Minimum Height Trees:无环无向图转化成最矮的树

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.

思路：一图胜千言，图片转自： @andyreadsall

引用@zhugejunwei的一句话叫“农村包围城市”。刚看到这句话的时候笑死我了。

思路是这样的，与其逐个定点设为根，去测试是否是最矮树的根节点，不如去寻找叶子，每一轮把叶子节点去掉，最后剩下的一个或者两个定点即为根。

class Solution {
 	public List<Integer> findMinHeightTrees(int n, int[][] edges) {
		if (n == 1)
			return Collections.singletonList(0);

		// 统计每个定点的度
		List<Set<Integer>> degree = new ArrayList<Set<Integer>>();
		for (int i = 0; i < n; ++i)
			degree.add(new HashSet<>());
		for (int i = 0; i < edges.length; i++) {
			degree.get(edges[i][0]).add(edges[i][1]);
			degree.get(edges[i][1]).add(edges[i][0]);
		}
		Set<Integer> leaves = new HashSet<Integer>();
		for (int i = 0; i < n; i++) {
			if (degree.get(i).size() == 1)
				leaves.add(i);
		}
		while (n > 2) {
			n = n - leaves.size();
			Set<Integer> newleaves = new HashSet<Integer>();
			for (int leaf : leaves) {
				int node = degree.get(leaf).iterator().next();
				degree.get(node).remove(leaf);
				if (degree.get(node).size() == 1)
				newleaves.add(node);
			}
			leaves = newleaves;
		}
		List<Integer> res = new ArrayList<Integer>();
		for (int i : leaves)
			res.add(i);
		return res;
	}
}