RecurringNumbers | Topcoder Archive

Problem Statement

A rational number is defined as a/b, where a and b are integers, and b is greater than 0. Furthermore, a rational number can be written as a decimal that has a group of digits that repeat indefinitely. A common method of writing groups of repeating digits is to place them inside parentheses like 2.85(23) = 2.852323 ... 23...

Given a decimal representation of a rational number convert it to a fraction formatted as "numerator/denominator", where both numerator and denominator are integers. The fraction must be reduced. In other words, the denominator must be as small as possible, but greater than zero.

Definition

Class:: RecurringNumbers
Method:: convertToFraction
Parameters:: String
Returns:: String
Method signature:: String convertToFraction(String decimal)
(be sure your method is public)

Constraints

decimal will have between 3 and 10 characters inclusive.
decimal will contain only characters '0' - '9', '.', '(' and ')'.
The second character in decimal will always be '.'.
There will be at most one '(' and ')' in decimal.
'(' in decimal will be followed by one or more digits ('0' - '9'), followed by ')'.
')' in decimal will not be followed by any other character.

Examples

```
"0.(3)"
```
```
Returns: "1/3"
```
0.(3) = 0.333... = 1/3
```
"1.3125"
```
```
Returns: "21/16"
```
Note there are no recurring digits here, although we could write it as 1.3125(0) or 1.3124(9).
```
"2.85(23)"
```
```
Returns: "14119/4950"
```
```
"9.123(456)"
```
```
Returns: "3038111/333000"
```
```
"4.(9)"
```
```
Returns: "5/1"
```
As strange as it seems, but 4.999... is the same as 5.

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