This looks like a pretty straightforward application of
Dijkstra's algorithm. However, details aren't quite clear.
If I jump five columns to the right, how many columns am I
using? Two or five?
ah maybe should have made that more clear. If you jump five columns to the right you would be using two columns not 5.
Is Dijkstra's algorithm appropriate still?
No, I don't think you can use Dijkstra's algorithm in this
case. Because in Dijkstra's algorithm, if you can go from
one node to another in say, two steps, it doesn't matter
which two steps you take, and furthermore, the best
overall solution will not take three steps between those
nodes. But that's not true in this matrix case.