LeetCode 310. Minimum Height Trees
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Problem Statement
(Source) 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 3return [1]
Example 2:
Given n = 6, edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]] 0 1 2 \ | / 3 | 4 | 5return [3, 4]
Hint:
- How many MHTs can a graph have at most?
Note:
(1) 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.”
(2) The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.
Solution
Tags: Breadth-first Search
, Graph
.
class Solution(object): def findMinHeightTrees(self, n, edges): """ :type n: int :type edges: List[List[int]] :rtype: List[int] """ edge = {i: set() for i in xrange(n)} for e in edges: u, v = e edge[u].add(v) edge[v].add(u) res = [u for u in edge if len(edge[u]) <= 1] while True: temp = [] for u in res: for v in edge[u]: edge[v].discard(u) if len(edge[v]) == 1: temp.append(v) if not temp: break else: for u in res: edge.pop(u) res = temp return res
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