 Correct 1 ms 460 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 4 ms 588 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 44 ms 4424 KB Output is correct
11 Correct 58 ms 6652 KB Output is correct
12 Correct 70 ms 6156 KB Output is correct
13 Correct 87 ms 6556 KB Output is correct
14 Correct 31 ms 13180 KB Output is correct
15 Correct 30 ms 13168 KB Output is correct
16 Correct 9 ms 16076 KB Output is correct

Subtask #4
31.0 / 31.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 4 ms 460 KB Output is correct
11 Correct 2 ms 332 KB Output is correct
12 Correct 1 ms 588 KB Output is correct
13 Correct 2 ms 588 KB Output is correct
14 Correct 1 ms 460 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 4 ms 588 KB Output is correct
17 Correct 1 ms 204 KB Output is correct
18 Correct 44 ms 4424 KB Output is correct
19 Correct 58 ms 6652 KB Output is correct
20 Correct 70 ms 6156 KB Output is correct
21 Correct 87 ms 6556 KB Output is correct
22 Correct 31 ms 13180 KB Output is correct
23 Correct 30 ms 13168 KB Output is correct
24 Correct 9 ms 16076 KB Output is correct
25 Correct 1 ms 204 KB Output is correct
26 Correct 97 ms 14748 KB Output is correct
27 Correct 83 ms 13276 KB Output is correct
28 Correct 87 ms 11216 KB Output is correct
29 Correct 22 ms 4784 KB Output is correct
30 Correct 16 ms 7048 KB Output is correct
31 Correct 12 ms 6988 KB Output is correct
32 Correct 9 ms 16076 KB Output is correct
33 Correct 337 ms 25228 KB Output is correct
34 Correct 85 ms 25124 KB Output is correct