Date: 2026-06-06
Time: 17:55
This file implements LeetCode 2481: Minimum Cuts to Divide a Circle. It contains both the solution function and its unit tests in a single module. Its responsibility is to compute the minimum number of straight cuts needed to divide a circle into n equal slices.
min_cuts(n: int) -> intThe core solver. It exploits a geometric insight with three cases:
n == 1: No cuts needed — the circle is already one "slice." Returns 0.n is even: Each cut through the center creates two slices. A diameter produces 2 slices, two perpendicular diameters produce 4, etc. So n // 2 cuts suffice. Returns n // 2.n is odd (and > 1): You can't reuse any cut as a shared diameter for two slices. Each cut produces exactly one new slice boundary, so you need n cuts. Returns n.TestMinCutsA unittest.TestCase covering all three branches: the n == 1 base case, several even values (2, 4, 6, 100), and several odd values (3, 5, 99). The boundary value n = 100 (the constraint maximum) is explicitly tested.
solution.py, with a separate testsolution.py that imports from it (visible in the importedby list).Imports: Only unittest from the standard library — no external dependencies.
Imported by: The testsolution.py in this same directory imports it. The massive importedby list in the prompt is an artifact of the repo's cross-referencing structure — those other test files don't actually import *this* solution; they follow the same structural pattern.
1. Caller passes an integer n (1 ≤ n ≤ 100).
2. The function checks n == 1 → returns 0.
3. Otherwise checks n % 2 == 0 → returns n // 2.
4. Falls through to the odd case → returns n.
No state, no mutation, no side effects.
n must be ≥ 1. The function doesn't validate this — it relies on LeetCode's guarantee that 1 <= n <= 100.n > 1, the result is always exactly half of n. For odd n > 1, the result equals n itself. This means odd inputs always require more cuts than even inputs of similar magnitude.None. Invalid inputs (n ≤ 0, non-integer) would produce silently wrong results rather than exceptions. This is typical for LeetCode solutions where the problem statement guarantees valid input.
minimum-cuts-to-divide-a-circle/test_solution.py — The external test file that imports this solution; may contain additional edge cases or a different test harnessminimum-cuts-to-divide-a-circle/plan.md — The planning document explaining the approach considered before implementationminimum-cuts-to-divide-a-circle/review.md — Post-implementation review notes on correctness and alternativeseven-odd-geometry-insight — Why even-numbered slices allow diameter reuse (each cut passes through the center and creates two boundaries) while odd-numbered slices don'to1-math-solutions — Other LeetCode solutions in this repo that reduce to closed-form math (e.g., count-of-matches-in-tournament, nim-game, divisor-game)min-cuts-three-branches — min_cuts has exactly three code paths: n==1 (returns 0), n even (returns n//2), n odd (returns n), covering all valid inputsmin-cuts-constant-time — The function runs in O(1) time and space with no loops, recursion, or data structuresmin-cuts-no-input-validation — The function does not validate that n >= 1; it trusts the caller to satisfy the LeetCode constrainteven-cuts-half-odd-cuts-full — For any even n > 1 the cut count is strictly less than n, while for any odd n > 1 the cut count equals n