The Power of MathForces
Intro
There was nowhere left to run. Back against the wall with my coach also looking at my spreadsheet, a nervous peek between my hands confirmed my worst fear: it was math week. I couldn’t delete the row from my tag list with my mentor looking and it was too late to try and distract him. My body seemed to go on autopilot from shock, as I navigated to the Codeforces Problemset. With the math tag and the cursor over “Apply”, I woke up from the nightmare.
Real Intro?
Welcome back everyone! If the title and the dramatic intro wasn’t enough of a hint, I’ll be talking about MathForces this week and how it’s elevated my skills. Deep down, we all know math is keystone topic to master for success in CP, yet we also choose to neglect it. After all, why work on boring math when you could be doing inverse convex hull matroid matrix multiplication (I promise I didn’t just mush together smart sounding words)? After seeing all the “Hope it isn’t Mathforces” talk on CF and being a very impressionable person, I went into the next week of math practice expecting little to no improvement. Oh boy was I wrong. I ended up practicing almost purely math for two weeks and ended it feeling as if I’d improved more in 2 weeks than I had in the last month. The following are some core aspects of CP that I’ve seen improve with math practice that you’ll see too if you decide to join me on the dark side.
Mindset
Before I started this practice, I’d often give myself the excuse that the idea in the problem was something I haven’t learned yet. This sort of thinking led to me giving up too early or checking the editorial and realizing I had already learned the concept in use. Math problems, on the other hand, were brutally exposing. I could only tell myself that GCD was too hard so many times before even I had to admit I wasn’t pushing hard enough. Solving math problems cultivates the idea that whatever problem you’re tackling is something within your grasp if you just think harder because unlike other tags, there aren’t many esoteric concepts that prevent you from getting AC. Just from not checking TCs/Editorial early, the efficacy of my training and virtual contest performance have greatly improved.
Logic & Observations
This is kind of hard to put into words, but MathForces really helped to clarify my thinking. As someone who struggled to solve even 1400s, every problem became a game of “Try a technique and hope it works”. The constant backtracking to try other options helped develop a better intuition of when to use what. I found that even when the problem at hand wasn’t math related, the speed at which I’m able to find the right line of thinking greatly increased. Although this skill seems like a very minor optimization, it plays a major role in contests where you don’t have time to implement every idea that crosses your mind. If you go about thinking about and implementing a wrong solution, it wastes both your time and your brain power. I’ll leave you to decide which one of those is more important in a CF contest.
Casework
Now that you’re able to figure out the right technique fairly quickly, it’s onto accuracy and precision. A strong general rule I developed when doing math is assuming there’s ALWAYS at least one edge case. Sometimes you’ll get a problem where there isn’t any edge case that your solution can’t handle, but by checking, you make sure the validity of your solution is airtight. Besides giving you a valid solution, compartmentalizing a problem into cases also helps you solve the problem. By testing and solving smaller constraints than the problem might provide in an OI-like fashion, you can quickly iterate through a wide array of ideas. Since implementation of math problems are relatively straightforward, almost all WAs will be from missed edge cases. This practice helps you identify edge cases in problem statements and conditions where you solution might fail which is a skill that applies to any kind of problem.
Outro
I hope you guys enjoyed this week’s post! If you really enjoyed this, feel free to share it and spread the MathForces propoganda. Keep an eye out for my special Christmas present coming soon, see you then my fellow MathForce Deciples. :)
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