The naive approach bites you immediately if you start zeroing things out as you go, because you lose track of which zeros were original.
Clarify the problem constraints and discuss the naive approach of using extra space, then optimize to O(1) space by using the first row and first column as markers. Walk through the algorithm step by step, handle edge cases, and analyze time and space complexity.
Pro tip: Mention that you can avoid using extra space by marking zeros in the first row and column, but be careful to handle the first row and column separately to avoid overwriting markers prematurely.
Ask clarifying questions: Can we modify in-place? What are the constraints on m and n? Are there any memory limitations? Confirm the expected output.
Explain the straightforward solution using two boolean arrays to track which rows and columns need to be zeroed, and analyze its O(m+n) space complexity.
Describe how to use the first row and first column as markers: iterate through the matrix, and when a zero is found, set the corresponding first row and first column elements to zero. Then use these markers to zero out the appropriate cells.
Separately track whether the first row and first column themselves contain zeros, and zero them out at the end if needed.
State that the time complexity is O(m*n) and space is O(1). Walk through a small example to verify correctness.
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