Solving a maze with DFS vs "wall following" Consider a problem where a "robot cleaner" is placed on a room modeled as a grid. Each cell in the grid can be empty or blocked and all accessible cells are connected, meaning, all empty cells will be accessible by the robot regardless of its starting position.

We are told that the robot cleaner can only take one of four actions: 


move forward
turn left (90 degrees, without moving)
turn right (90 degrees, without moving)
clean the current cell in the grid


We are asked to design an algorithm for the robot to clean the entire room.



My question is: Can this problem be framed as a maze solving problem? I mention this because a common strategy (if the maze is simply connected) for maze solving is to be a "wall follower" (e.g. always try right, or always try left), and I wonder if wall following would work here. 

More generally, why would "wall following" be a good strategy for either problem? Isn't it enough to do DFS (with backtracking) even if we pick an arbitrary order of directions that are "left to explore" from each grid position? (or explore directions at a given position in any order?)
Try it on some simple examples.  You'll quickly see why wall following is not sufficient.