## Friday, July 31, 2020

### A specific week

Codeforces Global Round 8 took place during the Jun 15 - Jun 21 week (problems, results, top 5 on the left, analysis). I got a great start by solving problem F 14 minutes earlier than the second solution to this problem (from Egor), but unfortunately could not solve G in the last hour even though I was quite close. Both ecnerwala and tourist solved their 8th problem in the last 10 minutes, and grabbed the first two places with less than 100 points separating them. Congratulations to both!

Here is the problem that I solved so fast: there are n lamps arranged in a circle, and two players are turning them on and off. Initially all lamps are off. The first player starts by turning on any subset of lamps that are off. Let the number of lamps turned on by the first player be k. Then the second player chooses any subset of k consecutive lamps (along the circle), and turns off all lamps in that subset that were on. Then the first player can turn on any subset of lamps that are off again, and so on. The first player can choose to finish the game instead of making their turn. The goal of the first player is to maximize the number of lamps that are on when the game is finished (and they have to finish the game at some point, they can't continue forever), and the second player tries to minimize that number. What is the optimal strategy for the first player?

AtCoder Grand Contest 046 followed on Saturday (problems, results, to 5 on the left, analysis). tourist would be ahead of everybody else with 5 problems even if he stopped competing an hour before the end, but he has used that hour to solve problem E as well. Congratulations on the commanding victory! I could not solve any of the three harder problems in the last two hours.

TopCoder SRM 787 wrapped up the week on Sunday night (problems, results, top 5 on the left, analysis). bqi343 has confirmed his qualification for TCO20 finals, but even with 200 challenge points he could not overtake ksun48 for the first place. Congratulations to both!

The hard problem in this round was somewhat standard, and could be solved by carefully implementing a few standard tricks. However, one could significantly cut down the implementation time and the chances for making a bug by considering the specifics of this problem, which is also a great skill. From the solutions I saw, I think pashka's demonstrates this skill the most (the actual logic of the solution on top of copy-pasted components starts from the line "for (auto b : br2) {"). No binary search, no tree dynamic programming necessary :)

Thanks for reading, and check back for more!