Question

Which of the following algorithms has the smallest time complexity?(1 point)
Responses

merge sort
merge sort

binary search
binary search

insertion sort
insertion sort

linear search

Answer 1

To determine which algorithm has the smallest time complexity, let's analyze the time complexities of each:

1. **Merge Sort**: This sorting algorithm has a time complexity of \(O(n \log n)\).

2. **Binary Search**: This algorithm, which is used to find an element within a sorted array, has a time complexity of \(O(\log n)\).

3. **Insertion Sort**: This sorting algorithm has a time complexity of \(O(n^2)\) in the worst case.

4. **Linear Search**: This search algorithm has a time complexity of \(O(n)\).

Among these, **Binary Search** has the smallest time complexity of \(O(\log n)\).

So the correct answer is **binary search**.