Rtab_10
The below algorithm, process_list, works with a sorted list and recursively processes the list by dividing it into smaller sections at each step, focusing on one part of the list based on comparisons.What is the best-case time complexity of this algorithm?

Question

Rtab_10
The below algorithm, process_list, works with a sorted list and recursively processes the list by dividing it into smaller sections at each step, focusing on one part of the list based on comparisons.What is the best-case time complexity of this algorithm?

BlackTom AI · Accepted Answer

The question describes an algorithm that operates on a sorted list by recursively dividing the list and focusing on a subpart based on comparisons. This is characteristic of a binary search pattern, where at each step you compare the target to the middle element and then proceed to either the left or right half.

Option 1: O(nlogn). This would imply the algorithm performs a linear amount of work n at each of log n levels, which is not the case for binary search; the work per level is constant (a single comparison), so the total does not scale as nlogn.

Option 2: O(n). A linear-time complexity would occur if you had to examine every element or traverse the list in sequence. Binary search never scans the entire list; it halves the search space each step, so this option is incorrect.

Option 3: O(1). Best-case scenarios for binary search occur when the target is found immediately on the first comparison (for example, if the target equals the middle element on the first step). In this situation only a constant amount of work is performed, hence O(1).

Option 4: O(n^2). This would require nested iterations over the list, which binary search does not do, so this option is inaccurate.

Option 5: O(logn). This is the typical time complexity for binary search in the general case (worst or average). It’s important to distinguish that O(log n) is not the best-case unless specified that the first comparison fails to terminate early; in classic binary search, you usually cite O(log n) as the time complexity for the search process over the general case.

Putting it together, the best-case scenario occurs when the target is found on the very first comparison, which yields O(1).

Rtab_10 The below algorithm, process_list, works with a sorted list and recursively processes the list by dividing it into smaller sections at each step, focusing on one part of the list based on comparisons.What is the best-case time complexity of this algorithm?

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