How do you calculate the lowest common ancestor in a binary tree?
This problem evaluates your understanding of tree traversal and recursive logic. It tests your ability to navigate hierarchical data structures efficiently.
Why Interviewers Ask This
Tree problems are common in Amazon interviews to test logical reasoning and recursion skills. The LCA problem specifically checks if you can traverse a tree to find relationships between nodes. It demonstrates your ability to break down a complex problem into smaller sub-problems.
How to Answer This Question
Explain the recursive strategy: if the current node is one of the targets, return it. Otherwise, search left and right subtrees. If both searches return non-null values, the current node is the LCA. If only one returns a value, propagate that up. Mention optimizations for BSTs if applicable.
Key Points to Cover
- Use post-order traversal logic
- Check conditions on both subtrees
- Return null if targets not found
- Time complexity is O(N)
Sample Answer
I would use a recursive approach where I check if the current node is either of the target nodes. If it is, I return the current node. Then, I recursively search the left and right subtrees. If both the left and right recursive calls return non-null values, it means the target nodes are in different subtrees, so the current node is the LCA. If only one side returns a value, that value is the LCA. This approach runs in O(N) time and handles general binary trees effectively.
Common Mistakes to Avoid
- Forgetting to handle the case where targets are not in the tree
- Confusing LCA with parent pointers
- Not handling the base case correctly
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