[LeetCode]Add Binary

Given two binary strings, return their sum (also a binary string).
For example, a = “11” b = “1” Return “100”.

class Solution {
public:
    string addBinary(string a, string b) {
        auto aIter = a.end() - 1;
        auto bIter = b.end() - 1;
        string c = ""; //結果
        bool carry = false;//進位
        while(true){//對應位相加
            if(*aIter == *bIter){
                if(carry)
                    c.insert(c.begin(),'1');
                else
                    c.insert(c.begin(),'0');
                if(*aIter =='1')
                    carry = true;
                else
                    carry = false;
            }
            else{
                if(carry)
                    c.insert(c.begin(),'0');
                else
                    c.insert(c.begin(),'1');
            }
            if(aIter == a.begin() || bIter == b.begin())
                break;
            --aIter;
            --bIter;
        }

        //若a,b等長，則不用高位補齊
        if((aIter == a.begin()) && (bIter == b.begin())){
            if(carry) 
                c.insert(c.begin(),'1');
            return c;
        }
        //高位補齊
       auto remE = (aIter == a.begin())? bIter:aIter;
       auto remB = (aIter == a.begin())? (b.begin()):(a.begin());
        while(carry){
            --remE;
            if(*remE == '1')
                c.insert(c.begin(),'0');
            else{
                c.insert(c.begin(),'1');
                carry = false;
            }
            if(remE == remB)
                break;
        }

        if(remE == remB){
            if(carry)        
                c.insert(c.begin(),'1');
        }
        else
           c.insert(c.begin(),remB,remE);
        return c;
}
};