RecurringNumbers (google code jam china 1000分真題)

 

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 in decimalNumber, 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 decimalNumber)
(be sure your method is public)

Constraints

-

decimalNumber will have between 3 and 10 characters inclusive.

-

decimalNumber will contain only characters '0' - '9', '.', '(' and ')'.

-

The second character in decimalNumber will always be '.'.

-

There will be at most one '(' and ')' in decimalNumber.

-

'(' in decimalNumber will be followed by one or more digits ('0' - '9'), followed by ')'.

-

')' in decimalNumber will not be followed by any other character.

Examples

0)

"0.(3)"

Returns: "1/3"

0.(3) = 0.333... = 1/3

1)

"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)

"2.85(23)"

Returns: "14119/4950"

2.85(23) = 2.852323... = 285/100 + 23/9900 = 28238/9900 = 14119/4950. Make sure to reduce the fraction, as shown in the final step.

3)

"9.123(456)"

Returns: "3038111/333000"

4)

"0.111(1)"

Returns: "1/9"

5)

"3.(000)"

Returns: "3/1"

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