Algorithms Analysis Practice Test 2025 – All-in-One Mastery Guide to Exam Success

The general process of binary search is to repeatedly divide the search interval in half. This algorithm is applied to a sorted array and begins by comparing the target value to the middle element of the array. If the target value is equal to the middle element, the search is complete. If the target value is less than the middle element, the search continues on the left half of the array. Conversely, if the target value is greater, the search proceeds on the right half.

This halving process significantly reduces the number of comparisons needed to find the target element compared to a linear search, which checks each element one by one. The efficiency of binary search is reflected in its time complexity, which is \( O(\log n) \), making it much faster for large datasets, provided the data is sorted.

In contrast, traversing all elements until the target is found involves checking each element sequentially, which yields linear time complexity. Sorting the array before searching, while necessary in some contexts, is not part of the binary search process itself since the algorithm assumes a sorted array. Lastly, searching the array in reverse order does not align with the methodology of binary search, which relies on the systematic division of the array based on comparisons with the middle element.