Hello! I'm beginner and would like a hint. I must learn all the pre-existing algorithms in order to solve the problems of programming competitions?
a hug. ;)
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I don't understand what do you mean when you say "pre-existing algorithms". If you mean some kinds of pre-existing algorithms like Floyd or Dijkstra then of course yes, because most of the problems solves with some algorithm or data structure and some idea.
To become red on topcoder you only need BFS, DFS, Dijkstra, Floyd and DP (the last one is not an algorithm but an important class of problems). Familiarity with some math will be handy (combinatorics, probabilities, sieve of Eratosthenes).
Are you cheating?
No.