Question

Which of the following algorithms has the smallest time complexity?(1 point)Responsesinsertion sortinsertion sortlinear searchlinear searchmerge sortmerge sortbinary search

Answer 1

To determine which algorithm has the smallest time complexity among the options provided, let's analyze each one:

1. **Insertion Sort**: Average time complexity is \(O(n^2)\), and the best case (when the array is already sorted) is \(O(n)\).

2. **Linear Search**: Time complexity is \(O(n)\) in the worst case.

3. **Merge Sort**: Time complexity is \(O(n \log n)\) for both average and worst cases.

4. **Binary Search**: Time complexity is \(O(\log n)\), but it requires the array to be sorted.

Among these options, **Binary Search** has the smallest time complexity of \(O(\log n)\), assuming that the input data is sorted (which is a requirement for its use).

So, the answer is **Binary Search**.