結果

問題 No.2504 NOT Path Painting
コンテスト
ユーザー emthrm
提出日時 2023-08-02 16:55:31
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 4,128 bytes
コンパイル時間 1,380 ms
コンパイル使用メモリ 101,072 KB
実行使用メモリ 21,288 KB
最終ジャッジ日時 2024-11-20 06:53:31
合計ジャッジ時間 35,180 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 13 TLE * 8
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ソースコード

diff #
raw source code 

#include <cassert>
#include <iostream>
#include <vector>

#include <atcoder/modint>
using mint = atcoder::modint998244353;

int ChoosePair(const int n) { return n * (n + 1) / 2; }

// <TLE>
// Õ(n^3) 時間？
mint Solve(const std::vector<std::vector<int>>& tree) {
  const int n = tree.size();
  const mint denominator = mint(ChoosePair(n)).inv();

  const auto F = [](const mint& probability) -> mint {
    return probability * (2 - probability) * (1 - probability).pow(2).inv();
  };
  const auto G = [&denominator, F](const int num1, const int num2) -> mint {
    return F(num1 * num2 * denominator);
  };

  std::vector<int> subtree(n);  // 部分木の大きさ
  const auto CalcSubtree = [&tree, &subtree](
      auto CalcSubtree, const int parent, const int vertex) -> void {
    subtree[vertex] = 1;
    for (const int neighborhood : tree[vertex]) {
      if (neighborhood != parent) {
        CalcSubtree(CalcSubtree, vertex, neighborhood);
        subtree[vertex] += subtree[neighborhood];
      }
    }
  };
  // 最後の操作前にそのパスが白く塗られている期待値を求める
  mint ans = 0;
  const auto dfs = [&tree, n, &denominator, G, &subtree, &ans](
      auto dfs, const int root, const int child_of_root,
      const int parent, const int vertex, const int distance, int bad_choice)
          -> void {
    for (const int neighborhood_of_vertex : tree[vertex]) {
      if (neighborhood_of_vertex != parent) {
        bad_choice += ChoosePair(subtree[neighborhood_of_vertex]);
      }
    }
    if (distance < n - 1 && root < vertex) {
      mint expected_value = G(n - subtree[child_of_root], subtree[vertex]);
      for (const int neighborhood_of_root : tree[root]) {
        if (neighborhood_of_root != child_of_root) {
          expected_value -= G(subtree[neighborhood_of_root], subtree[vertex]);
        }
      }
      for (const int neighborhood_of_vertex : tree[vertex]) {
        if (neighborhood_of_vertex != parent) {
          expected_value -=
              G(n - subtree[child_of_root], subtree[neighborhood_of_vertex]);
        }
      }
      for (const int neighborhood_of_root : tree[root]) {
        if (neighborhood_of_root == child_of_root) continue;
        for (const int neighborhood_of_vertex : tree[vertex]) {
          if (neighborhood_of_vertex == parent) continue;
          expected_value +=
              G(subtree[neighborhood_of_root], subtree[neighborhood_of_vertex]);
        }
      }
      ans += expected_value * bad_choice * denominator;
    }
    for (const int neighborhood : tree[vertex]) {
      if (neighborhood != parent) {
        dfs(dfs, root, child_of_root, vertex, neighborhood,
            distance + 1, bad_choice - ChoosePair(subtree[neighborhood]));
      }
    }
  };
  for (int root = 0; root < n; ++root) {
    CalcSubtree(CalcSubtree, -1, root);
    int bad_choice = 0;
    for (const int child : tree[root]) bad_choice += ChoosePair(subtree[child]);
    for (const int child : tree[root]) {
      dfs(dfs, root, child, root,
          child, 1, bad_choice - ChoosePair(subtree[child]));
    }
    // パス P = (root) のとき
    mint expected_value = F(1 - bad_choice * denominator);
    for (const int child : tree[root]) {
      expected_value -= G(n - subtree[child], subtree[child]);
    }
    const int children_num = tree[root].size();
    for (int i = 0; i < children_num; ++i) {
      for (int j = i + 1; j < children_num; ++j) {
        expected_value += G(subtree[tree[root][i]], subtree[tree[root][j]]);
      }
    }
    ans += expected_value * bad_choice * denominator;
  }

  return ans;
}

int main() {
  constexpr int kMaxT = 100000, kMaxN = 40000;

  int t;
  std::cin >> t;
  assert(1 <= t && t <= kMaxT);

  while (t--) {
    int n;
    std::cin >> n;
    assert(2 <= n && n <= kMaxN);
    std::vector<std::vector<int>> tree(n);
    for (int i = 0; i < n - 1; ++i) {
      int u, v;
      std::cin >> u >> v;
      assert(1 <= u && u <= n && 1 <= v && v <= n);
      --u; --v;
      tree[u].emplace_back(v);
      tree[v].emplace_back(u);
    }
    std::cout << Solve(tree).val() << '\n';
  }
  return 0;
}
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