Use the brute force algorithm to find a minimum Hamilton circuit for the graph.

Question

Use the brute force algorithm to find a minimum Hamilton circuit for the graph. Determine the total weight of the minimum Hamilton circuit. The minimum Hamilton circuit is and its total weight is. Use the brute force algorithm to find a minimum Hamilton circuit or minimum Hamilton circuits for the graph. Determine the total weight of the minimum Hamilton circuit(s). Which Hamilton circuits are the optimal solutions? A rightarrow B rightarrow D rightarrow C rightarrow A and A rightarrow C rightarrow D rightarrow B rightarrow A A rightarrow C rightarrow B rightarrow D rightarrow A and A rightarrow D rightarrow B rightarrow C rightarrow A A rightarrow B rightarrow C rightarrow D rightarrow A and A rightarrow D rightarrow C rightarrow B rightarrow A What is the weight of the optimal solution?

Explanation / Answer

Question 1)

Using brute force algorithm to list the all possible hamilton circuits and their corresponding weights and then we check which one is minimum to decide minimum hamilton circuit.

Possible hamilton circuits:

ABCDEA (Corresponding wieght is 69)

ABCEDA (Corresponding wieght is 83)

ABDECA (Corresponding wieght is 91)

ABDCEA (Corresponding wieght is 77)

ABEDCA (Corresponding wieght is 73)

ABECDA (Corresponding wieght is 73)

AEBCDA (Corresponding wieght is 72)

AEBDCA (Corresponding wieght is 80)

AECDBA (Corresponding wieght is 77)

AECBDA (Corresponding wieght is 77)

AEDCBA (Corresponding wieght is 69)

AEDBCA (Corresponding wieght is 69)

ADEBCA (Corresponding wieght is 86)

ADECBA (Corresponding wieght is 83)

ADCBEA (Corresponding wieght is 76)

ADCEBA  (Corresponding wieght is 73)

ADBCEA (Corresponding wieght is 90)

ADBECA  (Corresponding wieght is 94)

ACBDEA (Corresponding wieght is 90)

ACBEDA  (Corresponding wieght is 86)

ACDBEA (Corresponding wieght is 80)

ACDEBA (Corresponding wieght is 73)

ACEBDA (Corresponding wieght is 94)

ACEDBA (Corresponding wieght is 91)

Therefore, we can see that Hamilton Circuit with minimum weight is along ABCDEA and it's weight is 69.

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