# ---
# title: 851. Loud and Rich
# id: problem851
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Depth-first Search
# link: <https://leetcode.com/problems/loud-and-rich/description/>
# hidden: true
# ---
# 
# 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:
#     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 isn't 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.
#     
# 
# **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][0] != richer[i][1]`
#   6. `richer[i]`'s are all different.
#   7. The observations in `richer` are all logically consistent.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
