use the complete weighted graph shown to answer the question.

using the brute force method, which of the following is not an optimal solution?
i. a, b, c, d, a
ii. a, c, b, d, a
iii. a, b, d, c, a
iv. a, d, c, b, a

o ii
o iii
o iv
o i

Question

use the complete weighted graph shown to answer the question.

using the brute force method, which of the following is not an optimal solution?
i. a, b, c, d, a
ii. a, c, b, d, a
iii. a, b, d, c, a
iv. a, d, c, b, a

o ii
o iii
o iv
o i

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Hamilton Circuit", "Weighted Graph", "Edge Weight Identification" ], "new_concepts": [ "Brute Force Method" ], "current_concepts": [ "Hamilton Circuit", "Weighted Graph", "Edge Weight Identification", "Brute Force Method" ] } ## Identify edge weights from the graph $$ \begin{aligned} &w(A, B) = 43 \ &w(A, C) = 35 \ &w(A, D) = 18 \ &w(B, C) = 21 \ &w(B, D) = 37 \ &w(C, D) = 29 \end{aligned} $$ ## Calculate the total weight of each circuit $$ \begin{aligned} &\text{I. } A, B, C, D, A: \ &\quad w(A, B) + w(B, C) + w(C, D) + w(D, A) = 43 + 21 + 29 + 18 = 111 \ &\text{II. } A, C, B, D, A: \ &\quad w(A, C) + w(C, B) + w(B, D) + w(D, A) = 35 + 21 + 37 + 18 = 111 \ &\text{III. } A, B, D, C, A: \ &\quad w(A, B) + w(B, D) + w(D, C) + w(C, A) = 43 + 37 + 29 + 35 = 144 \ &\text{IV. } A, D, C, B, A: \ &\quad w(A, D) + w(D, C) + w(C, B) + w(B, A) = 18 + 29 + 21 + 43 = 111 \end{aligned} $$ ## Determine the non-optimal solution $$ \begin{aligned} &\text{Optimal weight} = 111 \ &\text{Non-optimal circuit} = \text{III (weight } 144\text{)} \end{aligned} $$

II

III

IV

I

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Hamilton Circuit" ] }

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QUESTION IMAGE

Question

Explanation:

Identify edge weights from the graph

Calculate the total weight of each circuit

Determine the non-optimal solution

Answer: