Question

Between the linear search and the binary search algorithms, which one will you select to search for a number in the following datasets and why? Also, what will be the time complexities? [Points: 2x(1+2+2) = 10]

100, 110, 170, 180, 120, 130, 210, 220, 230, 140, 150, 160, 190, 200, 240, 250

100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250

Answer 1

For an unordered dataset, a linear search is suitable with a time complexity of O(n). For an ordered dataset, a binary search is appropriate and has a time complexity of O(log n), being more efficient than linear search for large datasets.

Step-by-step explanation:

When deciding between the linear search and binary search algorithms for searching a number in a dataset, the choice largely depends on the organization of the data. For the first unordered dataset (100, 110, 170, etc.), you would use a linear search because the data is not sorted, which is a prerequisite for binary search. The time complexity of the linear search is O(n), where n is the number of elements in the dataset, because in the worst case you might have to check each element once.

For the second ordered dataset (100, 110, 120, etc.), the binary search algorithm is more efficient as it divides the dataset in half with each iteration. The time complexity of binary search is O(log n), where n is the number of elements in the dataset. This logarithmic time complexity is much more efficient than linear search's linear time complexity for large datasets.