Floor Tile Algorithm

You have to find all the possible ways to do so.

Floor tile algorithm. Hey algorithms first reddit post. Algorithms for tile size selection problem description. 2 is the correct shading. N 2 a 2 x 2 square with one cell missing is nothing but a tile and can be filled with a single tile.

While it s true that this 8 bit bitmasking procedure results in 256 possible binary values not every combination requires an entirely unique tile. The problem is to count the number of ways to tile the given floor using 1 x m tiles. A tile can either be placed horizontally i e as a 1 x 2 tile or vertically i e as 2 x 1 tile. Given a 2 x n board and tiles of size 2 x 1 count the number of ways to tile the given board using the 2 x 1 tiles.

It involves my favourite gbc games of all time namely the legend of zelda. The 4 bit example from earlier resulted in 2 4 16 tiles so this 8 bit example should surely result in 2 8 256 tiles yet there are clearly fewer than that there. Input n 3 output. 3 is the shading generated by the above algorithm.

N 2 m 3 output. Example 2 here is one possible way of filling a 3 x 8 board. Example 1 following are all the 3 possible ways to fill up a 3 x 2 board. An important parameter for tiling is the size of the tiles.

1 only one combination to place two tiles of. A tile can either be placed horizontally or vertically. We need 3 tiles to tile the board of size 2 x 3. Tiling is one of the most important locality enhancement techniques for loop nests since it permits the exploitation of data reuse in multiple loops in a loop nest.

The correct shading will be generated only for the border tiles and there will be some inaccuracies in the remaining shading. To tile a floor with alternating black and white tiles develop an algorithm that yields the color 0 for black and 1 for white given the row and column number. 1 shows the system without shading. Both n and m are positive integers and 2 m.

I link a video showing the floor tile puzzle from those games here. Below is the recursive algorithm. I have a rather odd game project i m working on. 4 and 5 are the lines of sight to the border that cause the incorrect shading to be generated.