Maximum Depth of Binary Tree
Detailed guide and Python implementation for the 'Maximum Depth of Binary Tree' problem.
1. Concept Overview
The 'Maximum Depth of Binary Tree' problem is a key challenge in the Trees section.
This implementation focuses on hard-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 Maximum Depth of Binary Tree.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Maximum Depth 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 its maximum depth.
A binary tree's maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.
The tree is represented as a level-order list where None represents a missing node. Implement a function maxDepth(root: list) -> int.
- •The number of nodes in the tree is in the range [0, 10000]
- •-100 <= Node.val <= 100
Examples
[3,9,20,None,None,15,7]
3
The tree has 3 levels: root [3], second level [9,20], third level [15,7]. The longest path is 3->20->15 or 3->20->7, both of depth 3.
[1,None,2]
2
The tree has root 1 with only a right child 2. Depth is 2.
[]
0
An empty tree has depth 0.
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 max_depth_opt(root):
if isinstance(root, list):
r = build_tree(root)
return max_depth_opt_helper(r)
return max_depth_opt_helper(root)
def max_depth_opt_helper(root: TreeNode) -> int:
if not root:
return 0
return 1 + max(max_depth_opt_helper(root.left), max_depth_opt_helper(root.right))Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def max_depth_brute(root):
if isinstance(root, list):
r = build_tree(root)
return max_depth_brute_helper(r)
return max_depth_brute_helper(root)
def max_depth_brute_helper(root: TreeNode) -> int:
if not root:
return 0
queue = [root]
depth = 0
while queue:
depth += 1
level_size = len(queue)
for _ in range(level_size):
curr = queue.pop(0)
if curr.left: queue.append(curr.left)
if curr.right: queue.append(curr.right)
return depthAlgorithm Pattern Checklist
When dealing with Trees data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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