12 B 11 6 Use the Brute-Force Algorithm to find the lowest-cost Hamilton circuit. For the first part, give one best answer as a list of vertices visited starting at A (example: ABCDA), and for the second part give the total cost for this best solution. 1. Give a lowest-cost Hamilton circuit: 2. Give the lowest cost:
12 B 11 6 Use the Brute-Force Algorithm to find the lowest-cost Hamilton circuit. For the first part, give one best answer as a list of vertices visited starting at A (example: ABCDA), and for the second part give the total cost for this best solution. 1. Give a lowest-cost Hamilton circuit: 2. Give the lowest cost:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Hamiltonian Circuit Problem Using Brute-Force Algorithm
In this section, you will learn how to use the Brute-Force Algorithm to determine the lowest-cost Hamiltonian circuit for a given graph.
#### Graph Description
The graph presented consists of four vertices, labeled A, B, C, and D. These vertices are connected by edges with the following weights:
- Vertex A to Vertex B: 7
- Vertex B to Vertex C: 12
- Vertex C to Vertex D: 5
- Vertex D to Vertex A: 6
- Vertex B to Vertex D: 11
- Vertex C to Vertex A: 2
The graph is a diamond shape with the vertices and edges connected as described. The goal here is to identify the Hamiltonian circuit with the lowest cost, starting at vertex A.
#### Brute-Force Approach
To find the lowest-cost Hamiltonian circuit using the Brute-Force Algorithm, list all possible Hamiltonian circuits. Calculate the total cost for each circuit, and identify the one with the lowest cost.
A Hamiltonian circuit visits each vertex exactly once and returns to the starting vertex.
1. **Give a lowest-cost Hamilton Circuit:**
Fill in the sequence of vertices visited, starting at A.
2. **Give the lowest cost:**
Calculate and provide the total cost of the lowest-cost Hamilton Circuit identified.
**Question:**
1. Give a lowest-cost Hamilton Circuit:
- [Your Answer]
2. Give the lowest cost:
- [Your Answer]
Utilize this information and apply the Brute-Force Algorithm to solve the Hamiltonian circuit problem efficiently.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e14e833-b473-4144-adde-e217b311654e%2F8a9b2f40-bbac-400f-a845-33cca0423be4%2F20wmo6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hamiltonian Circuit Problem Using Brute-Force Algorithm
In this section, you will learn how to use the Brute-Force Algorithm to determine the lowest-cost Hamiltonian circuit for a given graph.
#### Graph Description
The graph presented consists of four vertices, labeled A, B, C, and D. These vertices are connected by edges with the following weights:
- Vertex A to Vertex B: 7
- Vertex B to Vertex C: 12
- Vertex C to Vertex D: 5
- Vertex D to Vertex A: 6
- Vertex B to Vertex D: 11
- Vertex C to Vertex A: 2
The graph is a diamond shape with the vertices and edges connected as described. The goal here is to identify the Hamiltonian circuit with the lowest cost, starting at vertex A.
#### Brute-Force Approach
To find the lowest-cost Hamiltonian circuit using the Brute-Force Algorithm, list all possible Hamiltonian circuits. Calculate the total cost for each circuit, and identify the one with the lowest cost.
A Hamiltonian circuit visits each vertex exactly once and returns to the starting vertex.
1. **Give a lowest-cost Hamilton Circuit:**
Fill in the sequence of vertices visited, starting at A.
2. **Give the lowest cost:**
Calculate and provide the total cost of the lowest-cost Hamilton Circuit identified.
**Question:**
1. Give a lowest-cost Hamilton Circuit:
- [Your Answer]
2. Give the lowest cost:
- [Your Answer]
Utilize this information and apply the Brute-Force Algorithm to solve the Hamiltonian circuit problem efficiently.
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