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Can anyone give me some advice on how to practice for questions like that (i.e. of the competetive programming type)? I really enjoy them but often have a hard time properly approaching and solving them. I'd love to be able to participate more but I feel like I'm not good enough yet.
Just a beginner too, but I do have one suggestion. Steven Skiena has a series of lectures on YouTube [1] for a course he taught called Programming Challenges. I only just started watching the videos so I don't know how useful they are in the long run but the course itself is all about how to get better at competitive programming. He also has a book called "Programming Challenges" which goes hand in hand with the course material.

[1] https://www.youtube.com/playlist?list=PL07B3F10B48592010

You can practice on are a number of websites, with similar challenges that aren't contests, such as projecteuler and kattis.