<p>Given two non-negative integers, <code>num1</code> and <code>num2</code> represented as string, return <em>the sum of</em> <code>num1</code> <em>and</em> <code>num2</code> <em>as a string</em>.</p>

<p>You must solve the problem without using any built-in library for handling large integers (such as <code>BigInteger</code>). You must also not convert the inputs to integers directly.</p>

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

<pre>
<strong>Input:</strong> num1 = &quot;11&quot;, num2 = &quot;123&quot;
<strong>Output:</strong> &quot;134&quot;
</pre>

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

<pre>
<strong>Input:</strong> num1 = &quot;456&quot;, num2 = &quot;77&quot;
<strong>Output:</strong> &quot;533&quot;
</pre>

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

<pre>
<strong>Input:</strong> num1 = &quot;0&quot;, num2 = &quot;0&quot;
<strong>Output:</strong> &quot;0&quot;
</pre>

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

<ul>
	<li><code>1 &lt;= num1.length, num2.length &lt;= 10<sup>4</sup></code></li>
	<li><code>num1</code> and <code>num2</code> consist of only digits.</li>
	<li><code>num1</code> and <code>num2</code> don&#39;t have any leading zeros except for the zero itself.</li>
</ul>

class Solution {
public:
    string add(string num1 , string num2){
        int zyada=0;
        int n1=num1.size()-1;
        int n2=num2.size()-1;
        string ans;
        int sum;
        while( n2>= 0)
        {
            sum=num1[n1--]-'0'+ num2[n2--]-'0' +zyada;
            char c = '0' + sum %10;
            zyada= sum/10;
            ans = c + ans;
        }
        if( n1 == n2  && zyada == 1)
        {
            char c ='0'+1;
           ans= c + ans; 
           n1--;
        }
        while(n1 >=0 )
        {
            sum =num1[n1--] -'0' +zyada;
            char c ='0' +sum%10;
            zyada = sum/10;
            ans = c+ans ;
        }
        if( n1 ==-1 && zyada == 1){
            char c ='0' +1; 
           ans= c + ans;
        }
        return ans;
    }
    string addStrings(string num1, string num2) {
       if(num1.size() >= num2.size())
       return add(num1,num2);
       else
       return add(num2,num1);
    }
};
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