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3331. Find Subtree Sizes After Changes

  • Time: $O(nh)$
  • Space: $O(n)$
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class Solution {
 public:
  vector<int> findSubtreeSizes(vector<int>& parent, string s) {
    const int n = parent.size();
    vector<int> ans(n);
    vector<int> newParent = parent;
    vector<vector<int>> tree(n);

    for (int i = 1; i < n; ++i) {
      const int closest = findClosestAncestor(i, parent, s);
      if (closest != -1)
        newParent[i] = closest;
    }

    for (int i = 1; i < n; ++i)
      tree[newParent[i]].push_back(i);

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

 private:
  // Returns the closest ancestor of node `u` that has the same value as `u`.
  int findClosestAncestor(int u, const vector<int>& parent, const string& s) {
    for (int curr = parent[u]; curr != -1; curr = parent[curr])
      if (s[curr] == s[u])
        return curr;
    return -1;
  }

  int dfs(const vector<vector<int>>& tree, int u, vector<int>& ans) {
    int sz = 1;
    for (const int v : tree[u])
      sz += dfs(tree, v, ans);
    return ans[u] = sz;
  }
};

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class Solution {
  public int[] findSubtreeSizes(int[] parent, String s) {
    final int n = parent.length;
    int[] ans = new int[n];
    int[] newParent = parent.clone();
    List<Integer>[] tree = new ArrayList[n];

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

    for (int i = 1; i < n; ++i) {
      final int closest = findClosestAncestor(i, parent, s);
      if (closest != -1)
        newParent[i] = closest;
    }

    for (int i = 1; i < n; ++i)
      tree[newParent[i]].add(i);

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

  // Returns the closest ancestor of node `u` that has the same value as `u`.
  private int findClosestAncestor(int u, int[] parent, String s) {
    for (int curr = parent[u]; curr != -1; curr = parent[curr])
      if (s.charAt(curr) == s.charAt(u))
        return curr;
    return -1;
  }

  private int dfs(List<Integer>[] tree, int u, int[] ans) {
    int sz = 1;
    for (final int v : tree[u])
      sz += dfs(tree, v, ans);
    return ans[u] = sz;
  }
}

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class Solution:
  def findSubtreeSizes(self, parent: list[int], s: str) -> list[int]:
    n = len(parent)
    ans = [0] * n
    newParent = parent.copy()
    tree = [[] for _ in range(n)]

    for i in range(1, n):
      closest = self._findClosestAncestor(i, parent, s)
      if closest != -1:
        newParent[i] = closest

    for i in range(1, n):
      tree[newParent[i]].append(i)

    self._dfs(tree, 0, ans)
    return ans

  def _findClosestAncestor(self, u: int, parent: list[int], s: str) -> int:
    """
    Returns the closest ancestor of node `u` that has the same value as `u`.
    """
    curr = parent[u]
    while curr != -1:
      if s[curr] == s[u]:
        return curr
      curr = parent[curr]
    return -1

  def _dfs(self, tree: list[list[int]], u: int, ans: list[int]) -> int:
    sz = 1
    for v in tree[u]:
      sz += self._dfs(tree, v, ans)
    ans[u] = sz
    return sz