leetcode310. Minimum Height Trees

For an 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 :

Input: n = 4, edges = [[1, 0], [1, 2], [1, 3]]

        0
        |
        1
       / \
      2   3 

Output: [1]
Example 2 :

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

     0  1  2
      \ | /
        3
        |
        4
        |
        5 

Output: [3, 4]
Note:

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.”
The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.

  0
  |
  1
 / \
2   3

    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        if(n==1) return Collections.singletonList(0);
        //初始化邻接表
        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]);
        }
        
        List<Integer> leaves = new ArrayList<Integer>();
        for(int i = 0 ; i<adj.size() ; i++) {
            if(adj.get(i).size() == 1) {
                leaves.add(i);
            }
        }
        
        while(n > 2) {
            n -= leaves.size();
            List<Integer> newLeaves = new ArrayList<>();
            for (int i : leaves) {
                int j = adj.get(i).iterator().next();
                adj.get(j).remove(i);
                if (adj.get(j).size() == 1) newLeaves.add(j);
            }
            leaves = newLeaves;
        }
        return leaves;
    }

    public List<Integer> findMinHeightTrees2(int n, int[][] edges) {
        if(n==1) return Collections.singletonList(0);
        int[] connected = new int[n];
        int[] degree = new int[n];
        
        for(int[] edge : edges) {
            int v1 = edge[0];
            int v2 = edge[1];
            connected[v1] ^= v2;
            connected[v2] ^= v1;
            
            degree[v1]++;
            degree[v2]++;
        }
        
        LinkedList<Integer> queue = new LinkedList<Integer>();
        for(int i = 0 ; i<degree.length ; i++) {
            if(degree[i] == 1) {
                queue.offer(i);
            }
        }
        
        while(n > 2 && !queue.isEmpty()) {
            int size = queue.size();
            for(int i = 0 ; i<size ; i++) {
                int v = queue.poll();
                n--;
                int v1 = connected[v];
                connected[v1] ^= v;
                degree[v1]--;
                if(degree[v1] == 1) {
                    queue.add(v1);
                }
            }    
        }
        
        List<Integer> result = new ArrayList<Integer>();
        result.addAll(queue);
        return result;
    }