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:

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.

Code

public class Solution {
    public List<Integer> findMinHeightTrees(int n, int[][] edges) {

        if (n==0) return new ArrayList<Integer>();
        if (n == 1) return Collections.singletonList(0);

        //prepare to put all edges into List of HashSet
        //Example 2: adj: [[3], [3], [3], [0, 1, 2, 4], [3, 5], [4]]
        List<Set<Integer>> adj = new ArrayList<Set<Integer>>();
        for (int i=0; i<n; i++) adj.add(new HashSet<Integer>());
        for (int[] edge:edges){
            adj.get(edge[0]).add(edge[1]);
            adj.get(edge[1]).add(edge[0]);
        }

        //find all leaves
        //Example 2: leaves: [0, 1, 2, 5]
        List<Integer> leaves = new ArrayList<Integer>();
        for (int i=0; i<n; i++){
            if (adj.get(i).size()==1) leaves.add(i);
        }

        //move forward from all leaves
        //Example 2: 
        //1. remove 0,1,2 from [0, 1, 2, 4], add 4 
        //2. remove 5 from [3,5], add 3
        //return [3,4]
        while (n>2){
            n-=leaves.size();
            List<Integer> newLeaves = new ArrayList<Integer>();
            for (Integer i:leaves){
                int j = adj.get(i).iterator().next();//return next element in the iteration
                adj.get(j).remove(i);
                //所有的和j相连的leaves都除去了，j变成了新的leave
                if (adj.get(j).size()==1) newLeaves.add(j); 
            }
            leaves = newLeaves;
        }

        return leaves;
    }
}

Reference

Leetcode