<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 addStrings(string num1, string num2) {
        bool carry = false;
        string sum = "";
        int t;
        while (num1.size() < num2.size()) {
            num1 = "0" + num1;
        }
        while (num1.size() > num2.size()) {
            num2 = "0" + num2;
        }
        for (int i = num1.size() - 1; i >= 0; i--) {
            t = (toNum(num1[i]) + toNum(num2[i]) + carry);
            carry = t >= 10;
            sum += toChar(t % 10);
        }
        reverse(sum.begin(), sum.end());
        if (carry) sum = "1" + sum;
        return sum;
    }
    int toNum(char ch) {
        return int(ch) - 48;
    }
    char toChar(int num) {
        return char(num + 48);
    }
};
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