Implement polynomial multiplication API in C

Q: Implement polynomial multiplication API in C

This question evaluates proficiency in C programming, API design, low-level data representation for polynomials, and algorithmic competence in performing coefficient convolution while handling edge cases like differing degrees, zero and negative coefficients.

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Question

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Problem

Implement an API in C to multiply two polynomials.

A polynomial is represented by its coefficients. You must define the input and output format as if you were writing a small library function for other users.

Example polynomials:

$P(x) = x^3 - 2x + 5$
$Q(x) = x^2 + 2x + 4$

Requirements

Use C (not C++) .
Define a clear representation for a polynomial (e.g., array of coefficients where coeff[i] is the coefficient of $x^i$ ).
Provide a function (or set of functions) that multiplies two polynomials and returns the result.
Ensure the API handles:
- Different degrees for the two inputs
- Zero coefficients
- Negative coefficients

Output

Return (or fill) a polynomial representing $R(x) = P(x) \times Q(x)$ using your chosen representation.

Constraints (you may assume)

Degrees are non-negative integers.
Coefficients fit in 32-bit signed integers (or specify a larger type if you choose).
Time complexity should be better than enumerating all exponent pairs explicitly as strings (i.e., use coefficient convolution).

Implement polynomial multiplication API in C

Quick Overview

Problem

Requirements

Output

Constraints (you may assume)

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