I knew the general idea but fumbled the carry logic at first.
Clarify the problem constraints (e.g., digit order, sign handling, output format) and then propose a digit-by-digit multiplication algorithm that mimics manual multiplication, using an array to accumulate results and handle carries. Discuss time and space complexity, and consider edge cases like zeros and negative numbers.
Pro tip: Demonstrate awareness of potential pitfalls like integer overflow and leading zeros, and mention that you would write unit tests for edge cases to ensure correctness.
Ask about digit order (most significant first?), sign representation, and expected output format. Confirm whether the input arrays can be empty or contain non-digit characters.
Explain that you will multiply each digit of one number by each digit of the other, similar to grade-school multiplication, and accumulate results in a result array of size m+n.
Describe how to iterate from least significant digit to most, compute products, add to the current position, and propagate carries. Mention handling of signs separately.
State that time complexity is O(m*n) and space is O(m+n). Discuss edge cases: multiplication by zero, negative numbers, and leading zeros in the result.
Propose testing with small examples and large numbers. Mention potential optimizations like using Karatsuba for very large numbers, but note that the simple approach is usually sufficient.
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