CalkinWilf | Topcoder Archive

Problem Statement

The Calkin-Wilf tree is a rooted tree that contains each positive rational number exactly once. The definition of the tree is really simple:

The root of the tree contains the value 1/1.
Each node in the tree has one left child and one right child.
If a node contains the fraction a/b, its left child contains the fraction a/(a+b) and its right child contains the fraction (a+b)/b.

Here is an ASCII art drawing of the first few levels of the tree:

                ____________1/1____________
               /                           \
        ____1/2____                     ____2/1____
       /           \                   /           \
    1/3             3/2             2/3             3/1
   /   \           /   \           /   \           /   \
1/4     4/3     3/5     5/2     2/5     5/3     3/4     4/1

You are given the String path that describes a path down the tree. We start in the root and we read the characters of path one at a time. Here, 'L' means "go to the left child" and 'R' means "go to the right child".

Find the fraction a/b that will be written in the last node we visit. Return the int[] {a, b}.

Definition

Class:: CalkinWilf
Method:: findRational
Parameters:: String
Returns:: int[]
Method signature:: int[] findRational(String path)
(be sure your method is public)

Notes

The return value should be a int[] with two elements. Element 0 should be the numerator and element 1 should be the denominator of the fraction.

Constraints

path will contain between 0 and 30 characters, inclusive.
Each character in path will be either 'L' or 'R'.

Examples

```
""
```
```
Returns: {1, 1 }
```
If the path is empty, we end where we started: in the root.
```
"R"
```
```
Returns: {2, 1 }
```
Taking a single step right takes us to the node with the value 2/1.
```
"LRR"
```
```
Returns: {5, 2 }
```
This time we go 1/1 -> left to 1/2 -> right to 3/2 -> right to 5/2.

"LRLRLRLRLRLRLRLRLRLRLRLRLRLRLR"

Returns: {2178309, 1346269 }

This is one possible longest valid input.

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