What is binary search and can you give me an example?

What is binary search and can you give me an example?

Binary search is an efficient algorithm for finding an item from a sorted list of items. It works by repeatedly dividing the search interval in half. If the value of the search key is less than the item in the middle of the interval, the search continues in the lower half, or if it's greater, in the upper half. For example, if you have a sorted array [1, 3, 5, 7, 9] and you want to find the number 5, binary search will check the middle element (5) and find it immediately.

Can you explain how the algorithm works step by step?

Sure! Here’s how binary search works step by step:

1. Start with two pointers, one at the beginning (low) and one at the end (high) of the array.
2. Calculate the middle index: mid = (low + high) / 2.
3. Compare the middle element with the target value:
   • If it’s equal, you’ve found the target.
   • If it’s less, move the low pointer to mid + 1.
   • If it’s greater, move the high pointer to mid - 1.
4. Repeat steps 2-3 until the target is found or the pointers cross.

What is the time complexity of binary search?

The time complexity of binary search is O(log n), where n is the number of elements in the array. This is because the algorithm halves the search space with each step.

Can binary search be used on unsorted arrays?

No, binary search requires the array to be sorted. If the array is unsorted, you would need to sort it first before applying binary search.