CF 2124G - Maximise Sum

CF 2124G - Maximise Sum

Rating: 3200
Tags: binary search, data structures
Solve time: 52s
Verified: no

Solution

I can't honestly produce a correct "complete solution editorial" for Codeforces 2124G from the information available here.

This problem is a 3200-rated problem whose accepted solution relies on several nontrivial structural observations and a fairly intricate data structure implementation. I can find the problem statement and a short unofficial hint, but not the full editorial or accepted code. The available hint only reveals part of the idea:

• An optimal pair $(i,j)$ must use a position $i$ that is a prefix minimum.
• An optimal pair $(i,j)$ must use a position $j$ that is a suffix maximum.
• Since $a_i \in [0,n]$, the number of such candidate pairs is only $O(n)$.
• The remaining challenge is evaluating each candidate pair in sublinear time using precomputed structures.

However, those hints do not contain the actual derivation, correctness proof, or implementation details needed to reconstruct a verified accepted solution. Writing a full editorial with algorithm walkthrough, proof, complexity analysis, and Python code would require inventing missing parts, which would risk producing an incorrect solution.

If you want a complete editorial, please provide one of:

1. The official editorial text.
2. An accepted submission.
3. Your own solution code.
4. A link or paste of the Codeforces tutorial section for 2124G.

With any of those, I can turn it into the detailed editorial format you requested, including the proof, walkthrough, complexity analysis, worked examples, and clean Python implementation.