4. Which is the nearest neighbor method? a. Connect the dots. b. C. d. e. Calculate each Hamilton circuit to see which is best. Choose the next closest city. Choose the edges starting with the cheapest and going to the most expensive. Choose the next closest city with different starting points.

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### Question 4: Which is the nearest neighbor method?

**Options:**

a. Connect the dots.

b. Calculate each Hamilton circuit to see which is best.

c. Choose the next closest city.

d. Choose the edges starting with the cheapest and going to the most expensive.

e. Choose the next closest city with different starting points.

---

**Explanation for Educational Purposes:**

- **Option (a):** "Connect the dots." This is a vague statement that doesn't specify any systematic approach and is not typically associated with the nearest neighbor method.

- **Option (b):** "Calculate each Hamilton circuit to see which is best." This method involves evaluating all possible Hamiltonian circuits and choosing the optimal one; however, this is more aligned with the brute force method rather than the nearest neighbor method.

- **Option (c):** "Choose the next closest city." This option correctly describes the nearest neighbor method. In this method, you start from an initial city and repeatedly visit the nearest city that has not been visited yet until all cities are visited.

- **Option (d):** "Choose the edges starting with the cheapest and going to the most expensive." This approach is part of the Minimum Spanning Tree (Kruskal's or Prim's algorithm) and not the nearest neighbor method.

- **Option (e):** "Choose the next closest city with different starting points." This approach suggests a variation of the nearest neighbor method where the algorithm is run multiple times starting from different cities to identify the best possible tour. While valuable, this is not the simplest form of the nearest neighbor method.

**Correct Answer: (c) Choose the next closest city.**
This option accurately represents the nearest neighbor method, which is a heuristic used for solving the Traveling Salesman Problem (TSP).
Transcribed Image Text:### Question 4: Which is the nearest neighbor method? **Options:** a. Connect the dots. b. Calculate each Hamilton circuit to see which is best. c. Choose the next closest city. d. Choose the edges starting with the cheapest and going to the most expensive. e. Choose the next closest city with different starting points. --- **Explanation for Educational Purposes:** - **Option (a):** "Connect the dots." This is a vague statement that doesn't specify any systematic approach and is not typically associated with the nearest neighbor method. - **Option (b):** "Calculate each Hamilton circuit to see which is best." This method involves evaluating all possible Hamiltonian circuits and choosing the optimal one; however, this is more aligned with the brute force method rather than the nearest neighbor method. - **Option (c):** "Choose the next closest city." This option correctly describes the nearest neighbor method. In this method, you start from an initial city and repeatedly visit the nearest city that has not been visited yet until all cities are visited. - **Option (d):** "Choose the edges starting with the cheapest and going to the most expensive." This approach is part of the Minimum Spanning Tree (Kruskal's or Prim's algorithm) and not the nearest neighbor method. - **Option (e):** "Choose the next closest city with different starting points." This approach suggests a variation of the nearest neighbor method where the algorithm is run multiple times starting from different cities to identify the best possible tour. While valuable, this is not the simplest form of the nearest neighbor method. **Correct Answer: (c) Choose the next closest city.** This option accurately represents the nearest neighbor method, which is a heuristic used for solving the Traveling Salesman Problem (TSP).
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