The example they gave made it pretty obvious the answer was 5 since it showed up in all four rows.
Clarify the problem constraints and edge cases, then propose an efficient algorithm such as binary search on the first row or a k-way merge with a min-heap. Analyze time and space complexity, and discuss trade-offs between different approaches.
Pro tip: Mention that since each row is sorted, you can use binary search to check for the presence of a candidate in each row, leading to O(m log n) time, which is optimal for large matrices. Also, consider early termination if a row's smallest element exceeds the current candidate.
Ask about matrix dimensions, value ranges, and whether rows can be empty. Discuss what to return if no common element exists.
Start with a simple approach: iterate through the first row and for each element, check its presence in all other rows using binary search. This gives O(m * n log n) time.
Since the first row is sorted, use binary search to find the smallest element that appears in all rows. For each candidate, check other rows with binary search, achieving O(m log n) time.
Discuss a k-way merge using a min-heap to find common elements, or using hash sets for O(m*n) time but O(n) space. Compare trade-offs.
State time and space complexity of the chosen solution. Walk through an example and test edge cases like single row, no common element, and large matrices.
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