Is there a better way to calculate it?

#	User	Rating
1	tourist	4009
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2	Um_nik	163
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6	-is-this-fft-	158
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8	TheScrasse	154
9	Dominater069	153
9	nor	153

$$$(f \ast g)(t)=\max\limits_{i=0}^t (f_i+g_{t-i})$$$

I thought for a long time and tried something like FFT to solve it but failed.
In fact,I haven't find a algorithm better than brute force,which is $$$O(n^2)$$$.

hbhz_zcy's blog