<p>Given two binary strings <code>a</code> and <code>b</code>, return <em>their sum as a binary string</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> a = "11", b = "1"
<strong>Output:</strong> "100"
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> a = "1010", b = "1011"
<strong>Output:</strong> "10101"
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= a.length, b.length &lt;= 10<sup>4</sup></code></li>
	<li><code>a</code> and <code>b</code> consist&nbsp;only of <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code> characters.</li>
	<li>Each string does not contain leading zeros except for the zero itself.</li>
</ul>

class Solution {
public:
    string addBinary(string a, string b) {
        string ans;
        int i = a.size() - 1;
        int j = b.size() - 1;
        int carry = 0;
        while (i >= 0 && j >= 0) {
            if (a[i] - 48 + b[j] - 48 + carry == 1) {
                carry = 0;
                ans = ans + "1";

            } else if (a[i] - 48 + b[j] - 48 + carry == 0) {
                carry = 0;
                ans = ans + "0";

            } else {
              
                if (a[i] - 48 + b[j] - 48 + carry == 2)
                    ans = ans + "0";
                else
                    ans = ans + "1";

                carry = 1;
            }
            i--;
            j--;
        }
       
        while (i >= 0) {
            if (a[i] - 48 + carry == 1) {
                carry = 0;
                ans = ans + "1";

            } else if (a[i] - 48 + carry == 2) {
                carry = 1;
                ans = ans + "0";

            } else {
                ans = ans + "0";
            }
            i--;
        }
        
        while (j >= 0) {
            if (b[j] - 48 + carry == 1) {
                carry = 0;
                ans = ans + "1";

            } else if (b[j] - 48 + carry == 2) {
                carry = 1;
                ans = ans + "0";

            } else {
                ans = ans + "0";
            }
            j--;
        }
     
        while (carry != 0) {
            carry = 0;
            ans = ans + "1";
        }
      
        reverse(ans.begin(), ans.end());
        return ans;
    }
};
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