How do you solve Minimum Height Trees on LeetCode?

Minimum Height Trees (LeetCode #310) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Minimum height trees can have one or two roots.

What is the brute force solution for Minimum Height Trees?

The brute force approach for Minimum Height Trees is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves calculating the height of the tree for each node as a potential root. This means we will explore the tree from each node and determine the longest path to any leaf node, which is time-consuming but straightforward. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Height Trees?

Minimum Height Trees uses the following concepts: Depth-First Search, Breadth-First Search, Graph Theory, Topological Sort. The recommended patterns to study are: Graph Traversal, BFS/DFS, Tree Properties.

What are the interview tips for Minimum Height Trees?

Explain your thought process clearly when discussing the tree structure. Be prepared to discuss the properties of trees and their heights. Practice visualizing the tree structure to better understand the problem.

What are common mistakes when solving Minimum Height Trees?

Not recognizing that a tree can have one or two minimum height trees. Failing to properly manage the adjacency list during leaf removal.

#310

Minimum Height Trees

Medium

Depth-First SearchBreadth-First SearchGraph TheoryTopological SortGraph TraversalBFS/DFSTree Properties

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal approach uses a technique similar to finding the 'leaves' of the tree. By iteratively removing leaves, we can identify the nodes that will be the roots of the minimum height trees. This is efficient because it reduces the problem size quickly.

⚙️

Algorithm

4 steps

1Step 1: Create an adjacency list to represent the tree.
2Step 2: Initialize a queue with all leaf nodes (nodes with only one connection).
3Step 3: While there are more than two nodes, remove the leaves and update the graph.
4Step 4: The remaining nodes in the graph are the roots of the minimum height trees.

solution.py22 lines

1# Full working Python code
2from collections import defaultdict, deque
3
4def minHeightTrees(n, edges):
5    if n == 1:
6        return [0]
7    graph = defaultdict(list)
8    for u, v in edges:
9        graph[u].append(v)
10        graph[v].append(u)
11    leaves = deque([i for i in range(n) if len(graph[i]) == 1])
12    remaining_nodes = n
13    while remaining_nodes > 2:
14        size = len(leaves)
15        remaining_nodes -= size
16        for _ in range(size):
17            leaf = leaves.popleft()
18            for neighbor in graph[leaf]:
19                graph[neighbor].remove(leaf)
20                if len(graph[neighbor]) == 1:
21                    leaves.append(neighbor)
22    return list(leaves)

ℹ

Complexity note: The time complexity is O(n) because we process each node and edge a limited number of times. The space complexity is O(n) due to the adjacency list and the queue used for leaves.

1Minimum height trees can have one or two roots.
2Removing leaves iteratively helps in finding the roots efficiently.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.