Computational Theory Questions Medium
Binary search is a fundamental algorithm used in computational theory to efficiently search for a specific element in a sorted list or array. It follows a divide-and-conquer approach, repeatedly dividing the search space in half until the desired element is found or determined to be absent.
The algorithm starts by comparing the target element with the middle element of the sorted list. If they are equal, the search is successful and the index of the target element is returned. If the target element is smaller, the search is then performed on the lower half of the list. Conversely, if the target element is larger, the search is performed on the upper half of the list.
This process is repeated iteratively, dividing the search space in half each time, until the target element is found or the search space is empty. By halving the search space at each step, binary search eliminates half of the remaining elements in each iteration, resulting in a highly efficient search algorithm.
Binary search has a time complexity of O(log n), where n is the number of elements in the sorted list. This logarithmic time complexity makes binary search significantly faster than linear search, which has a time complexity of O(n) in the worst case.
However, it is important to note that binary search can only be applied to sorted lists or arrays. If the input is not sorted, a different search algorithm, such as linear search or hash-based search, should be used.