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Binary Search is an efficient searching algorithm used to find a particular element in a sorted collection of data. In Algorithm Design Lab, it is an important example of the divide-and-conquer technique because it repeatedly divides the search space into two approximately equal parts. Its efficiency becomes especially clear when it is compared with Linear Search. While Linear Search may examine every element one by one, Binary Search eliminates half of the remaining elements after every comparison. However, this efficiency is achieved only under appropriate conditions, particularly when the data is sorted and supports efficient access to its middle element. In Linear Search, the algorithm starts from the first element and compares each element with the required value until the value is found or the entire collection is examined. If there are (n) elements, the worst-case time complexity of Linear Search is (O(n)). For example, if an array contains 1,000 elements and the required element is at the last position or is absent, the algorithm may need to perform 1,000 comparisons. Even in the average case, a significant portion of the elements may need to be examined. Binary Search follows a fundamentally different approach. It begins by examining the middle element of a sorted array. If the middle element is equal to the target, the search is successful. If the target is smaller than the middle element, the algorithm continues searching only in the left half. If the target is greater, it searches only in the right half. Thus, approximately half of the remaining elements are discarded after every comparison. For example, consider a sorted array containing 16 elements. Binary Search initially examines the middle element. If the target is not found, ______ ______ _________ _________ ______.
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