let vs. let rec is in ML and Scheme and some other languages. But the compiler could transform the let rec into a let, and e.g. Haskell does it so the programmer does not have to.

It's not exactly a trivial algorithm as it involves finding strongly connected components from the dependency graph and then topologically sorting that.

I implemented this for a toy programming language compiler project, it was a fun one. Luckily I had SCC and topological sort from Haskell's Data.Graph module.