since the cost is the sum we can think of portals as a different edge to the "portal dimension". I didn't realize this until just now, so I had the following idea: there are two options. A — just walk the entire way or B — walk from the start to a portal, and then from a portal to the end. calculating A is possible with a graph search (but block visited nodes) calculating B is possible with 2 more searches. (it is actually 2 parts — from start to portal + from portal to end.

then the minimum cost of the 2 options is the true cost. note: time needed = cost

I am bad at explaining so my best attempt is to claim that you can prove this answer correct,