The Greedy Strategy

Edsger W. Dijkstra proposed a simple, "greedy" idea: "Always visit the closest possible node that you have not finished yet." Instead of a simple Queue (First-In-First-Out), you need a generic container that always gives us the smallest item inside it.

If you have two options: Go to $B$ (Cost $10$) Go to $C$ (Cost $1$) you should process $C$ first, because it is closer. Maybe $C$ gives us a shortcut to $B$.