Is competitive math useful in USACO

General Questions
#1

Hi, I’ve been doing USACO for just over a year now. I’ve noticed that problems from the past ~4-6 years tend to focus more towards problem analysis and creative thinking skills similar to competitive math. While I definitely welcome this, does anyone have any thoughts on how useful competitive math (AMC/AIME track or others) could be in practicing for competitive programming?
Specifically:

  • Could this help at all?
  • Which divisions could this help in?
  • Could it be comparable in efficiency to practicing from cf contests+problemset for those who have no competition math experience

Thank you, any ideas are welcome.

#2

I guess there is a bit of algebraic manipulation in some usaco contests, like in this question:
https://usaco.org/index.php?page=viewproblem2&cpid=1302
IMO for earlier levels AMC10/AIME knowledge is not required; not sure abt gold and plat tho.
Although you can check here:

and the other probably needed math concepts are also provided.
UPD I just noticed you probably do need to know a bit of coordinate geometry ie manhattan distance, eulerian distance, etc.

#3

I agree with that, although many of the algebraic manipulations etc. are either taught in standard curriculum or straightforward IMO. However, I was more focusing on observation-heavy problems such as
https://usaco.org/index.php?page=viewproblem2&cpid=1518
where you have to identify how to fix the parity among other things. IMO you have to spontaneously come up with solutions for problems like that unless you’ve done an extremely similar problem before, as it’s less of a “identify and apply a previously known algo” problem. My main question is whether competitive math can help you generate ideas for problems like these better.

#4

I am not sure about that. However, a recourse I would recommend for you to use to practice this - if you need to - is the codeforces constructive algorithm tag. Link below:

https://codeforces.com/problemset?order=BY_SOLVED_DESC&tags=constructive+algorithms

You can also adjust the rating range if some problems are too easy/hard for you.

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#5

As someone who has been doing competitive for 4 years now (top AIME), I still struggle (really badly) with constructive and creative problems lol:( But it is really helpful for higher usaco divisions and on other cp websites.

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#6

Yea same I also aime qualed and I also really struggle with constructives :frowning: