This is a note for 4.4 Shortest Paths, Algorithms, Part II.

Dijkstra’s algorithm is essentially the same with Prim’s algorithm. Both are in a family of algorithms that compute a graph’s spanning tree (BTW, DFS and BFS are also in this family). The main distinction is the rule used to choose next vertex for the tree:

• Dijkstra’s: Closest vertex to the source (via a directed path).
• Prim’s: Closest vertex to the tree (via an undirected edge).