To name a few concepts: "Permutation & Combination", "Proofs with induction", "Probability". I did learn some of them from university courses, but writing code for them(in terms of coding problems) helped cement few of the them for me.
How did you apply induction proofs in competitive programming?
Even using recursion is rarely a good idea as you loose control with your memory layout.
And using a language that supports the concept of proof by induction would surely leave you on the absolutely last place for competitive programming as most of the algorithms used use guarantees that are extremely difficult to reason about even with some of the most recent advances in formal methods.
I do see how combinatorics work with competitive programming, though. and to an extend also probability theory, though I never used any probabilistic algorithms myself.
I think most problem sets would be hard to solve without use of dynamic programming, irrespective of recursion or not. But yes, recursion with memorisation/accumulation would be a good place to start.
It seems like Java and Python are only just starting to get a place in COMPETETIVE programming :) I definitely think we will have to wait before we get stuff like Haskell or Idris in there.
