To solve the maze for lab 9, you need to make sure you don't get stuck
in a loop by trying the same path repeatedly. You need to be able to
*backtrack* to a previous "choice point" so that you can explore a
different path if the path you've followed led to a dead end.  You can
do this with a stack, recording on the stack the positions you've
visited and whether or not they are choice points.  However, an easier
way to accomplish this is to store values in the matrix itself.  When
the matrix was first "dug out", it only had values 0 (wall) or 1
(path).  However, we can store different values to indicate *how many
times we've been in a certain position*.  That is, we can increment
M[y][x] each time we visit position y,x.  The algorithm is then just
to pick the direction whose matrix value is the *smallest non-zero
number*.  Ties can be broken arbitrarily.  This scheme is valid
because, when you return to a branch point, the branch that you have
not yet explored (or have explored fewer times) will have a smaller
value.

The basic algorithm used here is called "depth-first search".  That is,
we continue in one direction until we get stuck, then back up to the
previous choice point and go in another direction.