310. 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.

解题要点：

“农村包围城市”

class Solution(object):
    def findMinHeightTrees(self, n, edges):
        """
        :type n: int
        :type edges: List[List[int]]
        :rtype: List[int]
        """
        if n == 1: return [0] 
        adj = [set() for _ in xrange(n)]
        for i, j in edges:
            adj[i].add(j)
            adj[j].add(i)
        leaves = [i for i in range(n) if len(adj[i]) == 1]
        while n > 2:
            n -= len(leaves)
            new = []
            for i in leaves:
                temp = adj[i].pop()
                adj[temp].remove(i)
                if len(adj[temp]) == 1:
                    new.append(temp)
            leaves = new
        return leaves