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Prealg Chapter 6 Quiz Fall 2020 Gradescope

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Chapter 6 Quiz Fall 2020 GRADESCOPE
1. Download directions for this hard copy.
2. Honor Code (see and “sign” in Gradescope)
3. What is the formula we would use to determine the TOTAL number of Hamilton circuits we
could create using the BRUTE-FORCE algorithm on a graph given any number, "n,"
vertices?
a.
b.
c.

d.

4. How many Hamilton circuits (TOTAL) would we have to check if we used the brute-force
algorithm on a graph with 6 vertices?
(6-1)! = 120
5. How many Hamilton circuits would we have to check if we used the brute-force algorithm on
a graph with 6 vertices BUT discarded the mirror images?
(6-1)!/2 = 60
6.1 What are the four methods for finding a Hamilton circuit that we have studied in this
chapter?
Brute Force Algorithm
Nearest-Neighbor Algorithm
Repetitive Nearest-Neighbor Algorithm
Cheapest-Link Algorithm
6.2 Which of the four methods listed above is guaranteed to provide an optimal solution?
Brute Force Algorithm

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6.3. If one of the methods listed in Question 6.1 gives an optimal solution, why do we even
consider using the other three methods?
Because each method offers a unique solution that can be
useful in case to case situations
7. What is the formula you would use to find the number of edges in a complete graph with "n"
vertices?
a.
b.
c.

d.

8. How many edges are there in a complete graph with 10 vertices?
10(10-1)/2 = 45
9. The neighborhood milk delivery truck driver stops in 5 different neighborhoods to deliver dairy
products. The neighborhoods are labeled A, B, C, D, and E. The distance between them is shown in
miles on the graph. Apply the nearest neighbor algorithm starting with vertex A.

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Chapter 6 Quiz Fall 2020 GRADESCOPE 1. Download directions for this hard copy. 2. Honor Code (see and “sign” in Gradescope) 3. What is the formula we would use to determine the TOTAL number of Hamilton circuits we could create using the BRUTE-FORCE algorithm on a graph given any number, "n," vertices? a. 4. (𝑛 − 1)! b. 𝑛(𝑛 − 1) c. (𝑛−1)! 2 d. 𝑛(𝑛−1) 2 How many Hamilton circuits (TOTAL) would we have to check if we used the brute-force algorithm on a graph with 6 vertices? (6-1)! = 120 5. How many Hamilton circuits would we have to check if we used the brute-force algorithm on a graph with 6 vertices BUT discarded the mirror images? (6-1)!/2 = 60 6.1 What are the four methods for finding a Hamilton circuit that we have studied in this chapter? Brute Force Algorithm Nearest-Neighbor Algorithm Repetitive Nearest-Neighbor Algorithm Cheapest-Link Algorithm 6.2 Which of the four methods listed above is guaranteed to provide an optimal solution? Brute Force Algorithm 6.3. If one of the methods listed in Question 6.1 gives an optimal solution, why do we even consider using the other three methods? Because each method offers a unique solution that can be useful in case to case situations 7. What is the formula you would use to find the number of edges in a complete graph with "n" vertices? a. (𝑛 − 1)! b. 𝑛(𝑛 − 1) c. (𝑛−1)! 2 d. 𝑛(𝑛−1) 2 8. How many edges are there in a complete graph with 10 vertices? 1 ...
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