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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) {
    const int n = quiet.size();
    vector<int> ans(n, -1);
    vector<vector<int>> graph(n);

    for (const vector<int>& r : richer) {
      const int u = r[1];
      const int v = r[0];
      graph[u].push_back(v);
    }

    for (int i = 0; i < n; ++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) {
    final int n = quiet.length;
    int[] ans = new int[n];
    List<Integer>[] graph = new List[n];

    Arrays.fill(ans, -1);

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

    for (int[] r : richer) {
      final int u = r[1];
      final int v = r[0];
      graph[u].add(v);
    }

    for (int i = 0; i < n; ++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 v, u in richer:
      graph[u].append(v)

    @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)))