972. Equal Rational Numbers

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:

• <IntegerPart> (e.g. 0, 12, 123)
• <IntegerPart><.><NonRepeatingPart> (e.g. 0.5, 1., 2.12, 2.0001)
• <IntegerPart><.><NonRepeatingPart><(><RepeatingPart><)> (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.](https://en.wikipedia.org/wiki/0.999...)]
"1." represents the number 1, which is formed correctly: (IntegerPart) = "1" and (NonRepeatingPart) = "".

Note:

1. Each part consists only of digits.
2. The <IntegerPart> will not begin with 2 or more zeros. (There is no other restriction on the digits of each part.)
3. 1 <= <IntegerPart>.length <= 4
4. 0 <= <NonRepeatingPart>.length <= 4
5. 1 <= <RepeatingPart>.length <= 4

# @lc code=start
using LeetCode

function is_rational_equal(s::String, t::String)
    function to_rational(s::String)::Rational
        pos1, pos2 = findfirst('.', s), findfirst('(', s)
        (pos1 === nothing) && return parse(Int, s)
        (pos1 == length(s)) && return parse(Int, s[1:end-1])
        pos2 === nothing && return parse(Int, s[1:pos1-1]) + parse(Int, s[pos1 + 1:end]) // 10 ^ (length(s) - pos1)
        pos3 = findlast(')', s)
        int_part = parse(Int, s[1:pos1-1]) |> Rational
        nr_part = pos1 == pos2 - 1 ? 0 : parse(Int, s[pos1+1:pos2-1]) // 10 ^ (pos2 - pos1 - 1)
        rp_part = parse(Int, s[pos2+1:pos3-1]) // (10 ^ (pos3 - pos2 - 1) - 1) // 10 ^ (pos2 - pos1 - 1)
        int_part + nr_part + rp_part
    end
    to_rational(s) == to_rational(t)
end
# @lc code=end
is_rational_equal("0.9(9)", "1.")

true

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