## A. Average Height

### Solutions:

Put all odd number together. And then put all even number together.

## B. TMT Document

### Solution:

Greedy. Firstly, let's count the number of M as count_m. And we mark first count_m T as leading T (the first T in TMT). And mark remained T as ending T (the last T in TMT).

Scan the string once.

• If we meet a leading T, then count_first++.
• If we meet a M, then count_first--;count_m--;count_last++.
• If we meet a ending T, then count_last--.

In this process, all these three counts can't less than 0. And after this process, all these three should be 0.

## C. The Sports Festival

It is a normal DP problem. We maintain the segment state. After sorting, just look at the smallest sum for a segment.

## D. Binary Literature

Simple structure problem. Find the proof for the existence of the answer first. And based on the proof, the solution can be given almost immediately.

I forgot to find the longest common sub-sequence during the contest. After the contest, I thought about it again. And I found that: it's easier to build based on the number of 0 and 1 by brute force.

## E. Almost Sorted

A little complex. Can split to two parts for this problem.

One part is the preprocessing of all the possibilities in the permutation of length $n$.

The second part is to construct the result based on the number of all the permutations.

The logic is a bit complicated, and you can think of a solution if you think about it.