Now you know the binary search algorithm inside and out. You can flawlessly implement it yourself, or take advantage of the standard library in Python. Having tapped into the concept of time-space complexity, you’re able to choose the best search algorithm for the given situation.

**Now you can:**

- Use the
module to do a binary search in Python`bisect`

- Implement binary search in Python
**recursively**and**iteratively** - Recognize and fix
**defects**in a binary search Python implementation - Analyze the
**time-space complexity**of the binary search algorithm - Search even
**faster**than binary search

**Congratulations, you made it to the end of the course!** What’s your #1 takeaway or favorite thing you learned? How are you going to put your newfound skills to use? Leave a comment in the *discussion* section and let us know.

hughdbrownon Oct. 27, 2020You mentioned that you should be careful to avoid integer overflow in calculating your middle index. Your preferred way was:

`middle = left + (right - left) // 2`

And this is fine, but there is a related way to do division by two:

`middle = left + (right - left) >> 1`

And the problem is that integer-division has different precedence from right-shift. To see this, take an example:

And the problem is that right-shift has lower precedence than plus, so

`left + (right - left) >> 1`

is the same as`(left + (right - left)) >> 1`

, and that is not what you want.I’d recommend using parentheses so clearly mark the desired grouping since it is easy to get wrong.