Start by locating the node with the value closest to t using a standard BST search in O(log n) time, then expand outward using two in-order iterators (predecessor and successor) to collect the k closest values. Compare the next predecessor and successor values, picking the one closer to t, until k values are collected or both iterators are exhausted. Handle edge cases like k > n, duplicates, and tie-breaking by defining a consistent rule (e.g., prefer smaller value on tie).
Pro tip: Emphasize that the O(h) space comes from the two stacks used by the iterators, and that the expected O(log n + k) time relies on the BST being balanced; if the tree is skewed, the search could degrade to O(n). Also, explicitly state your tie-breaking rule and how you handle duplicates to show attention to detail.
Confirm the definition of 'closest' (absolute difference), tie-breaking rule (e.g., prefer smaller value), and how to handle k > n (return all nodes) and duplicates (treat as separate nodes).
Perform a BST search to find the node with value closest to t, keeping track of the best candidate and its difference. This takes O(log n) expected time.
Set up two in-order iterators: one for predecessors (values <= closest) and one for successors (values >= closest). Each iterator uses a stack of size O(h).
Repeatedly compare the next predecessor and successor values, pick the one with smaller absolute difference to t, and add it to the result. Continue until k values are collected or both iterators are exhausted.
When differences are equal, apply the tie-breaking rule (e.g., choose the smaller value). For duplicates, ensure each occurrence is considered separately, possibly by advancing the iterator past equal values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Honestly the follow-up I was least prepared for.
First, clarify the original problem and solution for a BST, then explain how the approach changes for a general binary tree, focusing on the loss of ordering properties. Finally, discuss the impact on time and space complexity, and any trade-offs or alternative strategies.
Pro tip: Emphasize that while BSTs allow O(log n) operations, general binary trees often require O(n) traversal, but you can still optimize by using techniques like recursion with pruning or iterative traversals. Mention that the choice of traversal (pre-order, in-order, post-order) depends on the specific problem.
Briefly describe the algorithm and its complexity for a BST, highlighting how the BST property enables efficient search, insertion, or deletion.
Explain that without ordering, you cannot make assumptions about node values, so you must potentially visit all nodes, leading to O(n) time in the worst case.
Describe how to modify the approach, such as using a full traversal (e.g., DFS or BFS) and possibly additional data structures (e.g., hash map) to achieve the goal.
State the new time and space complexity, noting that time becomes O(n) and space may be O(n) for recursion or auxiliary structures, and discuss if any optimizations are possible.
Mention any trade-offs (e.g., time vs. space) and alternative approaches (e.g., iterative vs. recursive) that might be more suitable for a general binary tree.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.