# 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`

``````class Solution {
public:
bool isRationalEqual(string S, string T) {
return helper(S) == helper(T);
}
double helper(string S) {
auto i = S.find('(');
if (i != string::npos) {
string base = S.substr(0, i);
string rep = S.substr(i + 1, (int)S.length() - i - 2);
for (int k = 0; k < 20; ++k) base += rep;
return stod(base);
}
return stod(S);
}
};
``````

Github 同步地址:

https://github.com/grandyang/leetcode/issues/972

https://leetcode.com/problems/equal-rational-numbers/

https://leetcode.com/problems/equal-rational-numbers/discuss/214205/Java-Math-explained

https://leetcode.com/problems/equal-rational-numbers/discuss/214203/JavaC%2B%2BPython-Easy-Cheat

LeetCode All in One 题目讲解汇总(持续更新中…)

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