Minimum Height Trees

题目地址：
https://leetcode.com/problems/minimum-height-trees/#/description

题目：

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.

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 exactlyone 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.

解题思路：


这道题需要用bfs来解决。首先用一个List的set，这个是一个图叫做adj，然后用一个list的integer来作为leaves来存size为1的index，然后while循环来用bfs来做当n>=3的时候。

代码：

public List<Integer> findMinHeightTrees(int n, int[][] edges) {
    if(n == 1){
        List<Integer> rst = new ArrayList<Integer>();
        rst.add(0);
        return rst;
    }
    // initialize the adjcent list    List<Set<Integer>> adj = new ArrayList<Set<Integer>>(n);
    for(int i = 0; i <= n - 1; i++){
        adj.add(new HashSet<>());
    }
    for(int[] edge : edges){
        adj.get(edge[0]).add(edge[1]);
        adj.get(edge[1]).add(edge[0]);
    }
    List<Integer> leaves = new ArrayList<>();
    for(int i = 0; i <= n - 1; i++){
        if(adj.get(i).size() == 1){
            leaves.add(i);
        }
    }
    while(n >= 3){
        List<Integer> next = new ArrayList<>();
        n -= leaves.size();
        for(int leaf : leaves){
            int i = adj.get(leaf).iterator().next();
            adj.get(i).remove(leaf);
            if(adj.get(i).size() == 1){
                next.add(i);
            }
        }
        leaves = next;
    }
    return leaves;
}