This one looks manageable until you sit down and actually try to parse the string.
First, clarify the input format and constraints, then outline a parsing strategy to extract coefficients and exponents from each factor. Next, describe how to multiply the polynomials term-by-term, combine like terms, and format the result as a string sorted by descending exponent. Finally, discuss edge cases and complexity.
Pro tip: Mention that you would use a hash map (dictionary) to accumulate coefficients by exponent, which simplifies combining like terms and naturally handles missing exponents. Also, proactively discuss how to handle negative signs and zero coefficients.
Ask about input format (e.g., spaces, negative signs, zero coefficients) and output expectations (e.g., omit zero terms, handle constant terms). Confirm that the polynomial has exactly two factors and that exponents are non-negative integers.
Design a parser that extracts each term's coefficient and exponent from the string. Use regex or manual scanning to handle optional signs, coefficients (including implicit 1), and exponents (including implicit 1 for x).
Use a hash map to accumulate coefficients for each exponent: for each term in the first factor, multiply with each term in the second factor and add to the map. This efficiently combines like terms.
Sort exponents in descending order, skip zero coefficients, and build the string with proper signs and exponents (omitting exponent 1 and coefficient 1 where appropriate). Ensure no spaces or parentheses.
Discuss time complexity O(n*m) where n and m are the number of terms in each factor, and space complexity O(n+m). Mention edge cases like zero polynomial, negative coefficients, and large exponents.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.