Grokking the Coding Interview: Patterns for Coding Questions
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Problem Challenge 2: Minimum Height Trees (hard)
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Problem Statement

We are given an undirected graph that has the characteristics of a k-ary tree. In such a graph, we can choose any node as the root to make a k-ary tree. The root (or the tree) with the minimum height will be called Minimum Height Tree (MHT). There can be multiple MHTs for a graph. In this problem, we need to find all those roots which give us MHTs. Write a method to find all MHTs of the given graph and return a list of their roots.

Example 1:

Input: vertices: 5, Edges: [[0, 1], [1, 2], [1, 3], [2, 4]]
Output:[1, 2]
Explanation: Choosing '1' or '2' as roots give us MHTs. In the below diagram, we can see that the height of the trees with roots '1' or '2' is three which is the minimum.
Image

Example 2:

Input: vertices: 4, Edges: [[0, 1], [0, 2], [2, 3]]
Output:[0, 2]
Explanation: Choosing '0' or '2' as roots give us MHTs. In the below diagram, we can see that the height of the trees with roots '0' or '2' is three which is minimum.
Image

Example 3:

Input: vertices: 4, Edges: [[0, 1], [1, 2], [1, 3]]
Output:[1]

Constraints:

  • 1 <= vertices <= 2 * 10<sup>4</sup>
  • edges.length == n - 1
  • 0 <= a<sub>i</sub>, b<sub>i</sub> < n
  • a<sub>i</sub> != b<sub>i</sub>
  • All the pairs (a<sub>i</sub>, b<sub>i</sub>) are distinct.
  • The given input is guaranteed to be a tree and there will be no repeated edges.

Try it yourself

Try solving this question here:

Python3
Python3
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