Number of ways of tiling a 3*N board with 2*1 dominoes problem
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05-11-2019 - |
Question
I came across this problem, Tiling with Dominoes and initially I faced difficulty in understanding the logic behind recurrence relation, but after reading it from here , I understood it. But I had a doubt, why aren't we considering the below cases for the above problem?
In the solution only these cases are mentioned,
******** AA******* AA****** A*******
******** = BB******* + B******* + A*******
******** CC******* B******* BB******
f(n) = f(n-2) + g(n-1) + g(n-1)
But my question is there can be other case as well, like below, why aren't we adding them, because the problem asks for the number of possible cases-
******** AA******* AA****** A******* AB****** CC******
******** = BB******* + B******* + A******* + AB****** + AB******
******** CC******* B******* BB****** CC****** AB******
f(n) = f(n-2) + g(n-1) + g(n-1) + f(n-2) + f(n-2)
Why aren't we adding them? Thanks for your help.
No correct solution
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