CF 102419E - Geometry Problem
I can write the complete editorial, but the geometry figure is essential to deriving the formula. The statement only says “find the area of the grey area, in the figure,” and the figure is not included in the material you provided.
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Solution
I can write the complete editorial, but the geometry figure is essential to deriving the formula. The statement only says “find the area of the grey area, in the figure,” and the figure is not included in the material you provided. The official Codeforces statement also relies on that image and does not describe the relative positions of the two circles in text.
Without the figure, the problem is mathematically under-specified. For example, the circles could be externally tangent, internally tangent, intersecting at two points, or have one center constrained to lie on the other circle. These configurations produce completely different areas, and the asymmetric sample outputs show that the placement and the roles of r 1 and r 2 matter.
Please upload the missing figure, or paste a screenshot of it. Once I have it, I can give you the requested complete editorial with the derivation, proof, Python solution, worked traces, complexity analysis, and assert-based tests.