<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>

#include <cstdlib>

class Solution {
public:
    string addBinary(string a, string b) {
        string sum="";
        int diff=std::abs(static_cast<int>(a.length())-static_cast<int>(b.length()));
        string zeros="";
        int i=0;
        while(i<diff){
            zeros='0'+zeros;
            i++;
        }
        if(a.length()>b.length())  b=zeros+b;
        else if(a.length()<b.length())  a=zeros+a;

        int carry=0;
        for(int i=a.length()-1;i>=0;i--){
            if(a[i]=='1' && b[i]=='1'){
                if(carry==0) sum='0'+sum; //carry reamain 0
                if(carry==1) sum='1'+sum;
                carry=1;
            }
            else if(a[i]=='0' && b[i]=='0'){
                if(carry==0) sum='0'+sum; //carry reamain 0
                if(carry==1) sum='1'+sum;
                carry=0;
            }
            else{
                // 0,1 or 1,0
                if(carry==0){
                    sum='1'+sum;
                    carry=0;}
                if(carry==1){
                    sum='0'+sum;;
                    carry=1;}
            }
        }
        if(carry==1) sum='1'+sum;
        return sum;
    }
};
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