<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:

    //FUNCTION FOR SOLVING USING RECURSION:
    string solveUsingRecursion(string& num1,int p1,string& num2,int p2,int carry)
    {
        //BASE CASE:
        if(p1<0 && p2<0)
        {
            if(carry!=0)
            {
                return string(1,carry+'0');
            }
            return "";
        }


        //EK CASE SOLVE KARO:
        int n1 = (p1>=0 ? num1[p1] : '0') - '0';
        int n2 = (p2>=0 ? num2[p2] : '0') - '0';

        int csum = n1+n2+carry;
        int digit = csum%10;
        carry = csum/10;

        string ans = "";


        //BAAKI RECURSION SAMBHAAL LEGA:
        ans+=solveUsingRecursion(num1,p1-1,num2,p2-1,carry);
        ans.push_back(digit+'0');
        return ans;
    }


    string addStrings(string num1, string num2) {
        string ans = solveUsingRecursion(num1,num1.size()-1,num2,num2.size()-1,0);
        // reverse(ans.begin(),ans.end());
        return ans;
    }
};
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