Given two strings S and T, each of which represents a non-negative rational number, return True if and only if they represent the same number. The strings may use parentheses to denote the repeating part of the rational number.
In general a rational number can be represented using up to three parts: an integer part, a non-repeating part, and a repeating part. The number will be represented in one of the following three ways:
- (e.g. 0, 12, 123)
- <.> (e.g. 0.5, 1., 2.12, 2.0001)
- <.><(><)> (e.g. 0.1(6), 0.9(9), 0.00(1212))
The repeating portion of a decimal expansion is conventionally denoted within a pair of round brackets. For example:
1 / 6 = 0.16666666... = 0.1(6) = 0.1666(6) = 0.166(66)
Both 0.1(6) or 0.1666(6) or 0.166(66) are correct representations of 1 / 6.
Example 1:
Input: S = "0.(52)", T = "0.5(25)"
Output: true
Explanation:
Because "0.(52)" represents 0.52525252..., and "0.5(25)" represents 0.52525252525..... , the strings represent the same number.
Example 2:
Input: S = "0.1666(6)", T = "0.166(66)"
Output: true
Example 3:
Input: S = "0.9(9)", T = "1."
Output: true
Explanation:
"0.9(9)" represents 0.999999999... repeated forever, which equals 1. [See this link for an explanation.]
"1." represents the number 1, which is formed correctly: (IntegerPart) = "1" and (NonRepeatingPart) = "".
Note:
- Each part consists only of digits.
- The will not begin with 2 or more zeros. (There is no other restriction on the digits of each part.)
- 1 <= .length <= 4
- 0 <= .length <= 4
- 1 <= .length <= 4