Given a 3 x n board, find the number of ways to fill it with 2 x 1 dominoes.
Following are all the 3 possible ways to fill up a 3 x 2 board.
Here is one possible way of filling a 3 x 8 board. You have to find all the possible ways to do so.
Input : 2 Output : 3 Input : 8 Output : 153 Input : 12 Output : 2131
At any point while filling the board, there are three possible states that the last column can be in:
An = No. of ways to completely fill a 3 x n board. (We need to find this) Bn = No. of ways to fill a 3 x n board with top corner in last column not filled. Cn = No. of ways to fill a 3 x n board with bottom corner in last column not filled.
Note: The following states are impossible to reach:
Note: Even though Bn and Cn are different states, they will be equal for same ‘n’. i.e Bn = Cn
Hence, we only need to calculate one of them.
Final Recursive Relations are:
- Tiling Problem
- N consecutive ropes problem
- Maximum Bitwise OR pair from a range
- Check whether all the substrings have number of vowels atleast as that of consonants
- Best Way To Start With Competitive Programming - GeeksforGeeks CP Live Course
- Find closest integer with the same weight
- Minimum number of coins that can generate all the values in the given range
- Check whether the given decoded string is divisible by 6
- Maximum count of elements divisible on the left for any element
- Count of odd and even sum pairs in an array
- Maximum sum subarray of even length
- Find the parent of a node in the given binary tree
- Number of subsets with sum divisible by M | Set 2
- Number of ways to divide string in sub-strings such to make them in lexicographically increasing sequence
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.