<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:
    void addRE(string &num1, int p1, string num2, int p2,int carry, string &ans){
        // base case
        if(p1<0 &&p2 <0){
            if(carry!=0){
                ans.push_back(carry+'0');
                
            }
            return;
        }

        //process
        int n1= (p1>=0? num1[p1] :'0')-'0';
        int n2= (p2>=0? num2[p2]:'0')-'0';
        int sum=n1+n2+carry;
        int digit=sum%10;
        carry=sum/10;
        ans.push_back(digit+'0');

        //RE
        addRE(num1, p1-1, num2, p2-1,carry, ans);

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