My first instinct was to do a BFS and just print level by level, which is fine until you realize the centering constraint means you need to know where each child lands before you can place the parent.
First, clarify the exact formatting rules and edge cases (e.g., empty tree, single node, spacing). Then, outline a two-pass approach: compute the width and positions of each node via a recursive traversal, and then render the tree level by level using a grid. Finally, discuss trade-offs such as time/space complexity and possible optimizations.
Pro tip: Mention that you would write unit tests for edge cases like a tree with only left children or a skewed tree, and that you'd consider iterative vs recursive implementations for very deep trees to avoid stack overflow.
Ask about the exact output format: how many spaces between leaf slots, how to handle missing children, and what to do for an empty tree. Confirm that each parent is centered between its children.
Decide on a coordinate system (e.g., each node gets an x-position and a level y). Use a recursive function to compute the width of each subtree and assign positions, ensuring parents are centered.
Create a 2D grid (list of lists of characters) sized to the computed width and height. Place node values and '*' for missing children, then join rows into strings.
Discuss time and space complexity (O(n) for n nodes, but space can be O(n * height) for the grid). Mention alternatives like printing level by level with BFS if memory is a concern.
Walk through examples: a perfect tree, a skewed tree, and an empty tree. Verify that spacing and centering rules are met.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.