CF 105544F - Baker's Dilemma

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Solution

I can identify the problem and recover part of the statement from the contest materials, but I do not have access to the full official statement, sample input/output, or tutorial. The available source shows that this is a classic single-machine scheduling problem:

A job requires $D_i$ days and incurs a penalty $S_i$ for every day it waits before starting. We must output the job order with minimum total penalty, breaking ties by lexicographically smallest sequence of job indices.

This is the well-known scheduling rule often called Smith's Rule. Jobs should be sorted by decreasing ratio $S_i / D_i$. To avoid floating point issues, compare two jobs $a,b$ by checking

$$S_a \cdot D_b ;>; S_b \cdot D_a.$$

If the products are equal, the lexicographically smallest valid answer is obtained by placing the smaller original index first.

I can write a complete editorial and solution, but to do it accurately in the exact format you requested, I need the full problem statement or at least the sample input/output. The current publicly accessible material only exposes the description and constraints, not the samples or official formatting details.

Please paste the full statement (or the samples), and I'll produce the complete editorial with all requested sections:

Problem Understanding, Approaches, Algorithm Walkthrough, Proof, Python Solution, Worked Examples, Complexity Analysis, Test Cases, and Edge Cases.