Diameter of Binary Tree
Detailed guide and Python implementation for the 'Diameter of Binary Tree' problem.
1. Concept Overview
The 'Diameter of Binary Tree' problem is a key challenge in the Trees section.
This implementation focuses on medium-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Diameter of Binary Tree.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Diameter of Binary Tree carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Given the root of a binary tree, return the length of the diameter of the tree.
The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.
The length of a path between two nodes is represented by the number of edges between them.
The tree is represented as a level-order list. Implement a function diameterOfBinaryTree(root: list) -> int.
- •The number of nodes in the tree is in the range [1, 10000]
- •-100 <= Node.val <= 100
Examples
[1,2,3,4,5]
3
The longest path is 4->2->1->3 or 5->2->1->3, which has 3 edges.
[1,2]
1
The longest path is 2->1, which has 1 edge.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def diameter_opt(root):
if isinstance(root, list):
r = build_tree(root)
return diameter_opt_helper(r)
return diameter_opt_helper(root)
def diameter_opt_helper(root: TreeNode) -> int:
max_d = 0
def dfs(node):
nonlocal max_d
if not node:
return 0
left = dfs(node.left)
right = dfs(node.right)
max_d = max(max_d, left + right)
return 1 + max(left, right)
dfs(root)
return max_dBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def diameter_brute(root):
if isinstance(root, list):
r = build_tree(root)
return diameter_brute_helper(r)
return diameter_brute_helper(root)
def diameter_brute_helper(root: TreeNode) -> int:
max_d = 0
def get_depth(node):
nonlocal max_d
if not node: return 0
left = get_depth(node.left)
right = get_depth(node.right)
max_d = max(max_d, left + right)
return 1 + max(left, right)
get_depth(root)
return max_dAlgorithm Pattern Checklist
When dealing with Trees data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
Related Questions
Recommended Python Resources
Expand your knowledge with related interactive tutorials, cheat sheets, and code comparisons.
Python Loops
Learn how to use Python loops to iterate over data. Master for loops, while loops, break, continue, and loop best practices with interactive examples.
How to Find the Length of a List in Python
Learn how to find the length of a list in Python using the len() function. Understand the O(1) time complexity and checking counts.
Python String Methods
A complete reference guide for Python string manipulation. Master formatting, searching, splitting, replacing, and checking string properties.
Python vs JavaScript: Which Programming Language is Best?
A comprehensive comparison between Python and JavaScript. Explore syntax differences, performance, use cases (backend vs frontend), and coding examples.