How do you solve Find Minimum Diameter After Merging Two Trees on LeetCode?

Find Minimum Diameter After Merging Two Trees (LeetCode #3203) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n + m) time complexity and O(n + m) space complexity. Key insight: Understanding tree diameter is crucial for optimizing the solution.

What is the time complexity of Find Minimum Diameter After Merging Two Trees?

The optimal solution for Find Minimum Diameter After Merging Two Trees runs in O(n + m) time and uses O(n + m) space. The time complexity is O(n + m) because we traverse each tree once to calculate the diameter and longest paths, making it efficient for large inputs.

What is the brute force solution for Find Minimum Diameter After Merging Two Trees?

The brute force approach for Find Minimum Diameter After Merging Two Trees is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute-force approach, we will compute the diameter of both trees first. Then, for every possible pair of nodes from both trees, we will calculate the potential diameter by connecting them and check which connection yields the minimum diameter. The optimal Optimal Solution approach improves this to O(n + m).

What algorithm or data structure is used to solve Find Minimum Diameter After Merging Two Trees?

Find Minimum Diameter After Merging Two Trees uses the following concepts: Tree, Depth-First Search, Breadth-First Search, Graph Theory. The recommended patterns to study are: Depth-First Search (DFS), Tree Traversal, Dynamic Programming (for optimization).

What are the interview tips for Find Minimum Diameter After Merging Two Trees?

Always clarify the definition of diameter and ensure you understand how it applies to trees. Discuss your thought process out loud; it helps interviewers understand your approach. Consider edge cases, such as trees with only one node, to ensure your solution is robust.

What are common mistakes when solving Find Minimum Diameter After Merging Two Trees?

Not calculating the longest paths correctly from each node. Overlooking the fact that the diameter of the resulting tree is influenced by the chosen nodes.

#3203

Find Minimum Diameter After Merging Two Trees

Hard

TreeDepth-First SearchBreadth-First SearchGraph TheoryDepth-First Search (DFS)Tree TraversalDynamic Programming (for optimization)

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n + m)Space O(n + m)

In the optimal solution, we first compute the diameters of both trees and then focus on finding the longest paths from the nodes that we will connect. This allows us to minimize the diameter efficiently without checking every combination of nodes.

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Algorithm

4 steps

1Step 1: Calculate the diameter of tree 1 and tree 2 using DFS.
2Step 2: For each node in tree 1, calculate the longest path from that node.
3Step 3: For each node in tree 2, calculate the longest path from that node.
4Step 4: The minimum diameter can be calculated as the maximum of the two diameters plus the longest paths from the connected nodes plus one.

solution.py27 lines

1# Full working Python code
2from collections import defaultdict
3
4def dfs(tree, node, parent):
5    max_depth = 0
6    for neighbor in tree[node]:
7        if neighbor != parent:
8            max_depth = max(max_depth, dfs(tree, neighbor, node) + 1)
9    return max_depth
10
11def calculate_diameter_and_longest_paths(edges):
12    tree = defaultdict(list)
13    for a, b in edges:
14        tree[a].append(b)
15        tree[b].append(a)
16    diameter = dfs(tree, 0, -1)
17    longest_paths = [dfs(tree, i, -1) for i in range(len(edges) + 1)]
18    return diameter, longest_paths
19
20def find_minimum_diameter(edges1, edges2):
21    diameter1, longest_paths1 = calculate_diameter_and_longest_paths(edges1)
22    diameter2, longest_paths2 = calculate_diameter_and_longest_paths(edges2)
23    min_diameter = float('inf')
24    for a in longest_paths1:
25        for b in longest_paths2:
26            min_diameter = min(min_diameter, max(diameter1, diameter2, a + b + 1))
27    return min_diameter

ℹ

Complexity note: The time complexity is O(n + m) because we traverse each tree once to calculate the diameter and longest paths, making it efficient for large inputs.

1Understanding tree diameter is crucial for optimizing the solution.
2The longest paths from the nodes being connected directly influence the overall diameter.

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