592. Fraction Addition and Subtraction

Difficulty: Medium

Topics: Math, String, Simulation

Given a string expression representing an expression of fraction addition and subtraction, return the calculation result in string format.

The final result should be an irreducible fraction. If your final result is an integer, change it to the format of a fraction that has a denominator 1. So in this case, 2 should be converted to 2/1.

Example 1:

• Input: expression = "-1/2+1/2"
• Output: "0/1"

Example 2:

• Input: expression = "-1/2+1/2+1/3"
• Output: "1/3"

Example 3:

• Input: expression = "1/3-1/2"
• Output: "-1/6"

Constraints:

• The input string only contains '0' to '9', '/', '+' and '-'. So does the output.
• Each fraction (input and output) has the format ±numerator/denominator. If the first input fraction or the output is positive, then '+' will be omitted.
• The input only contains valid irreducible fractions, where the numerator and denominator of each fraction will always be in the range [1, 10]. If the denominator is 1, it means this fraction is actually an integer in a fraction format defined above.
• The number of given fractions will be in the range [1, 10].
• The numerator and denominator of the final result are guaranteed to be valid and in the range of 32-bit int.

Solution:

We need to carefully parse the input string and perform arithmetic operations on the fractions. The steps are as follows:

1. Parse the Input Expression: Extract individual fractions from the expression string.
2. Compute the Result: Add or subtract the fractions step by step.
3. Simplify the Result: Convert the final fraction to its irreducible form.

Let's implement this solution in PHP: 592. Fraction Addition and Subtraction

<?php
// Example usage
echo fractionAddition("-1/2+1/2"); // Output: "0/1"
echo "\n";
echo fractionAddition("-1/2+1/2+1/3"); // Output: "1/3"
echo "\n";
echo fractionAddition("1/3-1/2"); // Output: "-1/6"
?>

Explanation:

• gcd function: Computes the greatest common divisor of two numbers, which helps in simplifying the fraction.
• addFractions function: Adds two fractions. It computes the common denominator, adjusts the numerators accordingly, adds them, and then simplifies the resulting fraction.
• fractionAddition function: This is the main function that parses the input expression, uses regular expressions to extract all the fractions, and iteratively adds them up using the addFractions function.

Test Cases:

• fractionAddition("-1/2+1/2") returns "0/1".
• fractionAddition("-1/2+1/2+1/3") returns "1/3".
• fractionAddition("1/3-1/2") returns "-1/6".

This solution handles all the required operations and returns the correct output for each given expression.

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