FFT Fast Fourier transform

This thing is very magical, read a half-day online interpretation and courseware, studied for a long time, is probably understood its principle.

Don't say a word more first.

We ask for H (x) =f (x) *g (x), F (x) =σai*x^i,g (x) =σbi*x^i.

The simplicity of complexity is N2, but an X-order polynomial can be represented by a unique interpolation of x+1 points in the plane, so we can use the x+1 (Xi,f (xi)) and (Xi,g (xi)) and (Xi,f (xi)), and then we can reverse the expression of H (X).

Then we need to finish these two steps in the Nlogn time, first Xi's value needs special take, make Xi=ζ (n,i) (do not understand the plural students can Baidu), so that n (polynomial times, not enough words also to fill) =2^m, then

Not to be continued ....

FFT Fast Fourier transform