tl;dr

• Competitive programming roadmap here.
• It should be suitable both for newcomers and for people with some experience with CP: let's say, up to blue on Codeforces.
• It contains ~ 100 "must-know" problems about various topics: ad-hoc, STL, binary search, DP, number theory, graphs.
• There are solution sketches at the bottom, don't feel guilty reading them if stuck.

Why?

Many people new to Codeforces seek advice about how to get better / which problems to try. Other people are stuck on gray / green even after solving a lot of problems. This roadmap aims to be a solution.

My take: to be good at competitive programming, you have to know "what to think" and "how to think" when you try a problem.

• "What to think": you have to know a decent amount of standard problems / techniques. Sometimes, a problem requires steps / observations that seem obvious if you've already seen them. Other times, you may solve a problem by reducing it to a well-known sub-problem. On the other hand, you may realize you've done something wrong if you "reduce" the problem to something that you know it's unsolvable under the given constraints. All this isn't possible if you don't know those standard problems.
• "How to think": it comes down to "building" a path to the solution. Sometimes, you need to find new insights / observations by analyzing the process in the statement, manipulating math equations, etc. Other times, you need to find a twist to a well-known technique. You can practice "how to think" by solving ad-hoc / non-standard problems.

So, how to practice?

• Using the Codeforces problemset is quite good for experienced people, but it may turn out to be harmful for beginners. Surely, recent contests on Codeforces have a very good quality, and even the easiest problems are often original and can't be googled. However, this means there are no easy standard problems, so you don't really improve in "what to think" when you solve them.
  Also, even the easiest problems are supposed to require an "idea" that often turns out to be nontrivial to find / prove without looking at the sample input / output. So, in most cases, the most convenient way to solve easy problems is to find a pattern in the samples, and this does not actually teach you "how to think" to solve harder problems. For example, in problem 1768A - Greatest Convex it's way easier to observe that the solution is $$$k-1$$$ from the samples than to actually find it out. (Note: this doesn't mean it's a bad problem, but only practicing with this kind of problems may be a bad practice).
• CSES mainly contains standard problems, so it doesn't really teach "how to think".
• AtCoder problemset contains a lot of educational problems, and AtCoder Beginner Contests problems are quite good for practice. However, most of them are "trivial" if you already know the underlying idea and "impossible" otherwise.
• USACO Guide is very good, but it's more oriented to OI (Olympiads in Informatics) and it contains some problems with very long statements and where the bottleneck is the implementation.

How does the roadmap work?

The roadmap contains ~ 100 problems, mainly from AtCoder, Codeforces and an Italian online judge.

• "What to think": the problems are "standard-ish", and they cover most of the ideas required in problems ranging from easy (div2A) to medium (div2D-E). In other words, given a problem of such difficulty, there is a high chance it has at least one idea in common with a problem in the roadmap.
• "How to think": the problems are "not so standard", and most of them also require ad-hoc ideas or twists to standard ideas.
• The statements are short, and they require no "unnecessary" implementation details. Try to make your implementation as simple and short as possible.
• The problems are split into topics. However, sections $$$5$$$ and $$$6$$$ contain "summary problems" with no topic, so that you don't get used to solve problems knowing the topic in advance.
• The roadmap includes problems with various levels of difficulty, indicated by the number of stars (from $$$0$$$ to $$$6$$$).
• If you are stuck on a problem for a long time, you may want to read the solution sketch at the end of the document. These sketches are written in such a way that only new ideas (= not used in the previous problems in the roadmap) are highlighted. So, you may want to think again about the problem. If you are still stuck, you may want to read the editorial (available on Codeforces and AtCoder). Of course, you shouldn't always use the solution sketch or the editorial. Ideally, you should use the solution sketch in less than half of the problems above your level, and read the complete editorial few times. However, reading the solution sketch and the editorial after solving the problem is often useful, as they can contain tips, alternative solutions or variants of the problem.

Then?

After finishing the roadmap (excluding the "Final problems" in section $$$14$$$), probably you have built a small "database" of standard-ish problems in your head and you're much better in the "what to think" part. "How to think" is more complex and it requires more time / experience to be mastered. Anyway, there are many ways to make further progress.

• If you want to practice on a specific topic, you can use USACO Guide, or try the "bonus mashups" in the last section.
• You can try harder problems on the Codeforces problemset (guessing from the samples doesn't work on harder problems) and on AtCoder problemset (they are not "impossible" anymore, since you know more tools to solve them).

Conclusion

Of course, feedback / suggestions / corrections are welcome. The roadmap may contain a lot of typos or the solutions may be unclear, let me know and I will try to fix.

If you're starting the roadmap, good luck! I hope it will be useful.