Binary Search with PHP

Welcome to today's lesson! We're diving into Binary Search, a clever technique for locating specific elements within a sorted list. By repeatedly dividing the search interval in half, we can find the targeted item. It's akin to flipping through a dictionary — instead of going page by page, you'd start in the middle and then narrow down the section in half until you find your desired word.

Binary Search begins at the midpoint of a sorted list, halving the search area at each step until it locates the target. For example, if we were to look for the number 9 in a sorted list ranging from 1 to 10, we would start at the midpoint, 5. Since 9 is larger than the midpoint, we discard all numbers less than or equal to 5 and focus on the second half, leaving us with numbers 6 to 10. Next, we find the midpoint of this subset, which is 8. Since 9 is greater than 8, we eliminate numbers 6 through 8, leaving us with just 9 and 10. Now, the midpoint of this final subset is 9, which matches our target. Thus, we've located the number 9 after three steps, demonstrating how Binary Search efficiently narrows the search range with each comparison.