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#851
Medium Algorithms

Loud and rich

Array Depth-First Search Graph Theory Topological Sort
63.2% acceptance
Feb 22, 2026
1488
877
There is a group of n people labeled from 0 to n - 1 where each person has a different amount of money and a different level of quietness. You are given an array richer where richer[i] = [ai, bi] indicates that ai has more money than bi and an integer array quiet where quiet[i] is the quietness of the ith person. All the given data in richer are logically correct (i.e., the data will not lead you to a situation where x is richer than y and y is richer than x at the same time). Return an integer array answer where answer[x] = y if y is the least quiet person (that is, the person y with the smallest value of quiet[y]) among all people who definitely have equal to or more money than the person x.

Solution

Rust
Time O(n * m)
Space O(n * m)
LeetCode
solution.rs
/*
 * There is a group of n people labeled from 0 to n - 1 where each person has a different amount of money and a different level of quietness.
 * You are given an array richer where richer[i] = [ai, bi] indicates that ai has more money than bi and an integer array quiet where quiet[i] is the quietness of the ith person. All the given data in richer are logically correct (i.e., the data will not lead you to a situation where x is richer than y and y is richer than x at the same time).
 * Return an integer array answer where answer[x] = y if y is the least quiet person (that is, the person y with the smallest value of quiet[y]) among all people who definitely have equal to or more money than the person x.
 * Example 1:
 * Input: richer = [[1,0],[2,1],[3,1],[3,7],[4,3],[5,3],[6,3]], quiet = [3,2,5,4,6,1,7,0]
 * Output: [5,5,2,5,4,5,6,7]
 * Explanation:
 * answer[0] = 5.
 * Person 5 has more money than 3, which has more money than 1, which has more money than 0.
 * The only person who is quieter (has lower quiet[x]) is person 7, but it is not clear if they have more money than person 0.
 * answer[7] = 7.
 * Among all people that definitely have equal to or more money than person 7 (which could be persons 3, 4, 5, 6, or 7), the person who is the quietest (has lower quiet[x]) is person 7.
 * The other answers can be filled out with similar reasoning.
 * Example 2:
 * Input: richer = [], quiet = [0]
 * Output: [0]
 * Constraints:
 * n == quiet.length
 * 1 <= n <= 500
 * 0 <= quiet[i] < n
 * All the values of quiet are unique.
 * 0 <= richer.length <= n * (n - 1) / 2
 * 0 <= ai, bi < n
 * ai != bi
 * All the pairs of richer are unique.
 * The observations in richer are all logically consistent.
 */

impl Solution {
  pub fn loud_and_rich(richer: Vec<Vec<i32>>, quiet: Vec<i32>) -> Vec<i32> {
    let n = quiet.len();
    // Build graph: richer[i][1] has richer[i][0] as a richer person
    let mut adj: Vec<Vec<usize>> = vec![vec![]; n];
    for r in &richer {
      adj[r[1] as usize].push(r[0] as usize);
    }
    let mut ans: Vec<i32> = (0..n as i32).collect();
    let mut visited = vec![false; n];
    fn dfs(v: usize, adj: &Vec<Vec<usize>>, quiet: &Vec<i32>, ans: &mut Vec<i32>, visited: &mut Vec<bool>) {
      if visited[v] { return; }
      visited[v] = true;
      for &u in &adj[v] {
        dfs(u, adj, quiet, ans, visited);
        if quiet[ans[u] as usize] < quiet[ans[v] as usize] {
          ans[v] = ans[u];
        }
      }
    }
    for i in 0..n {
      dfs(i, &adj, &quiet, &mut ans, &mut visited);
    }
    ans
  }
}