Assess students' ability to analyze and compare time and space complexity and correctness of BFS, DFS, Dijkstra's, and A* when implemented with adjacency lists versus adjacency matrices on sparse and dense graphs. Tasks include deriving asymptotic running times and memory usage for each algorithm/representation combination, explaining correctness requirements (e.g., unweighted vs weighted edges, admissible heuristics for A*), identifying practical performance and storage trade-offs on sparse versus dense inputs, and selecting and justifying the best algorithm and graph representation for provided scenario descriptions or small example graphs.