# Exploring Calkin-Wilf Tree

Simple+

The nodes of the Calkin–Wilf tree, when read in level order so that the elements in each level are read from left to right, produce the linear sequence of all possible positive rational numbers. Almost as if by magic, this construction guarantees every positive integer fraction to appear exactly once in this sequence. Even more delightfully, this construction makes every rational number to make its appearance in its lowest reduced form!

The tree is rooted at the number 1 (1/1), and any rational number expressed in simplest terms as the fraction a/b has as its two children the numbers a/(a + b) and (a + b)/b.

Your function should return the `n`:th element of this sequence. Notice, that once you reach the position `n//2 + 1`, the queue already contains the result you need, so you can save a hefty chunk of time and space by not finding any new values. Besides, the linked Wikipedia page and other sources provide additional shortcuts to jump into the given position faster than sloughing your way the hard way there one element at a time.

Input: Integer (int).

Output: Two integers.

Examples:

```assert calkin_wilf(1) == (1, 1)
assert calkin_wilf(2) == (1, 2)
assert calkin_wilf(3) == (2, 1)
assert calkin_wilf(10) == (3, 5)
```

The mission was taken from Python CCPS 109. It is taught for Ryerson Chang School of Continuing Education by Ilkka Kokkarinen

Settings
Code:
Other:
Invalid hot key. Each hot key should be unique and valid
Hot keys:
•  to Run Code: to Check Solution: to Stop:
CheckiO Extensions

CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.

In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

`pip3 install checkio_client`

`checkio --domain=py config --key=`

Sync solutions into your local folder

`checkio sync`

(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)

`checkio serv -d`

Alternatevly, you can install Chrome extension or FF addon

`checkio install-plugin`
`checkio install-plugin --ff`
`checkio install-plugin --chromium`

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.

Pair Programming (Beta-version)

Welcome to Pair Programming! Engage in real-time collaboration on coding projects by starting a session and sharing the provided unique URL with friends or colleagues. This feature is perfect for joint project development, debugging, or learning new skills together. Simply click 'Start Session' to begin your collaborative coding journey!

Waiting for Pair Programming to start...

You are trying to join a pair programming session that has not started yet.

Please wait for the session creator to join.

Waiting for Pair Programming to reconnect...

It looks like the creator of the pair programming session closed the editor window.

It might happen accidentally, so that you can wait for reconnection.