How does the time complexity of Binary Search compare to Linear Search?

The time complexity of Binary Search is O(log n) while Linear Search is O(n). This distinction arises from the different methods these algorithms use to search for an element in a dataset.

Binary Search operates on a sorted array by repeatedly dividing the search interval in half. It checks the middle element and determines if the target value is in the left or right half, effectively eliminating half of the remaining elements with each comparison. This logarithmic reduction in search space leads to its time complexity of O(log n), where n is the number of elements in the array.

On the other hand, Linear Search examines each element one by one from the beginning of the array to the end until it finds the target or exhausts the list. In the worst-case scenario, it may have to look through all n elements, resulting in a time complexity of O(n).

Understanding these time complexities helps in choosing the right search algorithm based on the problem at hand. When a dataset is sorted, Binary Search is much more efficient than Linear Search due to its logarithmic nature.