Minimum Height Trees

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.

Format
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:

Given n = 4, edges = [[1, 0], [1, 2], [1, 3]]

        0
        |
        1
       / \
      2   3

return [1]

Example 2:

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

     0  1  2
      \ | /
        3
        |
        4
        |
        5

return [3, 4]

Hint:

1. How many MHTs can a graph have at most?

Note:

(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.

Given a tree with this manner. The MHT must lie on the middle of the longest end to end path in the graph. So there can at most be two roots for such MHT in a graph.
The idea is to tear off nodes layer. First we construct the graph using adjacency list, and add all nodes with only one neighbors to a list (the first layer). Now for each neighbor of the nodes in the layer list, we remove the node, i.e., the most outside layer is removed. Now we add all remaining nodes with only 1 neighbors to the layer list and iteratively remove those nodes until there are less than two nodes left. These one or two nodes are our MHT roots.

public List<integer> findMinHeightTrees(int n, int[][] edges) {
        List<integer> leaf = new ArrayList<>();
        if (n <= 2) {
            for (int i = 0; i < n; i++)
                leaf.add(i);
            return leaf;
        }
        List<set<Integer>> adjacentList = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            adjacentList.add(new HashSet<integer> ());
        }
        for (int[] edge : edges) {
            adjacentList.get(edge[0]).add(edge[1]);
            adjacentList.get(edge[1]).add(edge[0]);
        }
    
        for (int i = 0; i < n; i++) {
            if (adjacentList.get(i).size() == 1)
                leaf.add(i);
        }
        
        while (n > 2) {
            List<integer> nextLevel = new ArrayList<>();
            for (int v : leaf) {
                n--;
                for (int nb : adjacentList.get(v)) {
                    Set<integer> adj = adjacentList.get(nb);
                    adj.remove(v);
                    if (adj.size() == 1)
                        nextLevel.add(nb);
                }
            }
            leaf = nextLevel;
        }
        return leaf;
    }