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]]

return [1]

Example 2:

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

return [3, 4]

分析：

首先笨办法，假设每个点都是root, 然后利用BFS，看那个root到最后一个leaf的高度是多少，如果比目前找到的更小，则更新，如果相同，则把那个点加到list里。

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

         List<Integer> all = new ArrayList<Integer>();

         if (n <= ) {

             all.add();

             return all;

         }

         Map<Integer, List<Integer>> map = new HashMap<>();

         for (int i = ; i < n; i++) {

             map.put(i, new ArrayList<Integer>());

         }

         for (int[] edge : edges) {

             map.get(edge[]).add(edge[]);

             map.get(edge[]).add(edge[]);

         }

         int minHeight = Integer.MAX_VALUE;

         List<Integer> temp = new ArrayList<>();

         for (int i = ; i < n; i++) {

             int height = ;

             boolean[] visited = new boolean[n];

             visited[i] = true;

             List<Integer> list = map.get(i);

             while (list.size() != ) {

                 for (Integer k : list) {

                     if (!visited[k]) {

                         visited[k] = true;

                         temp.addAll(map.get(k));

                     }

                 }

                 list = temp;

                 temp = new ArrayList<>();

                 height++;

             }

             if (height < minHeight) {

                 all.clear();

                 all.add(i);

                 minHeight = height;

             } else if (height == minHeight) {

                 all.add(i);

             }

         }

         return all;

     }

更好的方法，先构成一棵树，把数的叶子逐层的砍掉（叶子的degree为1），当这棵树只剩下2颗或者不到两颗的节点的时候，就停止。

 public class Solution {

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

         List<Integer> leaves = new ArrayList<Integer>();

         if (n <= ) {

             leaves.add();

             return leaves;

         }

         List<Set<Integer>> graph = new ArrayList<>();

         for (int i = ; i < n; i++) {

             graph.add(new HashSet<Integer>());

         }

         for (int[] edge : edges) {

             graph.get(edge[]).add(edge[]);

             graph.get(edge[]).add(edge[]);

         }

         for (int i = ; i < n; i++) {

             if (graph.get(i).size() == ) {

                 leaves.add(i);

             }

         }

         while (n > ) {

             n -= leaves.size();

             List<Integer> newLeaves = new ArrayList<>();

             for (int leave : leaves) {

                 for (int newLeaf : graph.get(leave)) {

                     graph.get(newLeaf).remove(leave);

                     if (graph.get(newLeaf).size() == ) {

                         newLeaves.add(newLeaf);

                     }

                 }

             }

             leaves = newLeaves;

         }

         return leaves;

     }

 }

巴特西

Minimum Height Trees

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