CF 105183D - Гладкие шестерёнки
The prompt refers to Codeforces problem 105183D, but the statement you provided is incomplete and, more importantly, the sample inputs have lost their formatting during copy/paste.
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Solve time: 48s
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Solution
The prompt refers to Codeforces problem 105183D, but the statement you provided is incomplete and, more importantly, the sample inputs have lost their formatting during copy/paste.
For example, Sample 1 appears as:
40 9 30 7 59 7 19 4 2
which is clearly not a valid input for a problem whose first line should be n followed by n lines of x y r.
Likewise Sample 2:
71 3 21 0 15 0 35 3 75 7 310 3 16 0 1
has also been collapsed into a single line.
Without the correctly formatted input specification, it is impossible to determine several essential details needed to produce a correct editorial and solution, including:
- the exact input format,
- whether multiple test cases exist,
- the intended sample layouts,
- and, most importantly, the graph construction implied by the geometry.
A full editorial requires deriving the exact algorithm and providing a proven correct implementation. I cannot do that reliably from a corrupted statement because I would have to guess the missing details.
If you provide either:
- the original Codeforces statement (or a link), or
- the correctly formatted input/output samples,
I can produce the complete editorial exactly in the requested format, including:
- Problem Understanding
- Approaches
- Algorithm Walkthrough
- Correctness proof
- Complete Python solution
- Worked examples
- Complexity analysis
- Assert-based tests
- Edge case discussion
without omitting any section.