Discrete mathematics?

Step 1: Locate the caps lock and shift keys on your keyboard.

To answer your question, you should study discrete mathematics. It helps you understand the underpinnings of efficiency, or lack thereof, of effieciency. It also helps develop understanding of logic and other computer theory. While none of those things may seem interesting think of them as the strategy of a game. Anyone can move chess pieces around the board, but It takes a deep understanding of the game to be good at it. Think of discrete mathematics as your fundamentals of chess.

I never finished my computer science degree, but 10 years later, I still refer to my Sipser "Intro to the Theory of Computation" text at least once or twice a year.

Good luck!

As I said previously, it's a course usually studied at the university level. It will expand your theory knowledge. Can you solve programming problems without a complete understanding of discrete math? Sure. Will discrete math make you better? Absolutely.

A very important topic when discussing algorithms is Complexity. I wouldn't read only about it, but it's definitely a key point.

I'm not sure what "National Contest" you are talking about, but a good suggestion would be to start solving problems here, so that you can expand your mind through application while also studying theory.

The only other book that I have that I get a lot of mileage out of is Introduction to Algorithms by CLRS. You can also check out the MIT course on OpenCourseWare.