oj.uz

Submission #404802

# Submission time Handle Problem Language Result Execution time Memory
404802 2021-05-15T03:30:27 Z rama_pang Cat in a tree (BOI17_catinatree) C++17
100 / 100
 61 ms 11756 KB 
#include <bits/stdc++.h>
using namespace std;

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

  int N, D;
  cin >> N >> D;

  vector<vector<int>> adj(N);
  for (int i = 1; i < N; i++) {
    int p;
    cin >> p;
    adj[p].emplace_back(i);
  }

  // Solution:
  //
  // Similar to: https://atcoder.jp/contests/xmascon16noon/tasks/xmascon16_h
  //
  // For each node, we save the maximum number of picked nodes, which
  // also maximizes the minimum distance to current node. We additionally save the
  // number of nodes which has that maximum minimum distance.
  //
  // Consider 2 children of current node. Assume from child[1], we pick 1 node,
  // where the distance is a, and from the other child, we pick 2 nodes, where
  // the distance to current node is p + x and q + x (distance between the 2 nodes
  // is p + q).
  //
  // Then, we have p + q >= K. Moreover, if:
  // a + x + p < K
  // a + x + q < K
  // p + q >= K
  // Implies:
  // 2a + 2x + (p + q) < 2K
  // 2a + 2x < K
  // a + x < K / 2
  //
  // Then, since p + q >= K -> max(p, q) >= K / 2
  //
  // So, a + x + p < K and a + x + q < K only happens when:
  // p = q = K / 2
  // a + x < K / 2
  //
  // If p > K / 2, then a + x + p >= K, so we using the
  // explained data (maximum picked, distance to picked,
  // count nodes with that distance) is enough.
  //
  // We can also note that, since p, q is from same child,
  // then x >= 1. So, this a + x + p < K and a + x + q < K
  // case can only happen when a < K / 2 - 1. But in this case,
  // we can just not pick a to preserve the condition (by picking
  // p and q) instead. So, we only need to keep the minimum distance
  // instead.
  //
  // Time complexity: O(N).

  int ans = 0;
  const auto Dfs = [&](const auto &self, int u) -> int {
    ans += 1; // pick current node
    int dist = 0;
    for (auto v : adj[u]) {
      int other = self(self, v) + 1;
      if (dist + other < D) {
        ans -= 1; // we only need to decrease 1, by lemma above
        dist = max(dist, other);
      } else {
        dist = min(dist, other);
      }
    }
    return dist;
  };

  Dfs(Dfs, 0);

  cout << ans << '\n';
  return 0;
}

Subtask #1
11.0 / 11.0

# 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 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 312 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 256 KB Output is correct
18 Correct 1 ms 312 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct

Subtask #2
40.0 / 40.0

# 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 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 312 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 256 KB Output is correct
18 Correct 1 ms 312 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 2 ms 332 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 1 ms 316 KB Output is correct
28 Correct 1 ms 320 KB Output is correct
29 Correct 1 ms 332 KB Output is correct
30 Correct 1 ms 332 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 1 ms 332 KB Output is correct
35 Correct 1 ms 332 KB Output is correct
36 Correct 1 ms 332 KB Output is correct
37 Correct 1 ms 332 KB Output is correct
38 Correct 1 ms 332 KB Output is correct
39 Correct 1 ms 332 KB Output is correct
40 Correct 1 ms 332 KB Output is correct

Subtask #3
49.0 / 49.0

# 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 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 312 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 256 KB Output is correct
18 Correct 1 ms 312 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 2 ms 332 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 1 ms 316 KB Output is correct
28 Correct 1 ms 320 KB Output is correct
29 Correct 1 ms 332 KB Output is correct
30 Correct 1 ms 332 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 1 ms 332 KB Output is correct
35 Correct 1 ms 332 KB Output is correct
36 Correct 1 ms 332 KB Output is correct
37 Correct 1 ms 332 KB Output is correct
38 Correct 1 ms 332 KB Output is correct
39 Correct 1 ms 332 KB Output is correct
40 Correct 1 ms 332 KB Output is correct
41 Correct 38 ms 9572 KB Output is correct
42 Correct 25 ms 4812 KB Output is correct
43 Correct 25 ms 4804 KB Output is correct
44 Correct 23 ms 4840 KB Output is correct
45 Correct 24 ms 4840 KB Output is correct
46 Correct 61 ms 9348 KB Output is correct
47 Correct 57 ms 9348 KB Output is correct
48 Correct 57 ms 9284 KB Output is correct
49 Correct 57 ms 9368 KB Output is correct
50 Correct 14 ms 3532 KB Output is correct
51 Correct 15 ms 3600 KB Output is correct
52 Correct 14 ms 3636 KB Output is correct
53 Correct 29 ms 6852 KB Output is correct
54 Correct 35 ms 6832 KB Output is correct
55 Correct 28 ms 6860 KB Output is correct
56 Correct 1 ms 332 KB Output is correct
57 Correct 5 ms 1956 KB Output is correct
58 Correct 21 ms 8136 KB Output is correct
59 Correct 46 ms 11756 KB Output is correct
60 Correct 46 ms 10056 KB Output is correct
61 Correct 55 ms 9800 KB Output is correct