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
- Find the minimum number of preprocess moves required to make two strings equal
- Find the number of distinct pairs of vertices which have a distance of exactly k in a tree
- Count paths with distance equal to Manhattan distance
- Number of trailing zeroes in base 16 representation of N!
- Make a tree with n vertices , d diameter and at most vertex degree k
- Minimum edges to be added in a directed graph so that any node can be reachable from a given node
- Minimum operations to make counts of remainders same in an array
- Merge K sorted arrays of different sizes | ( Divide and Conquer Approach )
- Minimum number of elements that should be removed to make the array good
- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Ways to form an array having integers in given range such that total sum is divisible by 2
- Minimum number of given moves required to make N divisible by 25
- Print Stack Elements from Bottom to Top
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.