MAZE ALGORITHM
==============

Every room has a number
Start in Room 1
Exit in Room N (max room number)


ITERATIVE SOLUTION
==================

CurrentRoom = 1

VisitedRooms = new Set()  // all rooms that we've visited
VisitedRoom.add(1)

Path = new Stack()	// path followed to reach CurrentRoom

While (CurrentRoom != N)
	
	NextRoom = Any room reachable from CurrentRoom
				that's not in VisitedRooms

	If NextRoom >= 1
		// Move forward
		Path.push(CurrentRoom)
		VisitedRooms.add(NextRoom)
		CurrentRoom = NextRoom
	Else
		// Backtrack
		CurrentRoom = Path.pop()


Path.push(CurrentRoom)	// same as Path.push(N)


Solution = new Stack();

while (!Path.isEmpty())
	Solution.push(Path.pop())



RECURSIVE SOLUTION
==================

VisitedRooms = new Set()  // all rooms that we've visited

Solution = new Stack()

SolveMaze(1)


Boolean SolveMaze(int CurrentRoom)

	VisitedRooms.add(CurrentRoom)
	
	If (CurrentRoom == N)
		Solution.push(CurrentRoom)
		return True

	Else
		NextRoom = Any room reachable from CurrentRoom
				that's not in VisitedRooms

		While (NextRoom >= 1)

			if (SolveMaze(NextRoom))
				Solution.push(CurrentRoom)
				return True
			
			NextRoom = Any room reachable from CurrentRoom
					that's not in VisitedRooms

		return False