best data structure and algorithm for 2d grid movement

Question

I have a shaped grid with holes like shown in the following image:

I want to know what is the most memory efficient data structure to represent the grid in the image and what algorithm can I use with such a data structure so that my player won't exit the grid(the blue colored cells). I want the player to move along the grid. I realized that I only have to check for the neighboring cell next to the player when moving on the x or y axis, but I am not sure if a multidimensional array is the most memory efficient data structure in this case if I were to use a bigger grid.