The time complexity of a binary search algorithm is O(log n).

  In a binary search, the algorithm repeatedly divides the search space in half, narrowing down the possible range of values. It starts by comparing the target value with the middle element of the sorted array. If they are equal, the search is successful. If the target value is less than the middle element, the search continues in the lower half of the array. If the target value is greater, the search continues in the upper half.

  With each comparison, the search space is reduced by half. This means that the algorithm eliminates a large portion of the remaining values after each iteration. As a result, the time complexity of a binary search algorithm is logarithmic.

  To be more precise, in a binary search, if there are n elements in the array, the search space is reduced to approximately n/2, then n/4, then n/8, and so on. The number of iterations required to reach a single element is log2(n), where log2 denotes the logarithm base 2. Hence, the time complexity is O(log n).

  It is important to note that the binary search algorithm assumes that the array is sorted. If the array is not sorted, a sorting operation must be performed before applying the binary search algorithm, which would have a time complexity of O(n log n) for most efficient sorting algorithms like merge sort or quicksort.