The base LCA part was fine, I know that problem.
Start by clarifying the problem and constraints, then solve the BST LCA using the BST property with O(h) time and O(1) space. For the string editing extension, model the mouse interactions as a state machine and analyze the time complexity of each operation, considering trade-offs between different data structures.
Pro tip: Explicitly state your assumptions about the mouse interaction model (e.g., click positions, drag behavior) and discuss how you would test edge cases like empty strings or invalid clicks. This shows you think about real-world robustness, not just the algorithm.
Ask questions to understand the BST structure (e.g., are duplicates allowed?), the string editing operations (e.g., what mouse events are simulated?), and any performance requirements. Confirm the expected input/output format.
Explain the iterative approach: traverse from root, moving left if both nodes are smaller, right if both are larger, else return current node. State time complexity O(h) and space O(1).
Define a state machine for mouse interactions (e.g., click to position cursor, drag to select, type to replace). Map each interaction to string operations and choose an appropriate data structure (e.g., gap buffer, rope, or simple string with indices).
For each mouse event, derive the time complexity based on the chosen data structure. Compare trade-offs (e.g., O(n) for simple string vs O(log n) for balanced tree) and justify your choice.
Mention handling empty strings, invalid clicks, overlapping selections, and performance under repeated operations. Suggest unit tests for both problems.
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