Problem 1897. GJam 2014 China Rd A: Rational Number Tree

Created by Richard Zapor

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This Challenge is derived from <a href = "http://code.google.com/codejam/contest/2924486/dashboard#s=p1">GJam 2014 China Rational Number Tree</a>.The Goal is to determine the tree node if given [P,Q] or provide the [P,Q] if given a node. This is the small Challenge with a Max of 16 Tree levels. The large Challenge is 64 Tree levels.Consider an infinite complete binary tree where the root node is 1/1 and the left and right childs of node P/Q are P/(P+Q) and (P+Q)/Q, respectively.The Tree looks like:<pre> 1/1
 ______|______
 | |
 1/2 2/1
 ___|___ ___|___
 | | | |
1/3 3/2 2/3 3/1</pre>The nodes are 1/1, 1/2, 2/1, 1/3, 3/2, 2/3, 3/1,...Input: [N] or [P,Q] where N is an integer node or [P,Q] are terms of a NodeOutput: [P,Q] or [N] depends on Input typeExamples:<pre class="language-matlab">[Input] [Output]
 [2] [1 2]
 [1 2] [2]
 [5] [3 2]
 [3 2] [5]
</pre>Contest Performance: Best Delta Time of 14 minutes with 1193 out of 3058 completing in less than 3 hours.

This Challenge is derived from <http://code.google.com/codejam/contest/2924486/dashboard#s=p1 GJam 2014 China Rational Number Tree>.

The Goal is to determine the tree node if given [P,Q] or provide the [P,Q] if given a node. This is the small Challenge with a Max of 16 Tree levels. The large Challenge is 64 Tree levels.

Consider an infinite complete binary tree where the root node is 1/1 and the left and right childs of node P/Q are P/(P+Q) and (P+Q)/Q, respectively.

The Tree looks like:

1/1
    ______|______
    |           |
   1/2         2/1
 ___|___     ___|___
 |     |     |     |
1/3   3/2   2/3   3/1

The nodes are 1/1, 1/2, 2/1, 1/3, 3/2, 2/3, 3/1,...

*Input:* [N] or [P,Q] where N is an integer node or [P,Q] are terms of a Node

*Output:* [P,Q] or [N]  depends on Input type

*Examples:*

[Input]  [Output]
    [2] [1 2]
    [1 2] [2]
    [5] [3 2]
    [3 2] [5]

*Contest Performance:* Best Delta Time of 14 minutes with 1193 out of 3058 completing in less than 3 hours.

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Problem 1897. GJam 2014 China Rd A: Rational Number Tree

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Problem 1897. GJam 2014 China Rd A: Rational Number Tree

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