graph

Graph traversal underpins a huge class of interview problems. The signal is knowing the BFS-vs-DFS tradeoff (shortest path vs memory shape) and applying it cleanly, then handling the directed-vs-undirected cycle gotcha most candidates miss.

Topological sort orders a DAG so dependencies come first, the backbone of build systems, schedulers, and ML/data pipeline DAGs. The signal is Kahn's algorithm (or DFS) plus cycle detection. Here is the answer.

Union-Find answers 'are these in the same group?' near-instantly and powers connected-components, cycle detection, and clustering. The signal is path compression plus union by rank for near-O(1) operations. Here is the answer.

Course Schedule reduces to one question: is the prerequisite graph a DAG? The signal is spotting the graph framing and using topological sort or DFS to detect a cycle. Here is the answer.

Dijkstra finds single-source shortest paths in O((V+E) log V) with a min-heap, the backbone of routing and network latency problems. The signal is why it needs non-negative weights and how lazy deletion keeps the heap simple. Here is the answer.

Bellman-Ford handles negative edge weights that break Dijkstra and detects negative cycles, the basis of currency-arbitrage problems. The signal is the V-1 relaxation rounds and the extra Vth round that flags a negative cycle. Here is the answer.

Floyd-Warshall computes shortest paths between every pair of nodes in O(V cubed) with a tight three-line triple loop. The signal is the intermediate-node DP order and why k must be the outer loop. Here is the answer.

GNNs power recommendations, fraud, and molecule modeling by learning over graph structure. The signal is the message-passing mechanism, why k-hop matters, and why you keep them shallow. Here is the answer.

Hierarchies (org charts, bill-of-materials, category trees) need recursion, and a self-join only goes one level deep. The signal is the recursive CTE with its anchor plus recursive members, and knowing how it terminates.

An org-chart recursion walks a tree, but a general graph has multiple paths and back-edges. The signal is accumulating the visited path to prune cycles and ranking paths by cost to get the shortest one.

PYMK is graph recommendation at billion-node scale. The interviewer is screening for one instinct: do you generate candidates from the social graph, or naively try to score all pairs? Here is the design that survives the follow-ups.

Truth is not a label you can train on cheaply, and adversaries adapt the moment you ship. A strong answer fuses content, graph, and behavioral signals, puts humans in the loop where precision matters, and treats adversarial drift as a permanent operating condition, not a one-time training problem.