The key takeaway is to choose your algorithm based on your goal (distance vs. structure).
- BFS (Breadth-First Search) uses a queue to explore layer-by-layer. This makes it ideal for finding the shortest path in unweighted graphs.
- DFS (Depth-First Search) uses a stack (or recursion) to explore as deep as possible along a single path before backtracking. This is better for finding structural properties like cycles or a topological sort.
- Memory Tradeoff: BFS's memory usage depends on the graph's width (the size of the largest layer), while DFS's depends on its depth (the length of the longest path).
| Aspect | BFS | DFS |
|---|---|---|
| Data structure | Queue (FIFO) | Stack/Recursion (LIFO) |
| Order | By level (distance) | Depth-first |
| Best for | Unweighted shortest paths | Structure (cycles, topo) |
| Memory | Frontier width | Path depth |
| Time | O(V+E) | O(V+E) |