graph

Graph traversal sits beneath a large family of interview problems. What matters is knowing the BFS-vs-DFS tradeoff (shortest path vs memory shape) and applying it cleanly, then getting the directed-vs-undirected cycle gotcha that trips up most candidates.

Topological sort arranges a DAG so dependencies come first, the backbone of build systems, schedulers, and ML/data pipeline DAGs. Interviewers look for Kahn's algorithm (or DFS) plus cycle detection. The answer follows.

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

Course Schedule collapses to a single question: is the prerequisite graph a DAG? The signal is seeing the graph framing and applying topological sort or DFS to detect a cycle. Here is the answer.

Dijkstra computes 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 requires non-negative weights and how lazy deletion keeps the heap simple. Here is the answer.

Bellman-Ford copes with negative edge weights that break Dijkstra and detects negative cycles, the foundation of currency-arbitrage problems. The signal is the V-1 relaxation rounds plus 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 compact three-line triple loop. The signal is the intermediate-node DP order and why k has to be the outer loop. Here is the answer.

GNNs power recommendations, fraud, and molecule modeling by learning over graph structure. What matters 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) call for recursion, and a self-join reaches only one level down. The signal is the recursive CTE with its anchor plus recursive members, and understanding how it terminates.

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

PYMK is graph recommendation at billion-node scale. The interviewer is testing for one instinct: do you generate candidates from the social graph, or naively try to score every pair? Here is the design that holds up through the follow-ups.

Truth is not a label you can gather cheaply, and adversaries adapt as soon as you ship. A strong answer combines content, graph, and behavioral signals, places humans in the loop where precision matters, and treats adversarial drift as a permanent operating condition rather than a one-time training problem.