310 - Minimum Height Trees.

Medium

A tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any connected graph without simple cycles is a tree.

Given a tree of n nodes labelled from 0 to n - 1, and an array of n - 1 edges where <code>edgesi = a_i, b_i</code> indicates that there is an undirected edge between the two nodes <code>a_i</code> and <code>b_i</code> in the tree, you can choose any node of the tree as the root. When you select a node x as the root, the result tree has height h. Among all possible rooted trees, those with minimum height (i.e. min(h)) are called minimum height trees (MHTs).

Return a list of all MHTs' root labels. You can return the answer in any order.

The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.

Example 1:

Input: n = 4, edges = [1,0,1,2,1,3]

Output: 1

Explanation: As shown, the height of the tree is 1 when the root is the node with label 1 which is the only MHT.

Example 2:

Input: n = 6, edges = [3,0,3,1,3,2,3,4,5,4]

Output: 3,4

Constraints:

• <code>1 <= n <= 2 * 10⁴</code>

• edges.length == n - 1

• <code>0 <= a_i, b_i< n</code>

• <code>a_i != b_i</code>

• All the pairs <code>(a_i, b_i)</code> are distinct.

• The given input is guaranteed to be a tree and there will be no repeated edges.