Re:Recursion (Score 4, Informative)

Also, all problems are designed with a specific algorithm in mind, leading to a required time complexity.

The secret program inputs are then be designed to be large enough to be solved much much faster than the time limit with the correct complexity, but much much slower than the time limit with the wrong complexity.

You can typically look at the problem specification to see what the maximum input size is - and you should expect that you _will_ get inputs of that size, and do a rough estimate of how many operations that will require with your solution.

I've been in a competition where I used a O(n^2) algorithm where I didn't see the O(n*log n) solution (No it wasn't sorting, it was a Dynamic Programming-problem). I was convinced for a fairly long time that my algorithm was fast enough, so I spent time suboptimizing instead of solving the root problem - the wrong algorithm.
With the right algorithm, it passed right away.

That said, some problems are indeed expected to be solved by brute force, or by a combination of brute force and tricks to shrink the search space. These problems can mostly be identified by guarantees of small inputs in the description.