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By sudipta550, history, 4 weeks ago, In English

I need help in the tiling problem.This the problem I cannot understand how to count the total no of dominos in the case of blue colors. Should I write two dp tables one is the row-major matrix(for red) and the other is the column-major matrix(for blue)? I cannot understand how to write. Please help...

 
 
 
 
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4 weeks ago, # |
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Auto comment: topic has been updated by sudipta550 (previous revision, new revision, compare).

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4 weeks ago, # |
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112847614 You can look at this submission, it is quite neat.

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    4 weeks ago, # ^ |
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    Thanks for your response. ****This is going above my head. Can you please give me some intuition behind this solution?

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      4 weeks ago, # ^ |
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      dp[i] is the contribution to the answer if we have i consecutive white cells in a row/column.

      Let's take the case of row. If last cell if blue then it's equivalent to dp[i-1]. If last cell is red but 2nd last cell is blue it is equivalent to dp[i-2]. And the remaining case, if both last 2 cells are red, it is equivalent to dp[i-2] and a tile on last 2 positions. That tile will contribute for all the 1<<(i-2) states of the previous cells.

      Hence, dp[i]=dp[i-1]+2*dp[i-2]+a[i-2] where a[x]=2^x.

      That was the main intuition behind the solution.