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851. Loud and Rich

  • Time: $O(|V| + |E|)$, where $|V| = |\texttt{quiet}|$ and $|E| = |\texttt{richer}|$
  • Space: $O(|V| + |E|)$
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class Solution {
 public:
  vector<int> loudAndRich(vector<vector<int>>& richer, vector<int>& quiet) {
    vector<int> ans(quiet.size(), -1);
    vector<vector<int>> graph(quiet.size());

    for (const vector<int>& e : richer)
      graph[e[1]].push_back(e[0]);

    for (int i = 0; i < graph.size(); ++i)
      dfs(graph, i, quiet, ans);

    return ans;
  }

 private:
  int dfs(const vector<vector<int>>& graph, int u, const vector<int>& quiet,
          vector<int>& ans) {
    if (ans[u] != -1)
      return ans[u];

    ans[u] = u;

    for (const int v : graph[u]) {
      const int res = dfs(graph, v, quiet, ans);
      if (quiet[res] < quiet[ans[u]])
        ans[u] = res;
    }

    return ans[u];
  }
};
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class Solution {
  public int[] loudAndRich(int[][] richer, int[] quiet) {
    int[] ans = new int[quiet.length];
    List<Integer>[] graph = new List[quiet.length];

    Arrays.fill(ans, -1);

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

    for (int[] e : richer)
      graph[e[1]].add(e[0]);

    for (int i = 0; i < graph.length; ++i)
      dfs(graph, i, quiet, ans);

    return ans;
  }

  private int dfs(List<Integer>[] graph, int u, int[] quiet, int[] ans) {
    if (ans[u] != -1)
      return ans[u];

    ans[u] = u;

    for (final int v : graph[u]) {
      final int res = dfs(graph, v, quiet, ans);
      if (quiet[res] < quiet[ans[u]])
        ans[u] = res;
    }

    return ans[u];
  }
}
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class Solution:
  def loudAndRich(self, richer: List[List[int]], quiet: List[int]) -> List[int]:
    graph = [[] for _ in range(len(quiet))]

    for u, v in richer:
      graph[v].append(u)

    @functools.lru_cache(None)
    def dfs(u: int) -> int:
      ans = u

      for v in graph[u]:
        res = dfs(v)
        if quiet[res] < quiet[ans]:
          ans = res

      return ans

    return map(dfs, range(len(graph)))