First, clarify the problem definition and constraints, as 'balanced tree' can refer to height-balanced (AVL) or weight-balanced (red-black) trees. Then, outline an algorithm to check or maintain balance, discussing time and space complexity, and consider edge cases and potential optimizations.
Pro tip: Demonstrate awareness of real-world trade-offs: for example, in a database index, a B-tree is preferred over a binary balanced tree due to disk I/O considerations. This shows you think beyond textbook algorithms.
Ask clarifying questions to determine the exact definition of 'balanced' (e.g., height-balanced, weight-balanced) and the expected input/output (e.g., check if a tree is balanced, or implement a balanced tree insertion).
Select an appropriate algorithm: for checking balance, a recursive post-order traversal computing heights; for maintaining balance, describe rotations (AVL) or color flips (red-black).
State the time and space complexity of your approach, e.g., O(n) time and O(h) space for checking balance, and explain why it's optimal or trade-offs.
Discuss edge cases such as empty tree, single node, skewed tree, and duplicate values, and how your solution handles them.
Walk through a small example to verify correctness, and mention potential optimizations like early termination or iterative solutions to avoid stack overflow.
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