A cell is good if the board without this cell can be tiled by domino 1\times 212 tiles. What is the number of good cells? (just write a number in the answer field)
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found this problem on codeforces.
You are given a rectangular board of M × N squares. Also you are given an unlimited number of standard domino pieces of 2 × 1 squares. You are allowed to rotate the pieces. You are asked to place as many dominoes as possible on the board so as to meet the following conditions:
Each domino completely covers two squares.
No two dominoes overlap.
Each domino lies entirely inside the board. It is allowed to touch the edges of the board.
Find the maximum number of dominoes which can be placed under these restrictions.
The answer is ⌊MN/2⌋. Why is this always the case? I don't "see" why the dominoes somehow are always positioned correctly.
You are given a rectangular board of M × N squares. Also you are given an unlimited number of standard domino pieces of 2 × 1 squares. You are allowed to rotate the pieces. You are asked to place as many dominoes as possible on the board so as to meet the following conditions:
Each domino completely covers two squares.
No two dominoes overlap.
Each domino lies entirely inside the board. It is allowed to touch the edges of the board.
Find the maximum number of dominoes which can be placed under these restrictions.
The answer is ⌊MN/2⌋. Why is this always the case? I don't "see" why the dominoes somehow are always positioned correctly.
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