972. Equal Rational Numbers

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>
    <ul>
	<li>For example, <code>12</code>, <code>0</code>, and <code>123</code>.</li>
</ul>
</li>
<li><code>&lt;IntegerPart&gt;<strong>&lt;.&gt;</strong>&lt;NonRepeatingPart&gt;</code>
<ul>
	<li>For example, <code>0.5</code>, <code>1.</code>, <code>2.12</code>, and <code>123.0001</code>.</li>
</ul>
</li>
<li><code>&lt;IntegerPart&gt;<strong>&lt;.&gt;</strong>&lt;NonRepeatingPart&gt;<strong>&lt;(&gt;</strong>&lt;RepeatingPart&gt;<strong>&lt;)&gt;</strong></code>
<ul>
	<li>For example, <code>0.1(6)</code>, <code>1.(9)</code>, <code>123.00(1212)</code>.</li>
</ul>
</li>

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) = "".

 

Constraints:

  • Each part consists only of digits.
  • The <IntegerPart> does not have leading zeros (except for the zero itself).
  • 1 <= <IntegerPart>.length <= 4
  • 0 <= <NonRepeatingPart>.length <= 4
  • 1 <= <RepeatingPart>.length <= 4

Solutions