#972

Equal Rational Numbers

hard · verified · 46% accepted · 106 likes · top 30%

math · string

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Description

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.

A rational number can be represented using up to three parts: <IntegerPart>, <NonRepeatingPart>, and a <RepeatingPart>. The number will be represented in one of the following three ways:

 - <IntegerPart>

- For example, 12, 0, and 123.



- <IntegerPart><.><NonRepeatingPart>

- For example, 0.5, 1., 2.12, and 123.0001.



- <IntegerPart><.><NonRepeatingPart><(><RepeatingPart><)>

- For example, 0.1(6), 1.(9), 123.00(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).

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) = "".

Solution