Lesson 20.4 · Graph Fundamentals
Which Graph Algorithm?
The question decides the algorithm: reachability, fewest steps, ordering, grouping, cheapest path or cheapest network.
8 min
Think of it like this
A toolbox where each tool has a label: you don't need to remember how every tool works to pick the right one, only what job it does.
1.A quick map
Can I reach it / how many groups? DFS or BFS (Modules 21–22), or union-find (Module 25) when edges arrive over time.
Fewest steps, unweighted? BFS (Module 21). Cheapest path, non-negative weights? Dijkstra (Module 26). Negative weights? Bellman-Ford.
Is there a cycle? In what order can tasks run? Cycle detection and topological sort (Modules 23–24).
Connect everything at minimum total cost? Minimum spanning tree (Module 27).
Remember
- Name the question first, then pick the tool.
Common mistakes
- Using Dijkstra on an unweighted graph where BFS is simpler and faster.
- Using BFS on weighted graphs.