In graph and state-space search algorithms, Depth-First Search (DFS) is relatively more _______ efficient, whereas Breadth-First Search (BFS) is relatively more _______ efficient.
In graph and state-space search algorithms, Depth-First Search (DFS) is relatively more _______ efficient, whereas Breadth-First Search (BFS) is relatively more _______ efficient.
Multiple Choice Options
- A
Time, Space
- B
Time, Time
- C✓ Correct Option
Space, Time
- D
Space, Space
Detailed Technical Solution & Explanation
Comparing the standard performance characteristics of Breadth-First Search (BFS) and Depth-First Search (DFS):
1. Space Complexity:
- DFS requires only memory, storing only the active path from root to current node plus unexpanded sibling nodes. Hence, DFS is exceptionally space efficient.
- BFS must store every node generated in the frontier queue across each level, requiring exponential memory, which quickly exhausts RAM.
2. Time/Goal Optimality:
- BFS explores shallow nodes first and guarantees finding the optimal shortest path for unweighted graphs in minimal depth steps without getting trapped in infinite branches. Hence, for finding shallow solutions, BFS is more time/optimality efficient than DFS (which may get trapped traversing deep or infinite branches).