The naive approach is obvious and I went there first, which was probably a mistake to say out loud.
First, clarify the problem constraints and confirm that in-place modification is required with O(1) extra space. Then, propose using the first row and first column as markers to record which rows and columns need to be zeroed, handling the first row/column separately with boolean flags. Finally, walk through the two-pass algorithm: mark, then zero, and analyze time and space complexity.
Pro tip: Explicitly discuss the trade-off between using the matrix's own first row/column as markers versus allocating extra space, and mention how you'd handle edge cases like a zero in the first row or column. This shows you think about both efficiency and correctness under constraints.
Confirm that the matrix should be modified in-place and that O(1) extra space is required. Ask if the matrix can be assumed non-empty and if there are any constraints on data types.
Explain that you'll use the first row and first column to store flags indicating which rows and columns contain zeros. Use two separate boolean variables to track whether the first row and first column themselves contain any zeros.
First pass: iterate through the matrix (excluding first row/column) and set matrix[i][0] and matrix[0][j] to zero when a zero is found. Second pass: iterate again and set matrix[i][j] to zero if matrix[i][0] or matrix[0][j] is zero. Finally, handle the first row and column based on the boolean flags.
State that time complexity is O(M*N) and space is O(1). Discuss edge cases: zero in first row/column, single row/column, and all zeros.
Recap the solution, emphasizing the constant space usage, and ask if the interviewer would like you to code it or discuss alternative approaches.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.