An unexpected verdict week

Codeforces Round 658 was the first event of the Jul 20 - Jul 26 week (problems, results, top 5 on the left, my screencast, analysis). Benq has managed to finish all six problems in time, even though the first five would be enough for the first place anyway. Congratulations on the confident victory!

I have managed to dig myself out of the piecewise quadratic function world with just 8 minutes to go, which was still quite satisfying even though competing with Benq was completely out of question :)

TopCoder SRM 788 started the race for the first TCO21 spot (problems, results, top 5 on the left, my screencast, analysis). My easy-hard-medium strategy has hurt me this time, as after submitting the hard I saw others get 500+ points for the medium and submitted it without enough thinking, leading to a resubmit later. On the other hand, I could submit, stress-test, debug, fix and resubmit it without the pressure of "should I switch to the hard instead?" :) It was hard to fight for the top places with the resubmission. Even though the medium problem was much harder than the other two for lyrically as well, she got it right from the first attempt and earned 5 TCO21 points. Congratulations!

Here is the problem that caused all this mess: you are given an H times W grid (H*W<=500), with some of the boundaries between cells being passable, and some being walls. All outside boundaries are walls. Your goal is to remove some more non-outside walls in such a way that the remaining walls split the entire grid into rectangular areas without internal walls. What is the maximum number of such rectangles one can get?

Codeforces Round 659 then revealed the origin of "Polish Mafia" team name (problems, results, top 5 on the left, analysis). I could not solve problem C (neither could I solve problem F, but I did not spend much time on it), and I was not alone. That makes the performance of tourist, Benq and Radewoosh who solved all six problems even more impressive, well done! Even they have solved problem C as their last or next-to-last problem, suggesting it was also quite tricky for them.

Here is that problem: you are given a string of length up to 10⁵, consisting of the first 20 lowercase English letters. In one step, you can pick any set of characters in this string that are all equal (not necessarily all occurrences of that character), and change all of them to some other character (the same for all replacements in this step). What is the smallest number of steps needed to obtain the other given string of the same length?

I would also like to highlight the excellent investigation by maroonrk on the practical performance of modern flow algorithms :)

Thanks for reading, and check back for more!