Problem 1900. GJam 2014 China Rd A: Rational Number Tree (Large Values)

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 Large Challenge with a Max of 64 Tree levels. Processing of uint64 size data requires extra care.Consider an infinite complete binary tree where the root node is 1/1 and the left and right children 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 a uint64 integer node or [P,Q] (double) are terms of a NodeOutput: [P,Q](double) or [N](uint64) 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 only 368 able to process the large data set in less than 3 hours.Notes:1) Matlab has issues with uint64 for dec2bin and matrix multiplies.2) Example of uint64 read is provided in test suite comments3) Bitshift and bitget work on uint64

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 Large Challenge with a Max of 64 Tree levels. Processing of uint64 size data requires extra care.

Consider an infinite complete binary tree where the root node is 1/1 and the left and right children 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 a uint64 integer node or [P,Q] (double) are terms of a Node

*Output:* [P,Q](double) or [N](uint64) 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 only 368 able to process the large data set in less than 3 hours.

*Notes:*

1) Matlab has issues with uint64 for dec2bin and matrix multiplies.

2) Example of uint64 read is provided in test suite comments

3) Bitshift and bitget work on uint64

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Problem 1900. GJam 2014 China Rd A: Rational Number Tree (Large Values)

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Problem 1900. GJam 2014 China Rd A: Rational Number Tree (Large Values)

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