Check if two given Rational Numbers are equal or not

Given two stringsS and T representing non-negative rational numbers, the task is to check if the values of S and T are equal or not. If found to be true, then print "YES". Otherwise, print "NO".

Note: Any rational number can 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))

Examples:

Input: S = "0.(52)", T = "0.5(25)"
Output: YES
Explanation: The rational number "0.(52)" can be represented as 0.52525252... The rational number "0.5(25)" can be represented as 0.525252525.... Therefore, the required output is "YES".

Input: S = "0.9(9)", T = "1." Output: YES Explanation: The rational number "0.9(9)" can be represented as 0.999999999..., it is equal to 1. The rational number "1." can be represented as the number 1. Therefore, the required output is "YES".

Approach: The idea is to convert the rational numbers into fractions and then check if fractions of both the rational numbers are equal or not. If found to be true, then print "YES". Otherwise, print "NO". Following are the observations:

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.

Any rational numbers can be converted into fractions based on the following observations:

Let x = 0.5(25) —> (1) Integer part = 0, Non-repeating part = 5, Repeating part = 25 Multiply both sides of equation (1) by 10 raised to the power of length of non-repeating part, i.e. 10 * x = 5.(25) —> (2) Multiply both sides of equation (1) by 10 raised to the power of (length of non-repeating part + length of repeating part), 1000 * x = 525.(25) —> (3) Subtract equation (2) from equation (3)
1000 * x - 10 * x = 525.(25)-5.(25)
990 * x = 520
? x = 520 / 990

Follow the steps below to solve the problem:

• Convert both the rational numbers into fractions using the above observations.
• Check if both the fractions of the numbers are equal or not. If found to be true, then print "YES".
• Otherwise, print "NO".

Below is the implementation of the above approach:

YES

Time Complexity: O(N), where N is the maximum length of S and TAuxiliary Space: O(1)