Total Tetris : Tetris with Monominoes , Dominoes , Trominoes , Pentominoes , . .

نویسندگان

  • Erik D. Demaine
  • Martin L. Demaine
  • Sarah Eisenstat
  • Adam Hesterberg
  • Andrea Lincoln
  • Jayson Lynch
  • Y. William Yu
چکیده

We consider variations on the classic video game Tetris where pieces are k-ominoes instead of the usual tetrominoes (k = 4), as popularized by the video games ntris and Pentris. We prove that it is NP-complete to survive or clear a given initial board with a given sequence of pieces for each k ≥ 5, complementing the previous NP-completeness result for k = 4. More surprisingly, we show that board clearing is NP-complete for k = 3; and if pieces may not be rotated, then clearing is NP-complete for k = 2 and survival is NP-complete for k = 3. All of these problems can be solved in polynomial time for k = 1.

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تاریخ انتشار 2017