A Frobenius week

The 2nd Universal Cup Stage 19: Estonia was the only event of this week (problems, results, top 5 on the left, analysis). Team 03 Slimes, who are a distant third in the overall standings, won their second stage of the season in an impressive fashion, beating the top two teams in the overall standings by two problems. Judging by the +32, some squeezing was involved, potentially of an approach that was not intended to pass — but that is also an important skill in algorthmic competitions, so well done! I am also not sure who actually was on the team this time, as Mingyang Deng is also listed as part of MIT CopyPaste on the same scoreboard.

Possibly rejuvenated by the news that the 2022 ICPC World Finals seem to be finally happening in April, Harbour.Space P+P+P followed in second place — congratulations as well! (jk, they actually wrote this contest as part of the Osijek camp back in September, so they were still practicing towards the original dates).

Finally, this week an anonymous LGM published a very nice result that drops a logarithmic factor from matrix exponentiation. Of course, theoretically we already know ways to drop much more from the asymptotic complexity, but all of those are not really beneficial in practice on the time limits prevalent in the algorithmic competitions. This result, however, did allow to slash the fastest time to find a power of a 200x200 matrix roughly 3x (compared to the straightforward binary exponentiation method; the judge also has some fast submissions from November 2023 that start with "vector<ll> f=a.poly();", so possibly some other version or precursor of this result?..

I guess now it will be a bit harder to separate wrong submissions when preparing problems, on the other hand the squeezing toolkit just got a bump :)

Thanks for reading, and check back next week!