How do you compute the product of all array elements except self?
Given an array, return a new array where each element is the product of all other elements without using division. This challenges your spatial reasoning and prefix/suffix logic.
Why Interviewers Ask This
This problem evaluates your ability to solve constraints creatively, specifically avoiding division which might cause overflow or fail with zeros. Interviewers want to see if you can construct prefix and suffix products efficiently in linear time. It tests your skill in manipulating arrays to store intermediate results without excessive auxiliary space.
How to Answer This Question
Explain why division is problematic due to zero values and precision issues. Describe the two-pass approach: first calculate prefix products, then suffix products. Show how combining these gives the final result. Discuss space optimization by storing the output array directly instead of creating separate prefix/suffix arrays. Ensure clarity on handling edge cases like multiple zeros.
Key Points to Cover
- Avoiding division for robustness
- Prefix and suffix product construction
- Space optimization techniques
- Zero handling strategies
Sample Answer
I would solve this by calculating prefix and suffix products separately. In the first pass, I create an array where each index holds the product of all elements to its left. In the second pass, I traverse right-to-left m…
Common Mistakes to Avoid
- Using division which fails on zeros
- Creating unnecessary auxiliary arrays
- Incorrectly initializing prefix/suffix values
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