I knew the prefix/suffix product trick going in, so the core solution came out okay.
Use two passes: first compute prefix products (products of all elements before each index) and store them in the result array. Then traverse from right to left, maintaining a running suffix product and multiply it into the result array. This avoids division and achieves O(n) time and O(n) space (or O(1) extra space if output array is not counted).
Pro tip: Clarify upfront whether the output array counts toward space complexity; if not, you can achieve O(1) extra space. Also, mention edge cases like zeros and single-element arrays to show thoroughness.
Confirm constraints: array size, possible zeros, negative numbers, and whether the output array counts toward space complexity. Discuss handling of empty or single-element arrays.
Describe how to compute prefix products in a forward pass and store them in the result array, then compute suffix products in a backward pass and multiply them into the result.
Choose a small array (e.g., [1,2,3,4]) and manually demonstrate the prefix and suffix products to illustrate the algorithm step by step.
State that the algorithm runs in O(n) time with two passes, and uses O(n) space for the output array (or O(1) extra space if output is not counted).
Mention that division is disallowed, so this is optimal. If division were allowed, a simpler O(n) approach with product and zero-count could be used, but it has pitfalls with zeros.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where I almost embarrassed myself.
First, clarify the problem context and the specific algorithm or solution being discussed, then explain how zeros affect its behavior. Walk through the edge cases of one zero and multiple zeros, detailing how the solution detects and handles them, and conclude with the time/space complexity implications.
Pro tip: Proactively mention that handling zeros often requires special-casing to avoid division by zero or incorrect counts, and that multiple zeros can simplify certain problems (e.g., product of array except self). This shows you think about edge cases and robustness.
Restate the problem and the specific solution you're discussing to ensure alignment. Identify where zeros could impact the algorithm's logic or output.
Explain how your solution detects a single zero and adjusts its behavior, such as skipping division or setting specific outputs. Mention any conditions that change due to the zero.
Describe how your solution handles two or more zeros, often by short-circuiting or returning default values. Highlight any simplifications or additional checks required.
Cover related edge cases like all zeros or zeros at boundaries, and explain how they affect time and space complexity. Emphasize that the solution remains efficient.
Concisely recap how zeros are handled, and invite the interviewer to ask about specific scenarios or optimizations. This shows confidence and engagement.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.