My first instinct was to just count 1s per row linearly, which works but is obviously not what they're looking for.
Start by clarifying the problem constraints (e.g., matrix dimensions, memory limits) and discussing brute-force versus optimized solutions. Since each row is sorted, you can use binary search to find the first 1 in each row, giving O(m log n) time. Alternatively, start from the top-right corner and move left/down to find the row with the most 1s in O(m + n) time, which is optimal for large matrices.
Pro tip: Mention the trade-offs between the two approaches: binary search is simpler but O(m log n), while the staircase method is O(m + n) and more efficient for large matrices. Also, note that if multiple rows have the same maximum number of 1s, you should return the smallest index (or clarify with the interviewer).
Ask about matrix dimensions, whether rows can be empty, and if there are multiple rows with the same maximum. Confirm the return type (index or row itself).
Mention that a naive solution would scan each row to count 1s, taking O(m * n) time. This sets a baseline but is inefficient.
Explain binary search per row (O(m log n)) and the staircase method (O(m + n)). Describe how the staircase method works: start at top-right, move left if current cell is 1, else move down, keeping track of the row with the most 1s.
Compare time and space complexity of both optimized methods. Discuss edge cases: all zeros, all ones, single row/column, and duplicate maximum counts.
Write clean code for the chosen approach, then walk through a small example to verify correctness. Mention potential optimizations like early termination if a row has all 1s.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.