#851

Loud and Rich

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array · depth-first search · graph theory · topological sort

Description

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 i^th 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]

Solution