Here is the problem description:
For a undirected graph with tree characteristics, we can choose any node as the root. The result graph is then a rooted tree. Among all possible rooted trees, those with minimum height are called minimum height trees (MHTs). Given such a graph, write a function to find all the MHTs and return a list of their root labels.
The graph contains n nodes which are labeled from 0 to n - 1. You will be given the number n and a list of undirected edges (each edge is a pair of labels).
You can assume that no duplicate edges will appear in edges. Since all edges are undirected, [0, 1] is the same as [1, 0] and thus will not appear together in edges.
Example 1 :
Input: n = 4, edges = [[1, 0], [1, 2], [1, 3]]
0 | 1 / \ 2 3
Example 2 :
Input: n = 6, edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]
0 1 2 \ | / 3 | 4 | 5
Output: 3, 4
Here is the solution I tried to understand:
The basic idea is "keep deleting leaves layer-by-layer, until reach the root."
Specifically, first find all the leaves, then remove them. After removing, some nodes will become new leaves. So we can continue remove them. Eventually, there is only 1 or 2 nodes left. If there is only one node left, it is the root. If there are 2 nodes, either of them could be a possible root.
I'm not sure I understand it so I could explain it to somebody. Why does deleting leaves layer-by-layer give us the answer?