Question

Consider the following algorithms. Each algorithm operates on a list containing n elements, where n is a very large integer.

I. An algorithm that accesses each element in the list twice.
II. An algorithm that accesses each element in the list n times.
III. An algorithm that accesses only the first 10 elements in the list, regardless of the size of the list. Which of the algorithms run in reasonable time?
a. I only.
b. III only.
c. I and II only.
d. I, II, and III.

Answer 1

The algorithms that run in a reasonable time are I and III, with a time complexity of O(n) and O(10) respectively.

Step-by-step explanation:

The algorithms that run in a reasonable time are I and III. Algorithm I accesses each element in the list twice, resulting in a time complexity of O(2n), which is equivalent to O(n). Algorithm III only accesses the first 10 elements in the list, regardless of the list's size, so its time complexity is O(10). Both of these algorithms have linear time complexity and will run in a reasonable amount of time, even for a very large value of n.

Answer 2

The algorithm that runs in reasonable time is Algorithm III, which accesses only the first 10 elements of the list, regardless of its size.

Step-by-step explanation:

The algorithm that runs in reasonable time is Algorithm III, which accesses only the first 10 elements of the list, regardless of its size. This is because the time complexity of accessing a constant number of elements does not increase with the size of the list. On the other hand, Algorithms I and II both have time complexities that depend on the size of the list.

For Algorithm I, accessing each element in the list twice has a time complexity of O(2n) or simply O(n) - linear time. This means that as the size of the list increases, the time taken by the algorithm also increases linearly.

For Algorithm II, accessing each element in the list n times has a time complexity of O(n^2) - quadratic time. As the size of the list increases, the time taken by the algorithm increases exponentially.