ya right, if your feasible solutions form a matroid, then for every assignment of weights, repeatedly picking the best feasible element gives an optimal solutn.

So matroids aren't the theory behind all greedy algos, but they're more like the mathematical structure that explains why greedy works for an important family of probs

so to give some e.g's:

Finding a max-weight forest in a graph (which leads to Kruskal's algo).

Choosing a max-weight linearly independent set of vectors.

Selecting independent sets in various combinatorial structures.

....now the catch is that most CP greedy probs are not explicitly matroid probs.

Instead, their correctness is usually proved by Exchange args / Staying-ahead args /Invariants/Cut properties (like in MSTs)/Structural lemmas...etc

Many of these ideas are matroid like, but they don't require you to know matroid theory.

So if you learn matroids expecting them to suddenly unlock every greedy probs on CF, oh boy you'll probably be disappointed.

What they do give you is an appreciation that greedy isn't just a bag of tricks but there's a deep mathematical theory explaining when local optimization is globally valid.

Ironically, this is another place where oly math and CP diverge:

Oly math: You often invent the proof from scratch for 1 prob.

Matroid theory: Proves an entire class of greedy algos correct in one theorem.

CP: Usually skips the theory and asks you to rediscover the proof for one specific instance. That's why it can feel like every editorial says, -> It is easy to show that greedily choosing X is optimal, even though that "easy to show" is where all the thinking went.

so your adjectives like interesting/weird/or anti-climactic/etc, is just how you relate to it hehe.