Binary Tree Maximum Path Sum
A path is any sequence of nodes from some starting node to any node in the tree. Find the maximum path sum in a binary tree. This requires careful recursion tracking multiple sums.
Why Interviewers Ask This
Meta asks this to evaluate a candidate's mastery of recursive tree traversal and their ability to distinguish between local path sums and global maximums. It tests if you can handle the complexity where a single node might serve as a peak, connecting two subtrees, rather than just extending a single path downward.
How to Answer This Question
1. Clarify constraints: Ask if the tree is balanced or contains negative values, noting Meta's focus on edge cases. 2. Define the recursive function: Explain that it will return the maximum gain from a single branch (left or right) plus the current node, while simultaneously updating a global maximum for paths passing through the current node. 3. Handle base cases: Explicitly state how null nodes are treated, often returning zero or negative infinity depending on implementation. 4. Logic breakdown: Describe calculating the left and right gains, clamping negative values to zero since we want the maximum sum, and comparing the 'through-node' sum against the global max. 5. Complexity analysis: Conclude by stating O(N) time for visiting every node once and O(H) space for the recursion stack.
Key Points to Cover
- Distinguishing between the return value (single branch max) and the global update (path through node)
- Correctly handling negative numbers by treating them as zero contributions
- Explicitly defining the base case for null nodes to prevent infinite recursion
- Demonstrating understanding that the optimal path may not include the root
- Providing accurate Time and Space complexity analysis relative to N and H
Sample Answer
To solve the Binary Tree Maximum Path Sum problem, I would first clarify that a path must be non-empty and can start and end at any node. My approach uses a depth-first search with a helper function. This function return…
Common Mistakes to Avoid
- Returning the sum of both left and right branches from the recursive function, which violates the single-path constraint
- Failing to update the global maximum inside the recursion before returning the single-branch sum
- Ignoring negative values in the calculation, leading to incorrect sums when all nodes are negative
- Not clarifying that the path must contain at least one node, potentially causing errors with empty trees
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