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]

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.

Solution:

Obviously, for simple path graph, use the middle node (one or two ) as the root node.
Some basic observation is that nodes with degree of 1 are leaves, which is not going to be the root of the minimum height tree. We can keep removing leaves until only one or two nodes left which are the root nodes of the minimum height tree. 

 public List<Integer> findMinHeightTrees(int n, int[][] edges) {  
     int[] degree=new int[n];  
     HashMap<Integer,List<Integer>> map=new HashMap();  
     for(int i=0;i<edges.length;i++){  
       if(!map.containsKey(edges[i][0])) map.put(edges[i][0],new ArrayList<Integer>());  
       map.get(edges[i][0]).add(edges[i][1]);  
       if(!map.containsKey(edges[i][1])) map.put(edges[i][1],new ArrayList<Integer>());  
       map.get(edges[i][1]).add(edges[i][0]);  
       degree[edges[i][0]]++;  
       degree[edges[i][1]]++;  
     }  
     List<Integer> nextRemoved=new ArrayList<Integer>();  
     for(int i=0;i<n;i++){  
       if(degree[i]==1) nextRemoved.add(i);  
     }  
     int remaining=n;  
     while(remaining>2){  
       remaining-=nextRemoved.size();  
       List<Integer> temp=new ArrayList<Integer>();  
       for(int i:nextRemoved){  
         for(int j: map.get(i)){  
           degree[j]--;  
           if(degree[j]==1) temp.add(j);  
         }  
       }  
       nextRemoved=temp;  
     }  
     if(n==1) nextRemoved.add(0);  
     return nextRemoved;      
   }