Question

Algorithms Quick Check 2 of 52 of 5 Items Question Which of the following algorithms has the smallest time complexity?(1 point) Responses linear search linear search insertion sort insertion sort merge sort merge sort binary search binary search Skip to navigation page 13 of 13

Answer 1

To determine which algorithm has the smallest time complexity, let's look at the time complexities of the algorithms mentioned:

1. **Linear Search**: \(O(n)\)
2. **Insertion Sort**: \(O(n^2)\) in the average and worst cases, \(O(n)\) in the best case.
3. **Merge Sort**: \(O(n \log n)\) in all cases (best, average, worst).
4. **Binary Search**: \(O(\log n)\) (but requires the list to be sorted).

Among these algorithms, **binary search** has the smallest time complexity with \(O(\log n)\) when it comes to searching in a sorted array.

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