Which of the following statements correctly describes the traveling salesman problem?(1 point)

Question

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 time complexity than common sorts or searches.
The traveling salesman algorithm has a lower time complexity than common sorts or searches.

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.

Answer 1

The correct statement that describes the traveling salesman problem is:

The traveling salesman algorithm is a classic algorithm.

The traveling salesman problem (TSP) itself is a well-known optimization problem in computer science and operations research, where the goal is to determine the shortest possible route that visits a set of cities and returns to the origin city. The other statements are inaccurate. The TSP does not focus on finding the shortest path between two specific points nor does it have a lower time or space complexity compared to common sorting or searching algorithms; in fact, it is NP-hard, meaning it can be quite complex to solve optimally.

Answer 2

Which of the following algorithms has the smallest time complexity?(1 point)
Responses

merge sort
merge sort

binary search
binary search

insertion sort
insertion sort

linear search

Answer 3

To determine which algorithm has the smallest time complexity, let's analyze the time complexities of each option:

1. Merge Sort: O(n log n) — This is a comparison-based sorting algorithm that divides the array into halves and sorts them recursively.

2. Binary Search: O(log n) — This algorithm only works on sorted arrays. It continuously divides the search interval in half to find an element.

3. Insertion Sort: O(n^2) — This is a simple sorting algorithm that builds the final sorted array one element at a time. It is less efficient on larger lists compared to more advanced algorithms.

4. Linear Search: O(n) — This algorithm checks each element in the list until the desired element is found.

Among these algorithms, Binary Search has the smallest time complexity of O(log n). Therefore, the correct answer is:

binary search.