Binary search in 3 min python

sure! let's dive into binary search, a highly efficient algorithm for finding an item from a sorted list of items.

### what is binary search?

binary search operates on sorted arrays (or lists) by repeatedly dividing the search interval in half. if the target value is less than the middle element, it narrows the interval to the lower half. otherwise, it narrows it to the upper half. this process continues until the target value is found or the interval is empty.

### how it works

1. **initial setup**: start with two pointers, one at the beginning (`low`) and one at the end (`high`) of the list.
2. **middle element**: calculate the middle index (`mid`).
3. **comparison**:
- if the middle element is equal to the target value, you have found the target.
- if the target is less than the middle element, continue the search in the left half.
- if the target is greater, continue in the right half.
4. **repeat**: continue this process until the target is found or the pointers cross (`low high`).

### time complexity

- the time complexity of binary search is \( o(\log n) \), making it much faster than linear search \( o(n) \) for large datasets.

### python implementation

here’s a simple implementation of binary search in python:

### explanation of the code

1. **function definition**: the `binary_search` function takes a sorted list `arr` and the `target` value to find.
2. **while loop**: it continues as long as `low` is less than or equal to `high`.
3. **mid calculation**: the middle index `mid` is calculated.
4. **value comparison**: the function checks if the middle element is the target, or if it should search the left or right half.
5. **return value**: if the target is found, it returns the index; otherwise, it returns -1.

### conclusion

binary search is a powerful technique for efficiently finding elements in a sorted list. remember, the list must be sorted; otherwise, the binary search won't work correctly. this method drastically reduces the nu ...

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