## 851. Loud and Rich

In a group of N people (labelled `0, 1, 2, ..., N-1`), each person has different amounts of money, and different levels of quietness.

For convenience, we'll call the person with label `x`, simply "person `x`".

We'll say that `richer[i] = [x, y]` if person `x` definitely has more money than person `y`.  Note that `richer` may only be a subset of valid observations.

Also, we'll say `quiet[x] = q` if person x has quietness `q`.

Now, return `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 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:
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 isn't clear if they have more money than person 0.

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.
```

Note:

1. `1 <= quiet.length = N <= 500`
2. `0 <= quiet[i] < N`, all `quiet[i]` are different.
3. `0 <= richer.length <= N * (N-1) / 2`
4. `0 <= richer[i][j] < N`
5. `richer[i] != richer[i]`
6. `richer[i]`'s are all different.
7. The observations in `richer` are all logically consistent.

## Rust Solution

``````struct Solution;
use std::collections::HashSet;

impl Solution {
fn loud_and_rich(richer: Vec<Vec<i32>>, quiet: Vec<i32>) -> Vec<i32> {
let n = quiet.len();
let mut graph: Vec<HashSet<usize>> = vec![HashSet::new(); n];
for e in richer {
let u = e as usize;
let v = e as usize;
graph[v].insert(u);
}
let mut res = vec![n; n];
for i in 0..n {
Self::dfs(i, &mut res, &graph, &quiet, n);
}
res.into_iter().map(|x| x as i32).collect()
}
fn dfs(
u: usize,
stack: &mut Vec<usize>,
graph: &[HashSet<usize>],
quiet: &[i32],
n: usize,
) -> usize {
if stack[u] == n {
stack[u] = u;
for &v in &graph[u] {
let w = Self::dfs(v, stack, graph, quiet, n);
if quiet[w] < quiet[stack[u]] {
stack[u] = w;
}
}
}
stack[u]
}
}

#[test]
fn test() {
let richer = vec_vec_i32![[1, 0], [2, 1], [3, 1], [3, 7], [4, 3], [5, 3], [6, 3]];
let quiet = vec![3, 2, 5, 4, 6, 1, 7, 0];
let res = vec![5, 5, 2, 5, 4, 5, 6, 7];
assert_eq!(Solution::loud_and_rich(richer, quiet), res);
}
``````

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