Loud and Rich

arraydepth-first searchgraph theory

Problem Statement

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] = [a _i , b _i ] indicates that a _i has more money than b _i 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 .

Examples

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]
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 <= a _i , b _i < n

a _i != b _i

All the pairs of richer are unique .

The observations in richer are all logically consistent.

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDepth-First Search