binary search

Binary search is a fast search algorithm with time complexity O(log n). The algorithm works by repeatedly dividing in half the portion of the array that could contain the item, until the possible location of the target item is narrowed down to just one element. Here are the steps involved in a binary search:

1. Initialize variables for the first, last, and middle elements of the array.
2. Compare the middle element of the array with the target value.
3. If the middle element is equal to the target value, return the middle index.
4. If the middle element is greater than the target value, then the target is in the left half of the array. Update the last index to be the middle index - 1.
5. If the middle element is less than the target value, then the target is in the right half of the array. Update the first index to be the middle index + 1.
6. Repeat steps 2-5 until the target value is found or the first index becomes greater than the last index.
7. If the target value is not found, return -1 to indicate that the value does not exist in the array.

These steps efficiently locate the target value in a sorted array using the binary search algorithm.