<p>Given a string <code>expression</code> representing an expression of fraction addition and subtraction, return the calculation result in string format.</p>

<p>The final result should be an <a href="https://en.wikipedia.org/wiki/Irreducible_fraction" target="_blank">irreducible fraction</a>. If your final result is an integer, change it to the format of a fraction that has a denominator <code>1</code>. So in this case, <code>2</code> should be converted to <code>2/1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;-1/2+1/2&quot;
<strong>Output:</strong> &quot;0/1&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;-1/2+1/2+1/3&quot;
<strong>Output:</strong> &quot;1/3&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;1/3-1/2&quot;
<strong>Output:</strong> &quot;-1/6&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The input string only contains <code>&#39;0&#39;</code> to <code>&#39;9&#39;</code>, <code>&#39;/&#39;</code>, <code>&#39;+&#39;</code> and <code>&#39;-&#39;</code>. So does the output.</li>
	<li>Each fraction (input and output) has the format <code>&plusmn;numerator/denominator</code>. If the first input fraction or the output is positive, then <code>&#39;+&#39;</code> will be omitted.</li>
	<li>The input only contains valid <strong>irreducible fractions</strong>, where the <strong>numerator</strong> and <strong>denominator</strong> of each fraction will always be in the range <code>[1, 10]</code>. If the denominator is <code>1</code>, it means this fraction is actually an integer in a fraction format defined above.</li>
	<li>The number of given fractions will be in the range <code>[1, 10]</code>.</li>
	<li>The numerator and denominator of the <strong>final result</strong> are guaranteed to be valid and in the range of <strong>32-bit</strong> int.</li>
</ul>

class Solution:
    def fractionAddition(self, expression):
        num = 0
        denom = 1

        i = 0
        while i < len(expression):
            curr_num = 0
            curr_denom = 0

            is_negative = False

            # check for sign
            if expression[i] == "-" or expression[i] == "+":
                if expression[i] == "-":
                    is_negative = True
                # move to next character
                i += 1

            # build numerator
            while i < len(expression) and expression[i].isdigit():
                val = int(expression[i])
                curr_num = curr_num * 10 + val
                i += 1

            if is_negative:
                curr_num *= -1

            # skip divisor
            i += 1

            # build denominator
            while i < len(expression) and expression[i].isdigit():
                val = int(expression[i])
                curr_denom = curr_denom * 10 + val
                i += 1

            # add fractions together using common denominator
            num = num * curr_denom + curr_num * denom
            denom = denom * curr_denom

        gcd = abs(self._find_gcd(num, denom))

        # reduce fractions
        num //= gcd
        denom //= gcd

        return f"{num}/{denom}"

    def _find_gcd(self, a, b):
        if a == 0:
            return b
        return self._find_gcd(b % a, a)
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