Question

Given an array A of size n, we want to find if an element k belongs to this array. What will be the time complexity of this search operation?

1) O(1)
2) O(log n)
3) O(n)
4) O(n²)

Answer 1

The time complexity of searching in an array depends on the algorithm used. The worst case is O(n), but with a sorted array, a binary search algorithm can reduce it to O(log n).

Step-by-step explanation:

The time complexity of searching for an element in an array depends on the algorithm used. In the worst case scenario, where no optimization is performed, the time complexity is O(n). This means that the time taken to search for an element in the array increases linearly with the size of the array. For example, if the array has 10 elements, it may take up to 10 comparisons to find the element.

However, if the array is sorted, a more efficient algorithm like binary search can be used, which has a time complexity of O(log n). This means that even for very large arrays, the number of comparisons required to find the element is relatively small. For example, with an array of size 1024, it would take at most 10 comparisons to find the element.