What is the best case runtime of linear search(recursive) algorithm on an ordered set of elements?O(1)O(n)O(logn)O(nx)

Break Down the Problem

1. We need to analyze the best case runtime of a linear search algorithm when implemented recursively.
2. The given options for the best case runtime are: $O(1)$, $O(n)$, $O(\log n)$, and $O(n^x)$.

Relevant Concepts

1. Linear Search: A linear search algorithm checks each element in the list sequentially until the desired element is found or the list ends.
2. Best Case Scenario: The best case occurs when the element we are searching for is the first element in the list.

Analysis and Detail

1. In the recursive implementation of linear search, the function will check the first element and return immediately if it is the target, without making any further recursive calls.
2. Thus, in the best case scenario:
   • We perform one comparison.
   • This leads to a constant time complexity denoted as $O(1)$.

Verify and Summarize

1. Since the first check results in either finding the element or concluding its absence immediately, no additional iterations are needed.
2. This confirms that the best case runtime of the recursive linear search is indeed $O(1)$.

Final Answer

The best case runtime of linear search (recursive) algorithm on an ordered set of elements is $O(1)$.