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.]
"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

Rust Solution

struct Solution;

impl Solution {
    fn is_rational_equal(s: String, t: String) -> bool {
        let a = Self::parse(s);
        let b = Self::parse(t);
        dbg!(a);
        dbg!(b);
        (a - b).abs() < std::f64::EPSILON
    }

    fn parse(s: String) -> f64 {
        let n = s.len();
        if let Some(dot) = s.find('.') {
            let integer_part = &s[..dot];
            if let Some(lparen) = s.find('(') {
                let non_repeating_part = &s[dot + 1..lparen];
                let repeating_part = &s[lparen + 1..n - 1];
                Self::rational(integer_part, non_repeating_part, repeating_part)
            } else {
                let non_repeating_part = &s[dot + 1..];
                Self::rational(integer_part, non_repeating_part, "")
            }
        } else {
            s.parse::<f64>().unwrap()
        }
    }

    fn rational(integer_part: &str, non_repeating_part: &str, repeating_part: &str) -> f64 {
        let a = integer_part.parse::<f64>().unwrap_or(0.0);
        let n = non_repeating_part.len();
        let b = non_repeating_part.parse::<f64>().unwrap_or(0.0);
        let m = repeating_part.len();
        let c = repeating_part.parse::<f64>().unwrap_or(0.0);
        let mut d = 0.0;
        for _ in 0..m {
            d *= 10.0;
            d += 9.0;
        }
        let mut e = 1.0;
        for _ in 0..n {
            e *= 10.0;
        }
        if n == 0 && m == 0 {
            return a;
        }
        if n == 0 {
            return a + c / d;
        }
        if m == 0 {
            return a + b / e;
        }
        a + (b + c / d) / e
    }
}

#[test]
fn test() {
    let s = "0.(52)".to_string();
    let t = "0.5(25)".to_string();
    let res = true;
    assert_eq!(Solution::is_rational_equal(s, t), res);
    let s = "0.1666(6)".to_string();
    let t = "0.166(66)".to_string();
    let res = true;
    assert_eq!(Solution::is_rational_equal(s, t), res);
    let s = "0.9(9)".to_string();
    let t = "1.".to_string();
    let res = true;
    assert_eq!(Solution::is_rational_equal(s, t), res);
}

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