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
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
[0, 1] is the same as
[1, 0] and thus will not appear together in
n = 4,
edges = [[1, 0], [1, 2], [1, 3]]
0 | 1 / \ 2 3
n = 6,
edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]
0 1 2 \ | / 3 | 4 | 5
(1) According to the definition of tree on Wikipedia: “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.”
(2) The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.
Special thanks to @dietpepsi for adding this problem and creating all test cases.