[Karliss]

> Isn't Dijkstra the same as BFS?

That's because demonstrating Dijkstra on a grid is as useful as demonstrating air resistance in vacuum. In a grid with only horizontal and vertical Dijkstra will produce same order as BFS (but more slowly). You could see some difference if you treated diagonal moves as having sqrt(2) length, but such distance metric is rarely useful. Either you simplify things by having grid and not allowing diagonal movement or treating them like like them length 1, or you allow free 2D movement at arbitrary angles with proper euclidean geometry and distances. Treating diagonal distances as sqrt(2) is worst of both approaches. You loose most of the simplification provided by grid and can't evaluate it in head or on a paper, but it still doesn't produce geometrically accurate results.

One case where Dijkstra on a grid would make sense if you treated entering and exiting certain cells as slower=longer distance. Might be useful if you modeled a game where certain cells contain difficult to traverse terrain like mountains or swamp.