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the world of algorithms is vast but we can often split them into two distinct classes the first class is those that are inherently useful think of your standard graph algorithms like dfs or bfs these algorithms show up all over the place they are efficient and as a result we like to understand them the second class of algorithms we study are ones that are just purely beautiful think of the first time you saw the incredibly simple recursive implementation of towers of annoy if you have a soul you feel a sense of wonder a sense of awe at the elegance of such an algorithm it happens to not actually be that useful or efficient as a matter of fact but we still study it just as we like to read a work of fiction it inspires us and motivates out-of-the-box thinking today i want to talk about an algorithm that rightfully belongs in both classes and my personal favorite algorithm the fast fourier transform the fast fourier transform or fft is without exaggeration one of the most important algori
