Selecting the right traversal algorithm depends on your goal and the graph's structure.
- Need the shortest unweighted path? Choose BFS. Its level-by-level exploration guarantees finding the path with the fewest edges first.
- Need to know if a cycle exists (in an undirected graph), or compute a topological order (in a DAG)? Choose DFS. Its deep, backtracking nature is ideal for uncovering structural properties.
- If the graph is very wide (many nodes at the same level), BFS memory usage for the queue may become large.
- If the graph is very deep (long paths), the recursion stack for DFS might become a problem.
- The key takeaway is to match the algorithm to the problem: BFS for distance-related goals, and DFS for structure-related goals.
| Goal | Pick | Reason |
|---|---|---|
| Fewest edges path | BFS |
Levels are distances |
| Cycle (undirected) | DFS |
Back-edge to non-parent rule |
| Order constraints (DAG) | DFS |
Finish times → topological sort |