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]

JAVA代码：

public class Solution {
    public static List<Integer> findMinHeightTrees(int n, int[][] edges) {
ArrayList<HashSet<Integer>> G=new ArrayList<HashSet<Integer>>();
for(int i=0;i<n;i++) G.add(new HashSet<Integer>());

for(int[] edg:edges){
G.get(edg[0]).add(edg[1]);
G.get(edg[1]).add(edg[0]);
}
LinkedList<Integer> leaves=new  LinkedList<Integer>();
if(n==1)leaves.add(0);
for(int i=0;i<n;i++)if(G.get(i).size()==1)leaves.add(i);
while(n>2){
n-=leaves.size();
LinkedList<Integer> newleaves=new LinkedList<Integer>();
for(int i:leaves){
int j=G.get(i).iterator().next();
G.get(j).remove(i);
if(G.get(j).size()==1)newleaves.add(j);
}
leaves=newleaves;
}
return leaves;
    }
}

时间复杂度 O(N)