Leetcode 310. Minimum Height Trees

題目：

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.

解法：
由於樹就是兩個點被一條線連接的無向圖，因此先用一個list把樹存成無向圖的列表。能夠從頭邊同時進行，查看葉子節點並加入到葉子節點鏈表（遍歷一遍後，葉子節點鏈表size 爲1）。 將葉子節點保存下來。這些葉子節點不用再查，可是剩餘的中間節點，要依次查看，把跟第一層葉子節點有關的圖的矩陣裏對應的記錄所有刪除，相似於剝除最外面一圈全部的點。 這個時候就會有第二層葉子節點（那些在列表當中size爲1的點），用一樣的方法進行剝除。最後留在葉子節點list裏面的點便可覺得根。

代碼：

public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        List<Integer> leaves = new ArrayList<>();
        if (n == 1) {
            leaves.add(0);
            return leaves;
        }
        
        List<Set<Integer>> adj = new ArrayList<>();
        for(int i = 0; i < n; i++) adj.add(new HashSet<>());
        for(int[] edge : edges){
            adj.get(edge[0]).add(edge[1]);
            adj.get(edge[1]).add(edge[0]);
        }
        for(int i = 0; i < n; 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){
                for(int j : adj.get(i)){
                    adj.get(j).remove(i);
                    if(adj.get(j).size() ==1) newLeaves.add(j);
                }
            }
            leaves = newLeaves;
        }
        return leaves;
    }