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S 6 A 8 S-B-D-G S-A-D-G S-A-C-G S-G B 6 C 5 D 1 What path will A* algorithm takes? E 10 G 0

S 6 A 8 S-B-D-G S-A-D-G S-A-C-G S-G B 6 C 5 D 1 What path will A* algorithm takes? E 10 G 0

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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### Search Problem Representation 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 - **Vertices/States:** - S (Start State) - A - B - C - D - E - G (Goal State) - **Edges/Paths and Their Costs:** - S to A: 2 - S to B: 1 - A to C: 2 - A to D: 3 - B to D: 2 - C to G: 4 - D to G: 4 - D to E: 4 - A to S: 9 The graph illustrates a number of states and the connections between them, which represent possible paths to traverse during the search from the start state \( S \) to the goal state \( G \). Each edge shows the cost of moving from one state to another. This structure serves as the foundation for solving various problems using tree search algorithms, where the solution involves finding a path from the start state to the goal state with specified conditions such as minimal cost or optimal path. For heuristic-based questions, refer to the provided graph and edge costs.
Transcribed Image Text:### Search Problem Representation 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 - **Vertices/States:** - S (Start State) - A - B - C - D - E - G (Goal State) - **Edges/Paths and Their Costs:** - S to A: 2 - S to B: 1 - A to C: 2 - A to D: 3 - B to D: 2 - C to G: 4 - D to G: 4 - D to E: 4 - A to S: 9 The graph illustrates a number of states and the connections between them, which represent possible paths to traverse during the search from the start state \( S \) to the goal state \( G \). Each edge shows the cost of moving from one state to another. This structure serves as the foundation for solving various problems using tree search algorithms, where the solution involves finding a path from the start state to the goal state with specified conditions such as minimal cost or optimal path. For heuristic-based questions, refer to the provided graph and edge costs.
### Understanding the A* (A-Star) Algorithm The A* algorithm is commonly used in pathfinding and graph traversal. It aims to find the shortest path from a given start node to a goal node. A* is known for its use in many applications due to its completeness, optimality, and efficiency. #### Example Problem In the given problem, we are asked to determine the path that the A* algorithm will take. The image presents a directed graph and a heuristic table, which contains the estimated costs from different nodes to the goal node (G). #### Graph Explanation 1. **Vertices:** There are six nodes labeled S, A, B, C, D, E, G. 2. **Edges:** Directed edges connecting these nodes with associated weights, representing the cost to traverse from one node to another. - From S to A: cost = 1 - From S to B: cost = 4 - From A to C: cost = 3 - From B to D: cost = 1 - From C to D: cost = 2 - From D to G: cost = 4 - From E to G: cost = 4 ### Heuristic Table The heuristic table estimates the cost to reach the goal node (G) from the other nodes: - S: 6 - A: 8 - B: 6 - C: 5 - D: 1 - E: 10 - G: 0 #### Question What path will the A* algorithm take? #### Answer Choices 1. **S-B-D-G** 2. **S-A-D-G** 3. **S-A-C-G** 4. **S-G** ### Detailed Path Explanation Using A* Algorithm The A* algorithm uses the following formula to determine the cost: \[ f(n) = g(n) + h(n) \] - **f(n):** The total estimated cost of the cheapest solution through node n. - **g(n):** The cost to reach the node n from the start node. - **h(n):** The heuristic estimate of the cost to reach the goal from node n. Starting from the node S, let's calculate the path costs: 1. **At S:** - f(S) = g(S) + h(S) = 0 + 6 = 6. 2. **Moving
Transcribed Image Text:### Understanding the A* (A-Star) Algorithm The A* algorithm is commonly used in pathfinding and graph traversal. It aims to find the shortest path from a given start node to a goal node. A* is known for its use in many applications due to its completeness, optimality, and efficiency. #### Example Problem In the given problem, we are asked to determine the path that the A* algorithm will take. The image presents a directed graph and a heuristic table, which contains the estimated costs from different nodes to the goal node (G). #### Graph Explanation 1. **Vertices:** There are six nodes labeled S, A, B, C, D, E, G. 2. **Edges:** Directed edges connecting these nodes with associated weights, representing the cost to traverse from one node to another. - From S to A: cost = 1 - From S to B: cost = 4 - From A to C: cost = 3 - From B to D: cost = 1 - From C to D: cost = 2 - From D to G: cost = 4 - From E to G: cost = 4 ### Heuristic Table The heuristic table estimates the cost to reach the goal node (G) from the other nodes: - S: 6 - A: 8 - B: 6 - C: 5 - D: 1 - E: 10 - G: 0 #### Question What path will the A* algorithm take? #### Answer Choices 1. **S-B-D-G** 2. **S-A-D-G** 3. **S-A-C-G** 4. **S-G** ### Detailed Path Explanation Using A* Algorithm The A* algorithm uses the following formula to determine the cost: \[ f(n) = g(n) + h(n) \] - **f(n):** The total estimated cost of the cheapest solution through node n. - **g(n):** The cost to reach the node n from the start node. - **h(n):** The heuristic estimate of the cost to reach the goal from node n. Starting from the node S, let's calculate the path costs: 1. **At S:** - f(S) = g(S) + h(S) = 0 + 6 = 6. 2. **Moving
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