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g0901_1000.s0972_equal_rational_numbers.readme.md Maven / Gradle / Ivy

972\. Equal Rational Numbers

Hard

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: ``, ``, and a ``. The number will be represented in one of the following three ways:

*   ``
    *   For example, `12`, `0`, and `123`.
*   **<.>**
    *   For example, `0.5`, `1.`, `2.12`, and `123.0001`.
*   **<.>****<(>****<)>**
    *   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.](https://en.wikipedia.org/wiki/0.999...)] "1." represents the number 1, which is formed correctly: (IntegerPart) = "1" and (NonRepeatingPart) = "".

**Constraints:**

*   Each part consists only of digits.
*   The `` does not have leading zeros (except for the zero itself).
*   `1 <= .length <= 4`
*   `0 <= .length <= 4`
*   `1 <= .length <= 4`