<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 {
public:
    string fractionAddition(string expression) {
        int start=0;
        int end=0;
        bool isNeg=false;
        int n=expression.length();
        int ognum=0;
        int ogdim=1;
        while(end<n)
        {
            int currnum=0;
            int currdim=0;
            if(expression[end]=='+' || expression[end]=='-')
            {
                if(expression[end]=='-')
                {
                    isNeg=true;
                }
                end++;
            }
            start=end;
            while(end<n && isdigit(expression[end]))
            {
                end++;
            }
            currnum=stoi(expression.substr(start,end-start));
            if(isNeg==true)
            {
                currnum=currnum*-1;
                isNeg=false;
            }
            end++;
            start=end;
            while(isdigit(expression[end]))
            {
                end++;
            }
            currdim=stoi(expression.substr(start,end-start+1));
            ognum=(ognum*currdim)+(currnum*ogdim);
            ogdim=(currdim*ogdim);
            int gcd=getgcd(abs(ognum),ogdim);
            ognum/=gcd;
            ogdim/=gcd;
        }
        return to_string(ognum) + "/" + to_string(ogdim);
    }
    public: int getgcd(int a,int b)
    {
        if(a==0)
            return b;
        return getgcd(b%a,a);
    }
};
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