## Fast Fourier Transform

I know this name for a long time. But never learnt it. Now it’s time. Recap Previously, Karatsuba’s algorithm for integer multiplication. It computes the result in $O(n^{\log_2 3})$ where $n$ is the number of digits. Another recap: polynomial representation: $$ p(x) = \sum_{i = 0}^{n}p_ix^i $$ And we can represent this polynomial using an array of size $n$. Evaluations and additions of polynomials are straightforward computation. Can be done in $O(n)$ time....