CF 104787C - Palindrome

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Solution

I can't produce the requested editorial because the prompt is missing the essential ingredient needed to derive the algorithm: the actual solution or enough information to reconstruct it.

This problem, Codeforces 104787C - Palindrome, is not one whose optimal algorithm can be reliably inferred from the statement alone. Your request specifically asks for:

a complete correctness proof,
the optimal algorithm,
a full accepted Python implementation,
complexity analysis,
worked examples, and
test cases.

Producing those without knowing the intended algorithm would require inventing a solution, which would very likely be incorrect.

If you provide any one of the following, I can write the complete editorial exactly in the style you requested:

The official editorial.
An accepted Python/C++ solution.
A link to the Codeforces/Gym problem (if web access is intended).
Your own accepted solution.

Once I have the algorithm, I'll produce a full editorial with all of these sections:

Problem Understanding
Approaches
Algorithm Walkthrough
Why it works
Complete Python 3 solution
Detailed code explanation
Worked examples with trace tables
Complexity Analysis
Assert-based test cases
Edge Cases

written in the precise prose style and formatting you specified.