The no-division constraint is the whole point of the problem.
Use prefix and suffix products to compute the result in two passes without division. First, compute prefix products from left to right, then multiply by suffix products from right to left. This achieves O(n) time and O(n) space (or O(1) extra space if output array is reused).
Pro tip: Clarify edge cases upfront: what if the array contains zeros? The prefix-suffix approach handles zeros naturally, but be prepared to discuss how many zeros and their positions affect the result. Also, mention that you can optimize space by using the output array to store prefix products first, then update it with suffix products in a second pass.
Restate the problem: given an array, return an array where each element is the product of all other elements. Note the constraints: no division, O(n) time. Ask clarifying questions about input size, possible zeros, and whether the output array counts towards space complexity.
Consider brute force O(n^2) and explain why it's suboptimal. Think about how to avoid division: use prefix and suffix products. Discuss the idea of computing products of all elements to the left and right of each index.
Describe the two-pass approach: first pass compute prefix products and store in output array; second pass compute suffix products on the fly and multiply with the prefix products in the output array. This yields the desired result in O(n) time and O(1) extra space (excluding output).
State time complexity O(n) and space complexity O(n) for output (or O(1) extra). Discuss edge cases: empty array, single element, multiple zeros, negative numbers. Explain how the algorithm handles them.
Write clean code with meaningful variable names. Walk through a small example to verify correctness. If time permits, discuss potential optimizations or alternative approaches (e.g., using logarithms, but note precision issues).
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This one tripped me up more than I'd like to admit.
Clarify the rules and constraints, then propose an in-place solution using bit manipulation to encode the next state without extra space. Walk through the algorithm, handle edge cases, and analyze time and space complexity.
Pro tip: Mention that using two bits per cell (e.g., LSB for current state, next bit for next state) allows in-place updates and avoids extra memory, which is often expected at Meta. Also, discuss how to handle infinite boards if asked.
Confirm the exact survival and birth rules, and ask about board size, whether it's finite or infinite, and if in-place modification is allowed.
Decide on a representation that allows efficient updates, such as using two bits per cell to store both current and next state, or using a separate board if extra space is acceptable.
Iterate through each cell, count live neighbors using the current state, apply the rules, and store the next state in the extra bit or separate board.
After processing all cells, shift the next state into the current state (e.g., right shift by 1) to finalize the next generation.
State time complexity O(m*n) and space complexity O(1) if using bit manipulation, and discuss edge cases like empty board, single row/column, and all live/dead cells.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.