310. 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.

public class Solution {    public List<Integer> findMinHeightTrees(int n, int[][] edges) {        if(n == 1) {            List<Integer> res = new ArrayList<Integer>();            res.add(0);            return res;        }        List<Set<Integer>> dgr = new ArrayList<Set<Integer>>(n);        for (int i = 0; i < n; i++) dgr.add(new HashSet<Integer>());        for (int[] edge : edges) {            dgr.get(edge[0]).add(edge[1]);            dgr.get(edge[1]).add(edge[0]);        }        List<Integer> leave = new ArrayList<Integer>();        for(int i = 0; i < n; i++)            if(dgr.get(i).size() == 1) leave.add(i);        while(n > 2) {            n -= leave.size();            List<Integer> tmp = new ArrayList<Integer>();            for (int i : leave) {                int j = dgr.get(i).iterator().next();                dgr.get(j).remove(i);                if(dgr.get(j).size() == 1) tmp.add(j);            }            leave = tmp;        }        return leave;    }}