Nim — Who Wins?

Difficulty: Easy · Topic: Game theory

In Nim, players alternate removing any positive number of stones from a single pile; the player who takes the last stone wins. Given the pile sizes, return True if the first player wins with perfect play. The theorem: the first player wins iff the XOR of all pile sizes is non-zero.

Examples

nim_winner([1,2,3])
→ false

1^2^3 = 0 → first player loses.

nim_winner([1,2,4])
→ true

1^2^4 = 7 ≠ 0 → first player wins.

Target complexity: time O(n), space O(1)

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