q1 search trees

how many nodes are in the complete search tree for the given state space graph? the start state is s. you may find it helpful to draw out the search tree on a piece of paper.

Question

q1 search trees

how many nodes are in the complete search tree for the given state space graph? the start state is s. you may find it helpful to draw out the search tree on a piece of paper.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Search Trees", "State Space Graph" ], "current_concepts": [ "Search Trees", "State Space Graph" ] } ## Trace all paths from the start state S to the goal state G $$ \begin{aligned} &\text{Path 1: } S ightarrow A ightarrow B ightarrow G \ &\text{Path 2: } S ightarrow C ightarrow B ightarrow G \end{aligned} $$ ## Construct the complete search tree $$ \begin{aligned} &\text{Level 0 (Root): } S \ &\text{Level 1: } A \text{ (from } S\text{)}, \quad C \text{ (from } S\text{)} \ &\text{Level 2: } B \text{ (from } A\text{)}, \quad B \text{ (from } C\text{)} \ &\text{Level 3: } G \text{ (from } B \text{ under } A\text{)}, \quad G \text{ (from } B \text{ under } C\text{)} \end{aligned} $$ ## Count the total number of nodes in the search tree $$ \begin{aligned} N &= 1 \text{ (Root } S\text{)} + 2 \text{ (Level 1: } A, C\text{)} + 2 \text{ (Level 2: } B, B\text{)} + 2 \text{ (Level 3: } G, G\text{)} \ N &= 7 \end{aligned} $$ 7 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Others", "Search Trees" ] }

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Question

Explanation:

Trace all paths from the start state S to the goal state G

Construct the complete search tree

Count the total number of nodes in the search tree

Answer: