Question

What is the time complexity of the most time efficient algorithm for performing m searches for arbitrary items in a sorted array of n items (where m < n and the largest element < n)?

a) o(n m)
b) o(m)
c) o(m log2(n))
d) o(n log2 (n))
e) o(n log2 (m))

Answer 1

The most efficient algorithm for performing m searches in a sorted array of n items is O(m log n), as binary search with O(log n) complexity is used for each of the m searches.

Step-by-step explanation:

The time complexity of the most time efficient algorithm for performing m searches for arbitrary items in a sorted array of n items is O(m log n). This is because we can use binary search to find an element in a sorted array, which has a time complexity of O(log n). Since we are performing m searches, we multiply the time complexity of one binary search by the number of searches m, giving us the result O(m log n).

The time complexity of the most time efficient algorithm for performing m searches for arbitrary items in a sorted array of n items can be determined by considering the operations performed in each search.

Since the array is sorted, we can use the binary search algorithm which has a time complexity of O(log2(n)).

For each search, the algorithm performs a binary search, resulting in a time complexity of O(m log2(n)).