You can think of a maze as a network of passages and intersections. Passages are what you move…

You can think of a maze as a network of passages and intersections. Passages are what you move along as you explore a maze. Intersections are where explorers must make choices of which direction to go next, that is, they are places where passages meet.

Design a recursive algorithm for exploring mazes. You may write your algorithm in an abstract enough pseudocode that you needn't explain how to represent a maze, you may simply assume that whatever executes the algorithm can follow passages, recognize intersections, etc. Your algorithm will need to handle two particular problems in mazes though:

● Passages can have dead ends, and there can be some intersections from which all passages lead to dead ends. Thus, invocations of your algorithm may need to tell their invoker whether they eventually (possibly after several recursions) found a way out of the maze, or whether everything they could explore eventually came to a dead end. Designing the algorithm to return a value that provides this information might be a good idea. You may assume that whatever executes your algorithm can detect dead ends and exits from the maze.

● Passages can loop back to places the explorer has already visited. If your algorithm needs to recognize such “cycles,” you may assume that it can mark passages or intersections (for instance, by writing on the wall of the maze, dropping a crumb on the ground, etc.), and can tell whether a passage or intersection is marked.

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