Describe how a binary search algorithm works and why it is more efficient than a linear search for large, sorted lists.

Searching and Sorting Algorithms - Review

Explain the primary purpose of searching algorithms in computer science.

Describe how the binary search algorithm works and its time complexity.

What is the main advantage of using sorting algorithms in computer science?

Compare the time complexities of bubble sort and merge sort.

Why is it important to understand the trade-offs between different sorting algorithms?

Explain how a linear search algorithm works and in what scenarios it is most useful.

Describe how a binary search algorithm works and why it is more efficient than a linear search for large, sorted lists.

What are the prerequisites for using a binary search algorithm, and why are they necessary?

In what situations would a linear search be preferred over a binary search, despite its lower efficiency?

10.

What is the main advantage of using a binary search over a linear search, and what is a key limitation?

11.

Explain how the quicksort algorithm works and what its average-case time complexity is.

12.

Describe the merge sort algorithm and its space complexity.

13.

What is the insertion sort algorithm, and in what scenario is it most efficient?

14.

How does the selection sort algorithm work, and what is its primary disadvantage?

15.

What is the heap sort algorithm, and what is its time complexity?

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Instructor solution

AI InstructorMAY 20, 2024, 1:59:23 PM

A binary search algorithm works by repeatedly dividing a sorted list in half to locate a target value. It starts by comparing the target value to the middle element of the list. If the target is equal to the middle element, the search is complete. If the target is less than the middle element, the search continues in the lower half of the list; if greater, it continues in the upper half. This process is repeated until the target is found or the sublist is empty. Binary search is more efficient than linear search for large, sorted lists because it reduces the search space by half with each step, resulting in a time complexity of $O (\log n)$ compared to $O (n)$ for linear search.

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Which of the following best describes the time complexity of a binary search algorithm?

Select one of the following options:

A.
$O (n^{2})$
B.
$O (\log n)$
C.
$O (1)$
D.
$O (n)$

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