The naive merge-and-find approach works but they're clearly waiting for the binary search solution.
Start by clarifying the problem constraints (array sizes, sorted order, definition of median for even total length). Then present a binary search solution that partitions the two arrays into left and right halves of equal size, achieving O(log(min(m,n))) time. Walk through edge cases and compare with the simpler O(m+n) merge approach to show trade-offs.
Pro tip: At Apple, interviewers value clean, efficient code and clear communication. Before coding, explicitly state the time and space complexity of your approach and how it handles edge cases like empty arrays or one array being much larger than the other.
Ask about array sizes, whether they can be empty, and how to define the median for even total length (average of two middle elements). Confirm that the arrays are sorted in ascending order.
Mention the O(m+n) merge approach as a baseline, then propose the binary search on the smaller array for O(log(min(m,n))) time. Explain why binary search works: we partition both arrays such that all elements on the left are ≤ all elements on the right.
Define partition indices i and j for the two arrays. Ensure i + j = (m + n + 1) / 2. The correct partition satisfies: leftMax1 ≤ rightMin2 and leftMax2 ≤ rightMin1. Adjust the search range based on these conditions.
Handle cases where a partition is at the boundary (i=0 or i=m) by using sentinel values like -∞ and +∞. Compute the median: if total length is odd, it's max(leftMax1, leftMax2); if even, it's the average of max(leftMax1, leftMax2) and min(rightMin1, rightMin2).
State that time complexity is O(log(min(m,n))) and space is O(1). Walk through a few examples, including edge cases like one empty array, to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.