Graph Algorithms for Interviews

Graph Algorithms for Coding Interviews

Graph problems are considered the hardest category in coding interviews, appearing in approximately 15-20% of questions at FAANG companies. The key insight is that most graph problems reduce to BFS, DFS, or a well-known algorithm (Dijkstra, topological sort, union-find).

If you can implement BFS, DFS, and topological sort from memory, you can solve 80% of graph interview problems. Add Dijkstra and union-find for the remaining 20%.

Core Graph Algorithms

Algorithm	Use Case	Time Complexity
BFS	Shortest path (unweighted), level-order	O(V + E)
DFS	Cycle detection, connected components, path finding	O(V + E)
Topological Sort	Dependency ordering, course schedule	O(V + E)
Dijkstra	Shortest path (weighted, non-negative)	O((V+E) log V)
Union-Find	Connected components, cycle detection (undirected)	O(α(n)) ≈ O(1)
Bellman-Ford	Shortest path (negative weights)	O(V × E)

Graph Representation

Choose adjacency list (space-efficient for sparse graphs) vs adjacency matrix (O(1) edge lookup for dense graphs). Most interview problems use adjacency list representation.

Graph algorithms build on tree traversals and recursion patterns. Practice with AissenceAI's coding copilot.