Convert Sorted Array to Binary Search Tree
Given an integer array `nums` where the elements are sorted in ascending order, convert it to a height-balanced Binary Search Tree (BST).
Why Interviewers Ask This
Amazon asks this question to evaluate a candidate's mastery of divide-and-conquer strategies and their ability to implement recursive algorithms efficiently. Interviewers specifically look for the understanding that a sorted array allows for O(log n) tree height by always selecting the middle element as the root, ensuring the resulting Binary Search Tree is height-balanced.
How to Answer This Question
1. Clarify constraints: Confirm if the array contains duplicates or negative numbers, though standard BST rules apply. 2. Define the goal: State clearly that the output must be a height-balanced BST where left subtree values are smaller and right subtree values are larger than the root. 3. Propose the strategy: Explain the divide-and-conquer approach where you pick the middle element as the root, then recursively build the left subtree from the left half and the right subtree from the right half. 4. Analyze complexity: Explicitly mention that since every element is visited once, time complexity is O(n), and recursion depth is O(log n) for space complexity due to the balanced nature. 5. Walk through an example: Trace the logic with a small array like [-10, -3, 0, 5, 9] to demonstrate how the mid-point selection prevents skewing.
Key Points to Cover
- Explicitly state the divide-and-conquer strategy as the primary solution pattern
- Identify the middle element as the optimal root choice to ensure balance
- Define clear base cases where the recursion terminates (start > end)
- Correctly analyze time complexity as O(n) due to single-pass node creation
- Demonstrate understanding of Amazon's focus on clean, efficient algorithmic thinking
Sample Answer
To solve this problem efficiently, I would use a recursive divide-and-conquer approach. The core insight here is that since the input array is already sorted, we can guarantee a height-balanced tree by always choosing th…
Common Mistakes to Avoid
- Building the tree sequentially without skipping elements, which creates a skewed linked list instead of a balanced tree
- Failing to handle the empty array edge case, leading to potential runtime errors during initialization
- Using linear search to find the middle element instead of calculating it via integer division of indices
- Neglecting to explain why the sorted property is crucial for achieving O(log n) height in the final tree
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