Math

This was written jointly by errorgorn and me and published on errorgorn’s blog, and the original post is here. Hi everyone! Today nor sir and I would like to talk about generating uniform bracket sequences. Over the past few years when preparing test cases, I have had to generate a uniform bracket sequence a few times. Unfortunately I could not figure out how, so I would like to write a post about this now....

This post was originally written on Codeforces; relevant discussion can be found here. This post will be more about developing ideas about certain structures rather than actually coding up stuff. The ideas we’ll be developing here have many applications, some of which involve: Number Theoretic Möbius Inversion Principle of Inclusion-Exclusion Directed Acylic Graphs Subset Sum Convolution Finite Difference Calculus (and prefix sums) Note that some of the terminology used below might be non-standard....