I'm interested in improving efficiently, and the main advice I see (on blogs, comments, CP Discord, etc.) is "solve more problems". For someone who's not solving any problems yet, this is great advice. Additional detail seems unhelpful because getting started is WAY more important than nitpicking and prematurely worrying about efficiency.
But how can someone who's already solving a lot of problems improve more efficiently?
I have a lot of unanswered questions about this:
How should we choose problem difficulties?
Someone who's already Expert probably won't get to the next level by solving 500 problems that are all Div2A. I often hear "solve problems that are slightly above your current level", and once again this is great advice. But it's important to sometimes mix in "easy" problems for practicing speed and staying motivated. How should we balance the two?
How should we choose problem topics?
I've heard arguments for choosing problems randomly, but it makes sense to sometimes choose specific topics to address weak points or review important concepts. When should we do one or the other?
How should we structure our training schedules?
My friend who does competitive gymnastics said that his training schedule goes "Hard, Hard, Easy" (two sessions of intense training followed by one session of lighter training, to help with recovery). How should competitive programmers structure their training schedules?
What should we do after getting AC?
One way is to just move on to the next problem. But Polya's book "How to Solve It" talks about four steps in problem solving: understand the problem, make a plan, carry out the plan, and look back. What are good ways to do "look back" so we can get the most out of each problem?
What other activities should we do?
Obviously, there's participating in contests. But besides that, is it helpful to read textbooks? Prove theorems? Watch streams? Play Zachtronics games? How helpful are these activities compared to only solving problems? How should we divide our time between these different activities?
I know there's no single answer to these questions that works for everybody in every situation, but I'm still interested in hearing your ideas.
