Help in a math problem

Revision en1, by Karry5307, 2020-09-30 12:43:08

Could anyone give a solution to the problem below with $$$O(n\log n)$$$ or $$$O(n\log^2n)$$$ time plz?

Given two sequences $$$g,h$$$ with length $$$n$$$ and a binary function $$$F(n,k)$$$, calculate the sequence $$$f$$$ which satisfies:

$$$f_{i}=\left(\sum\limits_{k=0}^{i}F(i,k)g_kh_{i-k}\right)\bmod 998244353$$$

And $$$F(n,k)$$$ can be $$$1$$$, $$$\binom{n}{k}$$$, $$$n^k$$$ or $$$k^n$$$.

Tags #math, #fft

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en2 English Karry5307 2020-09-30 15:33:32 23
en1 English Karry5307 2020-09-30 12:43:08 376 Initial revision (published)