What condition must be fulfilled to apply binary search?

For binary search to function correctly, the primary requirement is that the array must be sorted in either ascending or descending order. This is crucial because binary search works by repeatedly dividing the search interval in half. If you start with a sorted array, you can confidently eliminate half of the remaining elements based on whether the target value is greater than or less than the middle element. This elimination process relies on the order of the elements to correctly direct the search.

In unsorted arrays or if the elements are in a random order, binary search cannot guarantee that the search will correctly find the target value, as the necessary condition of order is violated. This is the reason why sorting is mandatory before applying binary search. Hence, selecting a sorted array is what enables the efficient logarithmic time complexity of binary search, which is O(log n).