finding the derivative of a polynomial
math, python
Solution
A polynomial in a single variable can be represented simply as an array containing the coefficients. So for example 1 + 5x3 - 29x5 can be expressed as `[1, 0, 0, 5, 0, -29]`. Expressed in this form the derivative is easy to compute.
suppose `poly` is a python list as above. Then
deriv_poly = [poly[i] * i for i in range(1, len(poly))]
For sparse polynomial other representations are relatively easy, such as a list of pairs `(coefficient, exponent)` or dictionary mapping exponents to coefficients.
Parsing the expression is more complicated but using various parsing frameworks should be easy because the grammar is comparatively simple.
Problem
I wondering symbolically how you would parse a polynomial into a function and return the derivative. What data structure would I use or method to parse the polynomial? Preferably without using any libraries, as this question could pop up in a technical interview. ``` polynomial-> of nth degree def derivative(polynomial): return derivative Example: f(x) = 2x^2+3x+1 f'(x) = 4x+3 ``` I don't want a solution, this is not homework but a hint of where I would start.