## Python Binary Search Explained

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Binary search is an efficient algorithm used to locate a specific element within a sorted list or array. It works by repeatedly dividing the search interval in half and comparing the middle element with the target value. Based on this comparison, it can quickly determine whether the target element is in the left or right half of the remaining interval.

## Here's how binary search works step by step:

- 1. Start with the entire sorted list or array.
- 2. Calculate the middle index of the current search interval by averaging the indices of the first and last elements.
- 3. Compare the middle element with the target value:
- - If they match, the search is successful, and the index of the target element is returned.
- - If the middle element is greater than the target value, narrow the search interval to the left half of the current interval and repeat the process there.
- - If the middle element is less than the target value, narrow the search interval to the right half of the current interval and repeat the process there.
- 4. Repeat steps 2 and 3 until the target element is found or the search interval becomes empty (indicating that the element is not in the list).

Binary search is an efficient algorithm with a time complexity of O(log n) in the worst-case scenario, where n is the number of elements in the sorted list. This makes it much faster than linear search (O(n)) for large datasets. Binary search is widely used in various applications, including searching in databases, sorting algorithms like quicksort, and data retrieval in computer science and information retrieval systems.