What path will the Best First Search takes? S-G S-A-C-G S-A-D-G S-B-D-G
What path will the Best First Search takes? S-G S-A-C-G S-A-D-G S-B-D-G
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![**Search Problem Represented as a Graph**
Consider the following search problem, represented as a graph. The start state is S and the only goal state is G. Note that the following problems reference tree search. This means the algorithm establishes a tree structure for search. For questions which require a heuristic, use the one given below:
![Graph Representation of Search Problem]
In the graph:
- The nodes are labeled as S, A, B, C, D, E, and G.
- Arrows (directed edges) connect these nodes, indicating the possible paths and directions one can take from one node to another.
- The numbers on the arrows represent the costs associated with traveling along that path.
Details of the Graph:
- From node S, you can move to node A with a cost of 2, to node B with a cost of 1, and to node G directly with a cost of 9.
- From node A, you can move to node C with a cost of 2, to node B with a cost of 2, and to node D with a cost of 3.
- From node B, you can move to node D with a cost of 2 and to node E with a cost of 4.
- From node C, you can move to node G with a cost of 4.
- From node D, you can move to node G with a cost of 4.
- Node E has no outgoing paths shown.
The goal is to find the most optimal path from the start node S to the goal node G using the given tree structure graph. For heuristic-based problems, additional heuristic values may be provided elsewhere or assumed as necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71f309ce-3c3d-4315-8a6b-c8c8322162e4%2F6734c512-ab04-4648-855d-84dde5df5f83%2F8pv5o5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Search Problem Represented as a Graph**
Consider the following search problem, represented as a graph. The start state is S and the only goal state is G. Note that the following problems reference tree search. This means the algorithm establishes a tree structure for search. For questions which require a heuristic, use the one given below:
![Graph Representation of Search Problem]
In the graph:
- The nodes are labeled as S, A, B, C, D, E, and G.
- Arrows (directed edges) connect these nodes, indicating the possible paths and directions one can take from one node to another.
- The numbers on the arrows represent the costs associated with traveling along that path.
Details of the Graph:
- From node S, you can move to node A with a cost of 2, to node B with a cost of 1, and to node G directly with a cost of 9.
- From node A, you can move to node C with a cost of 2, to node B with a cost of 2, and to node D with a cost of 3.
- From node B, you can move to node D with a cost of 2 and to node E with a cost of 4.
- From node C, you can move to node G with a cost of 4.
- From node D, you can move to node G with a cost of 4.
- Node E has no outgoing paths shown.
The goal is to find the most optimal path from the start node S to the goal node G using the given tree structure graph. For heuristic-based problems, additional heuristic values may be provided elsewhere or assumed as necessary.
Transcribed Image Text:**Best First Search Pathfinding Analysis**
In this section, we will determine the path taken by the Best First Search algorithm using the provided graph data and heuristic values.
### Graph And Heuristic Table
The provided graph can be annotated as follows:
- Node connections and their respective heuristic values:
- From S to A: 6
- From S to B: 7
- From A to C: 8
- From B to D: 4
- From C to D: 4
- From D to E: 1
- From E to G: 10
- From D to G: 0
### Heuristic Table
| | S | A | B | C | D | E | G |
|---|---|---|---|---|---|---|---|
| S | | 6 | 7 | | | | |
| A | | | | 8 | | | |
| B | | | | | 4 | | |
| C | | | | | 4 | | |
| D | | | | | | 1 | 0 |
| E | | | | | | | 10|
| G | | | | | | | 0 |
### Best First Search Path
Given the heuristic values, the Best First Search algorithm will look for the smallest heuristic value at each step. The goal is to determine the optimal path from the start node `S` to the goal node `G`.
#### Step-by-Step Path Analysis:
1. **Start at S:**
- Current heuristic values: A(6), B(7)
- Choose the node with the smallest heuristic value: A(6)
2. **Move to A:**
- New heuristic values from A: C(8)
- Compare current paths from S: B(7)
- Choose the node with the next smallest heuristic value: B(7)
3. **Move to B:**
- New heuristic values from B: D(4)
- Compare current paths from S: C(8)
- Choose the node with the next smallest heuristic value: D(4)
4. **Move to D
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