I am not so good at the algorithm, just try to master fundamental methods and solve some kinds of problems in Codeforces. I can solve some D and E in Div. 2.

However, now I want to take part in the real industrial IT. How do I prepare for the interview and the work after that?

It allows an average time of one hour to solve a national-level olympiad problem. For ICPC, we are expected to solve each problem in 30 minutes. Codeforces wants 15-20 minute time is reasonable for each of their problems.

Why do we need to solve problems very fast?

1) Because the world is moving very fast, so are we?

2) Because there are so many good men, so we must use timing as a way to classify the level of contestants?

3) Or other technical reasons (like decreasing the cheating in the contest)?

My last words are "Is it possible for us to make the contest slower?".

Representation theory is a powerful method in mathematics. It allows us to represent a structure, such as a type of search space in programming problems, to a well-understood structure like vector space or module.

However, I have been fail to find a systematic way to apply ideas from representation theory to programming problems. Can anyone give me a guide or a way to approach this direction?

My problem is: Given a sequence of integers (a_n): a_1, a_2, ..., a_n. We do Q queries, each of them (l, r) requires reverse elements from a_l to a_r.

For example, Given a sequence: 2, 3, 4, 5. The query (1, 3) changes the sequence into 4, 3, 2, 5.

After performing Q queries, the problem asks us to print out the modified sequence.

How to solve this problem, if n and Q are large integers (such as 10^5)?

I hear that the solution uses an approach of Splay Tree.

Please help me and thank you.