Editorial for CTU Open Contest 2018 - Split Game

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  • Each impartial game is equivalent to NIM.
  • Sum of games has nimber equivalent to XOR of nimbers of individual games.
  • Note that adding two same piles does not change the outcome.
  • We precompute nimbers up to piles of size 2000 (DP).
  • XOR nimbers of games on the input.
  • If XOR is zero second player wins, otherwise first player wins.

Complexity \mathcal O(N^2 \log N)

If you try hard, you can achieve \mathcal O(N^2)

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