AALL10 · Chapter 10Mock Test 03🏛️ Past Licensure QuestionID: fbf27f31

In artificial intelligence search algorithms, what is the best-case time complexity of Best-First Search with a perfect heuristic that directs search directly along the optimal path to depth $m$ ?

Multiple Choice Options

A
$O(b \cdot m)$
✓ Correct Option
B
$O(b^m)$
C
$O(m)$
D
$O(1)$

Detailed Technical Solution & Explanation

With an ideal heuristic that perfectly guides search toward the goal, at each of the $m$ levels along the path, the search only expands the best node, but must generate all $b$ branch successors at each step. Thus, it examines at most $b \cdot m$ nodes, giving $O(b \cdot m)$ time complexity.

Option Analysis:

•

Option A (O(b

\cdot

m)): Correct. Generating

b

children along depth

m

with a perfect heuristic.

•

Option B (O(b^m)): Worst-case exponential complexity when the heuristic provides no guidance.

•

Option C (O(m)): Ignores the branching factor

b

required to generate successor nodes.

•

Option D (O(1)): Impossible since depth

m

must be traversed.

Reference: Mock Test 03NEC Licensure Syllabus

In artificial intelligence search algorithms, what is the best-case time complexity of Best-First Search with a perfect heuristic that directs search directly along the optimal path to depth $m$ ?

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

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In artificial intelligence search algorithms, what is the best-case time complexity of Best-First Search with a perfect heuristic that directs search directly along the optimal path to depth $m$ ?

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

Want to practice this topic interactively?