This is a problem I solved in C++.
The problem assumes that the Prince (indicated by 1) is at the top floor and that the Princess (indicated by 2) is at the ground floor. The dots '.' represent the open ways, and the 'o' points represent the walls.
I solved this problem by recursion.
To compile the program just run the command make in the shell.
Feel free to modify the map (in the main.cpp) and check the output.