I knew the prefix/postfix trick going in, which helped, but the no-division constraint still trips people up if they haven't seen it before.
Use two passes: first compute prefix products (product of all elements to the left) and store them in the output array, then traverse from right to left maintaining a running suffix product and multiply it into each output position. This achieves O(n) time and O(1) extra space since the output array is reused.
Pro tip: Explicitly state that the output array is not counted as extra space, and clarify that the running suffix product is a single variable, so space is O(1). This shows you understand the problem's constraints precisely.
Confirm that division is not allowed, time must be O(n), and extra space O(1) beyond the output. Ask about empty array, single element, and zeros.
Describe how to compute prefix products in the first pass and store them in the output array, then multiply by suffix products in the second pass.
Use a small array like [1,2,3,4] to demonstrate the prefix and suffix products and the final output.
State that time is O(n) and space is O(1) extra. Mention that the output array is reused, and compare with a division-based approach (if allowed) which would be simpler but violates the constraint.
Discuss how zeros are handled naturally by the algorithm, and confirm the solution works for arrays of any size.
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Acknowledge that zeros and negatives are common edge cases that can break assumptions like 'all positive' or 'non-zero'. Walk through how your solution handles them, focusing on algorithmic invariants, data structure behavior, and any special-case logic. If the solution doesn't handle them, explain how you would modify it to do so robustly.
Pro tip: Proactively mention that you test with zeros and negatives during development, and describe how you'd use property-based testing or boundary value analysis to catch issues. This shows you think about edge cases before they become bugs.
Restate the problem and confirm whether zeros and negatives are valid inputs. Ask if there are constraints like 'array contains only positive integers' to avoid assumptions.
Explain how zeros or negatives could break the algorithm: e.g., division by zero, incorrect comparisons, hash collisions, or invalid indices.
Walk through the algorithm step-by-step with a small example containing zeros and negatives, highlighting where special handling occurs.
If the solution doesn't handle these cases, suggest changes such as adding checks, using absolute values, or adjusting data structures.
Mention how you would test with edge cases, including zeros, negatives, and mixed signs, to ensure correctness and robustness.
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Start by clarifying the language and integer types, then systematically discuss detection and prevention strategies. Emphasize trade-offs between performance, correctness, and code complexity, and relate to real-world scenarios like Amazon's high-scale systems.
Pro tip: Mention that Amazon often uses languages like Java where overflow is silent, so proactive measures like using Math.multiplyExact or BigInteger are critical. Also, highlight the importance of unit tests with boundary values to catch overflow early.
Ask about the language, integer types (e.g., int32, int64), and whether the products are part of a larger computation. This shows you consider the environment before proposing solutions.
Explain how to detect overflow before it happens, such as checking operand magnitudes or using built-in functions like checked arithmetic in C# or Math.addExact in Java.
Discuss prevention techniques: using wider types (e.g., long for int multiplication), arbitrary-precision libraries (BigInteger), or restructuring the algorithm to avoid large intermediates.
If overflow is unavoidable, decide on a strategy: throw an exception, saturate to max/min values, or wrap around (if acceptable). Justify based on requirements.
Compare performance, memory, and complexity of each approach. For example, BigInteger is safe but slower; using long is faster but may still overflow for very large inputs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.