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2049. Count Nodes With the Highest Score 👍

  • Time: $O(n)$
  • Space: $O(n)$
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class Solution {
 public:
  int countHighestScoreNodes(vector<int>& parents) {
    int ans = 0;
    vector<vector<int>> tree(parents.size());

    for (int i = 0; i < parents.size(); ++i) {
      if (parents[i] == -1)
        continue;
      tree[parents[i]].push_back(i);
    }

    dfs(tree, 0, 0, ans);
    return ans;
  }

 private:
  int dfs(const vector<vector<int>>& tree, int u, long&& maxScore, int& ans) {
    int count = 1;
    long score = 1;
    for (const int v : tree[u]) {
      const int childCount = dfs(tree, v, move(maxScore), ans);
      count += childCount;
      score *= childCount;
    }
    const int aboveCount = tree.size() - count;
    score *= max(aboveCount, 1);
    if (score > maxScore) {
      maxScore = score;
      ans = 1;
    } else if (score == maxScore) {
      ++ans;
    }
    return count;
  }
};

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class Solution {
  public int countHighestScoreNodes(int[] parents) {
    List<Integer>[] tree = new List[parents.length];

    for (int i = 0; i < tree.length; ++i)
      tree[i] = new ArrayList<>();

    for (int i = 0; i < parents.length; ++i) {
      if (parents[i] == -1)
        continue;
      tree[parents[i]].add(i);
    }

    dfs(tree, 0);
    return ans;
  }

  private int ans = 0;
  private long maxScore = 0;

  private int dfs(List<Integer>[] tree, int u) {
    int count = 1;
    long score = 1;
    for (final int v : tree[u]) {
      final int childCount = dfs(tree, v);
      count += childCount;
      score *= childCount;
    }
    final int aboveCount = tree.length - count;
    score *= Math.max(aboveCount, 1);
    if (score > maxScore) {
      maxScore = score;
      ans = 1;
    } else if (score == maxScore) {
      ++ans;
    }
    return count;
  }
}

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class Solution:
  def countHighestScoreNodes(self, parents: List[int]) -> int:
    tree = [[] for _ in range(len(parents))]

    for i, parent in enumerate(parents):
      if parent == -1:
        continue
      tree[parent].append(i)

    ans = 0
    maxScore = 0

    def dfs(u: int) -> int:  # Returns node count
      nonlocal ans
      nonlocal maxScore
      count = 1
      score = 1
      for v in tree[u]:
        childCount = dfs(v)
        count += childCount
        score *= childCount
      score *= len(parents) - count or 1
      if score > maxScore:
        maxScore = score
        ans = 1
      elif score == maxScore:
        ans += 1
      return count

    dfs(0)
    return ans