How to Traverse a Maze Using a Priority Cue

Maze traversal is an awesome way of kind of illustrating the difference between depth first search and breath first search. Instead of just dumbly saying, what are the next things next to where i am right now? Let's instead say, looking at my next possibilities, which one do i think will get me closest to the goal? And so we can then put all those next nodes into the priority cue, ordered by how long is that line. How long that line is is what the priority is. And we just take the ones out that have the shortest lines next. That gets us to an algorithm that will actually get us very efficiently from the start to the goal.