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Binary search is a search algorithm used to find a specific element in a sorted array efficiently. It follows a divide and conquer approach by repeatedly dividing the search space in half until the desired element is found or the search space is empty.
The process of searching for an element in an array using binary search can be described as follows:
1. Start by defining the search space, which is the entire array. Set the lower bound (start) to the first index of the array and the upper bound (end) to the last index of the array.
2. Calculate the middle index of the search space by taking the average of the lower and upper bounds: middle = (start + end) / 2.
3. Compare the middle element of the array with the target element that you are searching for.
4. If the middle element is equal to the target element, then the search is successful, and the index of the target element is returned.
5. If the middle element is greater than the target element, then the target element must be in the lower half of the search space. Update the upper bound to be one index less than the middle index: end = middle - 1.
6. If the middle element is less than the target element, then the target element must be in the upper half of the search space. Update the lower bound to be one index more than the middle index: start = middle + 1.
7. Repeat steps 2 to 6 until the target element is found or the search space is empty (start > end). In each iteration, the search space is halved, reducing the number of elements to search.
8. If the target element is not found after the search space becomes empty, then it does not exist in the array, and the search is unsuccessful.
Binary search has a time complexity of O(log n), where n is the number of elements in the array. This makes it significantly faster than linear search for large arrays. However, it requires the array to be sorted in ascending order for the algorithm to work correctly.