Add Binary

    题意是计算两个二进制的字符串的和，返回值依然是个二进制字符串。直接写自然不好搞，于是把整个步骤拆解为两个二进制字符与进位相加。实际上任意类似的加法都可以这样拆解。

// add a and b and carry, return a + b + carry.
// carry will be updated when add char.
char add_char(char a, char b, char &c)
{
    if (a == b && a == '1')
    {
        char ret = c;
        c = '1';
        return ret;
    }
    else if (a == b && a == '0')
    {
        char ret = c;
        c = '0';
        return ret;
    }
    else
    {
        if (c == '1')
        {
            return '0';
        }
        else
        {
            return '1';
        }
    }
}

// Given two binary strings, return their sum (also a binary string).
// For example,
// a = "11"
// b = "1"
// Return "100".
string add_binary(string a, string b)
{
    // Init result with the longest string.
    string result = a.size() > b.size() ? a : b;
    // Init carry with '0'.
    char carry = '0';

    const char *pa = a.data() + a.size() - 1;
    const char *pb = b.data() + b.size() - 1;
    string::iterator pc = result.begin() + result.size() - 1;

    while (pa != a.data() - 1 || pb != b.data() - 1)
    {
        if (pa == a.data() - 1)
        {
            *pc-- = add_char('0', *pb--, carry);
        }
        else if (pb == b.data() - 1)
        {
            *pc-- = add_char(*pa--, '0', carry);
        }
        else
        {
            *pc-- = add_char(*pa--, *pb--, carry);
        }
    }

    if (carry == '1')
    {
        return "1" + result;
    }

    return result;
}