Question 2 By eliminating impossible paths, the best time complexities that can be obtained...
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By eliminating impossible paths, the best time complexities that can be obtained by general algorithms is
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By eliminating impossible paths (such as in topological DAG shortest paths or pruned branch searches), the optimal lower bound for graph traversal/search is linear in vertices and edges, O(V + E).
Step-by-step Derivation:
Step 1: In graph theory, visiting every reachable state and pruning impossible edges reduces the exploration to optimal linear graph traversal.
Step 2: Visiting each vertex once takes O(V) and exploring each valid edge takes O(E).
Step 3: Hence, the optimal complexity achieved is O(V + E).