Minimum Depth of Binary Tree
Given a binary tree, find its minimum depth. The minimum depth is the number of nodes along the shortest path from the root node down to the nearest leaf node.
Why Interviewers Ask This
Amazon asks this question to evaluate a candidate's ability to handle edge cases in recursive tree traversals, specifically distinguishing between null nodes and leaf nodes. Interviewers look for the competency to choose between Depth-First Search and Breadth-First Search based on the goal of finding the shortest path efficiently. It tests if you understand that stopping at the first leaf found is crucial for performance compared to calculating all depths.
How to Answer This Question
1. Clarify the definition: Explicitly state that a leaf node has no children, ensuring you don't stop at a node with only one child.
2. Select the algorithm: Propose BFS (Breadth-First Search) as the optimal approach because it explores level by level, guaranteeing the first leaf encountered is at the minimum depth.
3. Discuss the alternative: Briefly mention DFS as a valid but potentially less efficient O(N) solution where you must traverse the entire tree to find the true minimum.
4. Handle edge cases: Specifically address the scenario where the root is null or a node has only a left or right child, which often causes logical errors in naive implementations.
5. Walk through an example: Trace the logic using a small tree to demonstrate how the queue processes nodes and why the first leaf triggers the return value immediately.
Key Points to Cover
- Explicitly define a leaf node as having zero children, not just one missing child
- Prioritize BFS to achieve early termination upon finding the first leaf
- Demonstrate understanding of time complexity trade-offs between BFS and DFS
- Handle the edge case where the input tree is completely empty (null root)
- Show awareness of skewed tree scenarios where one branch is much deeper than the other
Sample Answer
To solve the Minimum Depth problem efficiently, I would prioritize a Breadth-First Search approach over Depth-First Search. The core reason is that BFS naturally explores the tree layer by layer. This means the very firs…
Common Mistakes to Avoid
- Treating a node with only one child as a leaf, which returns an incorrect shallow depth
- Using DFS without pruning, leading to unnecessary traversal of deep branches when a shallow leaf exists
- Failing to check if the root is null at the start, causing runtime errors on empty inputs
- Returning the maximum depth instead of the minimum due to misinterpreting the problem statement
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