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@magurofly(Fish Maguro)

ARC176 A - 01 Matrix Again

Last updated at Posted at 2024-04-22
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  • $N$ 行 $N$ 列の白いマス目がある
  • うち $M$ マスは黒く塗られている
    image.png
  • 追加で何マスか黒く塗って、
    どの行も列も黒マス $M$ 個にする

image.png

解き方（一例）

  • ナナメの直線を足すと、どの行も列も $1$ マス増える
    image.png
  • すでにある黒マスから直線を引いてみる
    image.png
  • まだ足りない場合は、適当に
    白マスを選んで直線を引く
    image.png

計算量

  • 線を $1$ 本引くのに $O(N)$ かかる
  • 線は $M$ 本ある
  • → $O(MN)$ で解くことができた
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