Assess students' ability to analyze and compare correctness, time and space complexity, and practical trade-offs of BFS, DFS, Dijkstra, Bellman-Ford, and A* when applied to weighted and unweighted graphs. Tasks include: justify algorithm correctness on sample graphs (including negative weights), derive and compare Big-O time/space using different data structures (adjacency list vs matrix, array vs priority queue), evaluate A* heuristic admissibility and impact on performance, and choose the most appropriate algorithm given constraints (graph size, weight properties, memory limits).