Question
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.
Solution
如果是一条线的话,我们知道选中间的点当root会是minimum height tree。类似的,如果是一堆点,我们通过BFS一层层拨开外面的叶子,那么剩下的就是中心的点。一开始还是需要构建图的adjacency list。
BFS时间复杂度是O(N)
1 class Solution: 2 def findMinHeightTrees(self, n: int, edges: List[List[int]]) -> List[int]: 3 if n == 1: 4 return [0] 5 adjacency_list = [set() for i in range(n)] 6 # Build adjacnecy list 7 for edge in edges: 8 adjacency_list[edge[0]].add(edge[1]) 9 adjacency_list[edge[1]].add(edge[0]) 10 # Build leaves list 11 leaves = [i for i in range(n) if len(adjacency_list[i]) == 1] 12 # BFS 13 while n > 2: 14 n -= len(leaves) 15 new_leaves = [] 16 while leaves: 17 leaf = leaves.pop() 18 neighbor = adjacency_list[leaf].pop() 19 adjacency_list[neighbor].remove(leaf) 20 if len(adjacency_list[neighbor]) == 1: 21 new_leaves.append(neighbor) 22 leaves = new_leaves 23 return leaves
原文地址:https://www.cnblogs.com/ireneyanglan/p/11517863.html