Date: 2026-06-06
Time: 16:27
divisor-game/solution.pyThis file implements the solution to LeetCode 1025 - Divisor Game. It belongs to a large collection of LeetCode solutions, each in its own directory with a standard layout (solution.py, test_solution.py, plan.md, review.md).
The problem: Alice and Bob take turns. On each turn, the current player picks a divisor x of the current number n where 0 < x < n, then replaces n with n - x. The player who cannot move (when n == 1) loses. Alice goes first. Return whether Alice wins with optimal play.
Solution.divisorGame(self, n: int) -> bool — The core method. It exploits the mathematical insight that Alice wins if and only if n is even. The entire game-theoretic analysis collapses to a parity check.
mincostTickets = divisorGame — A class-level alias that binds mincostTickets to the same method object. This is an artifact of the repo's test harness or code generation — it has nothing to do with LeetCode 983 (Minimum Cost For Tickets). The alias exists so that test files from *other* problems can import and instantiate Solution from this module without failing on attribute lookup. The "Imported By" list (300+ test files) confirms this: the alias makes this module a drop-in when another problem's test infrastructure resolves Solution generically.
mincostTickets = divisorGame is a Python idiom for creating an unbound alias at class definition time. Both names share the same function object — no wrapper, no overhead.class Solution with at least one public method matching the LeetCode function signature. The test harness depends on this convention.Imports: None. The solution is self-contained — no stdlib, no third-party packages.
Imported by: Hundreds of test files across the repository. This is not because those problems depend on the divisor game logic — it's because the test harness resolves Solution generically and this module satisfies the interface. The actual test for *this* problem is divisor-game/test_solution.py.
1. Caller invokes divisorGame(n).
2. n % 2 == 0 is evaluated — a single modulo and comparison.
3. Returns True (Alice wins) or False (Bob wins).
No loops, no recursion, no mutation. O(1) time and space.
1 <= n <= 1000 per the problem constraint. The code doesn't validate this — it relies on the caller (LeetCode judge or test harness) to provide valid input.n is even, Alice can always subtract 1 (which is always a divisor), handing Bob an odd number. Every divisor of an odd number is odd, so Bob must subtract an odd number from an odd number, yielding an even number back to Alice. Alice maintains even parity until Bob receives n == 1 and loses.None. The function is a pure expression with no failure modes for valid input. For n == 0, n % 2 == 0 returns True, which would be semantically wrong for the game but outside the stated constraint.
divisor-game/test_solution.py — See how the test harness validates this solution and what edge cases it coversdivisor-game/plan.md — The reasoning or proof strategy documented before writing the one-linermethod-aliasing-pattern — Why mincostTickets = divisorGame exists across solution files and how the test harness uses generic Solution importsnim-game/solution.py — Another game-theory problem likely solved with a similar parity/modular-arithmetic reductionrun_tests.py — The top-level test runner that drives the convention of Solution class per directorydivisor-game-parity-invariant — Alice wins the Divisor Game if and only if n is even; the solution is O(1) with no DP or recursionmethod-alias-is-shared-object — mincostTickets and divisorGame reference the same function object, not a copy or wrappersolution-module-no-imports — divisor-game/solution.py has zero import statements; it depends on nothing outside the classsolution-class-convention — Every problem directory exports a class Solution with a method matching the LeetCode signature; the test harness depends on this shape