I'm about to enter my second semester as a mathematics undergrad. However one of my favorite areas is combinatorics, and this summer I started to learn how to program and I have been solving project Euler problems and I have found them to be fun.
I used to compete in math olympiads in high school and I plan to continue participating in math olympiads in university. All of my experience in programming has come from solving project euler problems in java (I'm near the 50 problem mark).
My question is where I can train for actual contests like the IOI and specifically the AMC-ICPC and college programming contests. Online practice would be ideal, but books are also accepted, I know of Cormen's introduction to algorithms,How to solve it by computer and Donald Knuth's concrete mathematics.
I would also like to know if there are online competititions which I can participate in from the commodity of my house.
Thank you very much in advance. Regards.
Added: Also, projecteuler only requires that you type the answer, but I think in the ioi and AMC-ICPC you need to send them the program and they'll do some test trials. With it, I don't know how to code my program so the testing-machine accepts it.
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