This post was originally written on Codeforces; relevant discussion can be found here. Disclaimer: I am not an expert in the field of the psychology of learning and problem-solving, so take the following with a grain of salt. There is not much “scientific” evidence for this post, and the following is validated by personal experience and the experiences of people I know (who fall everywhere on the “success” spectrum — from greys to reds in competitive programming, from beginners in math to IMO gold medalists, and from people with zero research experience to people with monumental publications for their own fields). This post only covers one possible way of thinking about knowledge organization and retrieval that I have been using for the past decade or so, but there definitely will be other models that might work even better. Even though I just have a few courses worth of formal psychology experience, I still think the content of this post should be relevant to people involved with problem-solving. ...

This post was originally written on Codeforces; relevant discussion can be found here. Firstly, the CF Catalog is a great feature that makes it much easier to learn topics by having a lot of educational content in the same place, so thanks MikeMirzayanov! I was originally going to post this as a comment under the catalog announcement post, but it became too large for a single comment, and it will probably need some more discussion. ...

This post was originally written on Codeforces; relevant discussion can be found here. People often say C++ is much more cumbersome to write than any sane language should be, but I think that is mainly due to lack of knowledge about how to write modern C++ code. Here’s how you can write code more smartly and succinctly in C++(20): Negative indexing with end Have you ever found yourself using a vector like a stack just because you have to also access the last few positions, or writing a sliding window code using a deque (where the size might be variable, but you want to access an element at some offset from the end)? ...

This post was originally written on Codeforces, relevant discussion can be found here. This post is intended to be an introduction to permutations for beginners, as there seem to be no resources other than cryptic (for beginners) editorials that talk about some cycles/composition, and people unfamiliar with permutations are left wondering what those things are. We’ll break the post into three major parts based on how we most commonly look at permutations. Of course, even though we will treat these approaches separately (though not so much for the last two approaches), in many problems, you might need to use multiple approaches at the same time and maybe even something completely new. Usually, you’d use these ideas in conjunction with something like greedy/DP after you realize the underlying setup. ...

This post was originally written on Codeforces; relevant discussion can be found here. I’ve been involved with testing a lot of Codeforces contests and coordinating contests for my uni, and have seen various kinds of issues crop up. However, I was able to come up with a stable system for my uni contests that helped make the experience as educational and error-free as possible, and I have found the lack of some of those things to be the main reason behind issues faced by Codeforces contests. ...

This post was originally written on Codeforces; relevant discussion can be found here. Disclaimer: This is not an introduction to greedy algorithms. Rather, it is only a way to formalize and internalize certain patterns that crop up while solving problems that can be solved using a greedy algorithm. Note for beginners: If you’re uncomfortable with proving the correctness of greedy algorithms, I would refer you to this tutorial that describes two common ways of proving correctness — “greedy stays ahead” and “exchange arguments”. For examples of such arguments, I would recommend trying to prove the correctness of standard greedy algorithms (such as choosing events to maximize number of non-overlapping events, Kruskal’s algorithm, binary representation of an integer) using these methods, and using your favourite search engine to look up more examples. ...

This post was originally written on Codeforces; relevant discussion can be found here. Recently, I retired from competitive programming completely, and I found myself wondering about what I’ll do with all the competitive-programming-specific knowledge I have gained over the years. For quite some time, I’ve been thinking of giving back to the community by writing about some obscure topics that not a lot of people know about but are super interesting. However, every time I ended up with ideas that are either too obscure to be feasibly used in a competitive programming problem, too technical to ever be seen in a contest, or having too many good posts/articles about them anyway. ...

This post was originally written on Codeforces; relevant discussion can be found here. This post was initially meant to request updates to the C compiler on Codeforces (given the large number of posts complaining about “mysterious” issues in their submissions in C). While writing it, I realized that the chances of the said updates would be higher if I mentioned a few reasons why people would like to code in C instead of C++ (some of the reasons are not completely serious, as should be evident from the context). ...

This post was originally written on Codeforces; relevant discussion can be found here. Since someone recently asked me about my competitive programming setup, and I like tinkering with my setup to make it as useful and minimal as possible, I thought I should share my setup that I’ve used for the past few years and a modified version that I’ve used at onsite ICPC contests. I’ve also talked to a few people who went to IOI and had a similar setup, and I’m fairly confident that at least some people will be able to successfully use this without having to worry too much about the details, like I did. This is definitely NOT the only way to set up a basic environment, but it was the way that worked for me for quite a long time. ...

This post was originally written on Codeforces; relevant discussion can be found here. Recently someone asked me to explain how to solve a couple of problems which went like this: “Find the expected time before XYZ happens”. Note that here the time to completion is a random variable, and in probability theory, such random variables are called “stopping times” for obvious reasons. It turned out that these problems were solvable using something called martingales which are random processes with nice invariants and a ton of properties. ...