Course Solutions Uncategorized (Solved) : 2 Marks Describe Multiply Two N Degree Polynomials Together O N Logn Time Using Fast Fouri Q36463406 . . . .

(Solved) : 2 Marks Describe Multiply Two N Degree Polynomials Together O N Logn Time Using Fast Fouri Q36463406 . . . .

June 27, 2024June 27, 2024| adminadmin| 0 Comment| 8:32 pm
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[2 marks]Describe how to multiply two n-degree polynomialstogether in O(n logn) time, using the Fast Fourier Transform (FFT).You do not need to explain how FFT works – you may treat it as ablack box.

In this part we will use the Fast Fourier Transform (FFT)algorithm described in class to multiply multiple polynomialstogether (not just two).

Suppose you have K polynomials P1, . . . , Pk so that

degree(P1) +···+ degree(PK) =S

(i)[6 marks]Show that you can find the product of these Kpolynomials in O(K SlogS)time.

Hint: How many points do you need to uniquely determine anS-degree polynomial?

(ii)[12 marks]Show that you can find the product

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