What is pretest?

Is pretest just comes with thought: "We just want full-test contest, but we are running out of server. So, we will judge a subset of testdata, which we think quite strong with various edge cases." ?

Why pretests are not shown to us (including who locked their code)? Pretests are kind of hidden informations which can influence contest directly using hacking.

Actually what is hacking for problem coordinators?

While I was solving problem, I have encountered this problem: https://www.acmicpc.net/problem/17111

(Description is written in English, so you can see it.)

How can I solve this problem? I do not have any idea of solving it, and thought that Codeforces community is helpful.