Can you explain binary search with a visualization?

Can you explain binary search with a visualization?

Sure! Binary search is an efficient algorithm for finding an item from a sorted list. It works by repeatedly dividing the search interval in half. Let's visualize it with an example. Imagine you have a sorted array: [1, 3, 5, 7, 9, 11]. If you're looking for the number 7, you start by checking the middle element.

What happens if the middle element is not the target?

If the middle element is not the target, you compare it with the target. If the target is greater, you narrow your search to the right half; if it's smaller, you search the left half. For example, if the middle element is 5, you would search the right half: [7, 9, 11].

Can you show me a step-by-step visualization of that process?

Absolutely! Let's visualize it step-by-step:

1. Start with the full array: [1, 3, 5, 7, 9, 11].
2. Check the middle element (5).
3. Since 7 is greater than 5, focus on the right half: [7, 9, 11].
4. Now, the new middle is 9. Since 7 is less than 9, focus on the left half: [7].
5. Finally, you find 7!

What is the time complexity of binary search?

The time complexity of binary search is O(log n), which makes it very efficient for large datasets compared to linear search.