Dijkstra

Shortest paths when edges have different costs: the breadth-first walk, plus a heap that always extends the cheapest path so far.

Breadth-first search finds the fewest edges only when every edge costs the same. When edges have weights, a path of many cheap edges can beat a path of one expensive edge. Counting edges would give the wrong answer. Dijkstra's algorithm is the repair, and this course names it without asking you to build it.

It is the same walk, with a heap instead of a plain queue. The heap always hands you the vertex you can reach for the smallest total cost so far. From there you relax the outgoing edges: if arriving via this vertex is cheaper than the best cost you had stored for a neighbour, you update that neighbour and push it. The first time you settle the target, the cost you have is the cheapest.

The reason to know the name is so that "shortest path" does not automatically mean a queue. Equal weights: breadth-first search. Unequal weights: a heap plus this relaxation. The heap lesson is the piece you would reuse.