Final answer:
Binary search uses a divide-and-conquer strategy on a sorted array, reducing the search space by half with each comparison, leading to a logarithmic time complexity, which makes it highly efficient compared to linear search methods.
Step-by-step explanation:
The logic behind a binary search is to reduce the number of elements to be searched by half in each step. This is achieved by comparing the middle element of a sorted array to the target value. If the middle element is the target, the search is complete. If the target is less than the middle element, the search continues on the left half of the array; if the target is greater, it continues on the right half. This halving continues until the target is found or the array cannot be split further, meaning the target is not present.
Efficiency in the context of binary search refers to the reduction of the search space at each step, which leads to a logarithmic time complexity of O(log n). This makes binary search highly efficient compared to linear search methods, which have a linear time complexity of O(n).