Graph Algorithms and Traversal Questions

Covers fundamental representations, traversal techniques, and classical algorithms for graph structured data. Candidates should understand graph representations such as adjacency list and adjacency matrix and the tradeoffs in time and space for each. Core traversal skills include implementing and reasoning about breadth first search and depth first search for reachability, traversal order, and unweighted shortest path discovery, as well as tree traversal variants and their relationship to graph traversals. Algorithmic topics include cycle detection, topological sorting for directed acyclic graphs, connected components and strongly connected components, and shortest path and pathfinding algorithms for weighted graphs including Dijkstra algorithm and Bellman Ford algorithm with discussion of negative weights and appropriate use cases. Candidates should be able to analyze time and space complexity, choose appropriate auxiliary data structures such as queues, stacks, priority queues, and union find, handle directed versus undirected and weighted versus unweighted graphs, discuss implementation details and trade offs, and explain practical applications such as dependency resolution, scheduling, pathfinding, connectivity queries, and roles of graph algorithms in system design and data processing.