Question

Which of the following statements correctly describes the traveling salesman problem?(1 point) Responses The traveling salesman problem finds the shortest path between two points in a graph. The traveling salesman problem finds the shortest path between two points in a graph. The traveling salesman algorithm has a lower space complexity than common sorts or searches. The traveling salesman algorithm has a lower space complexity than common sorts or searches. The traveling salesman algorithm is a classic algorithm. The traveling salesman algorithm is a classic algorithm. The traveling salesman algorithm has a lower time complexity than common sorts or searches

Answer 1

The most accurate statement that describes the traveling salesman problem (TSP) is:

The traveling salesman algorithm is a classic algorithm.

The other statements contain inaccuracies:

1. The TSP seeks the shortest possible route that visits each city once and returns to the origin city, not just the shortest path between two points in a graph.
2. The TSP is NP-hard, and while there are various approximation algorithms, it does not inherently have a lower space or time complexity compared to common sorting or searching algorithms. In fact, the time complexity for solving the TSP exactly is typically much higher than that of common sorts or searches.

Answer 2

Which of the following explains different types of efficiency?(1 point) Responses Time complexity refers to the amount of memory used. Space complexity refers to the amount of time needed. Time complexity refers to the amount of memory used. Space complexity refers to the amount of time needed. Space complexity refers to the amount of memory used. Time complexity refers to the amount of time needed. Space complexity refers to the amount of memory used. Time complexity refers to the amount of time needed. Code complexity refers to the number of characters in the code. Code length refers to the effort needed to understand the code. Code complexity refers to the number of characters in the code. Code length refers to the effort needed to understand the code. Code length refers to the number of characters in the code. Code complexity refers to the effort needed to understand the code.

Answer 3

The correct responses explaining different types of efficiency are:

• Time complexity refers to the amount of time needed.
• Space complexity refers to the amount of memory used.

The other statements contain inaccuracies or misrepresentations of the concepts of time complexity, space complexity, code complexity, and code length.

Time complexity focuses on how the execution time of an algorithm grows relative to the size of the input, while space complexity pertains to how the amount of memory required by an algorithm grows with the input size.

For the latter parts concerning code complexity and code length, it is generally understood that:

• Code complexity refers to the effort needed to understand the code.
• Code length refers to the number of characters in the code.

Therefore, the most accurate statements are the first pair mentioned.

Answer 4

Which of the following is a true statement about correctness?(1 point) Responses Correctness can be shown without identifying specifications. Correctness can be shown without identifying specifications. Correctness can be shown through formal logic. Correctness can be shown through formal logic. Correctness can be shown by testing many possible input values. Correctness can be shown by testing many possible input values. Correctness cannot be shown through mathematical proof. Correctness cannot be shown through mathematical proof.

Answer 5

The true statements about correctness are:

• Correctness can be shown through formal logic.

  This statement is accurate because formal methods and logic can be used to prove that an algorithm meets its specifications.

The other statements are generally false:

1. Correctness can be shown without identifying specifications. - This is false; specifications are crucial for defining what correctness means in the context of a given program or algorithm.

2. Correctness can be shown by testing many possible input values. - While testing can provide evidence of correctness, it cannot definitively prove correctness because it cannot account for all possible inputs.

3. Correctness cannot be shown through mathematical proof. - This is also false; mathematical proof is a valid way to demonstrate correctness, particularly in formal verification methods.

Thus, the true statement about correctness is that it can be shown through formal logic.