Leetcode67 二进制求和

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

思路：二进制加法和普通加法的思路没什么差别，甚至更简单。所需要注意的细节就是进位。从最低位开始，进位可能伴随计算直到最高位。所以每一位的加法运算都要将上一次的进位加进去。

对于某一位a和b，上一为的进位c，该为求和之后的和是(a+b+c)%2，进位是(a+b+c)/2

class Solution {
public:
    string addBinary(string a, string b) {
        if(a.size()==0||a=="0") return b;
        if(b.size()==0||b=="0") return a;
        int lena=a.size()-1,lenb=b.size()-1,increase=0;
        string sum="";
        while(lena>=0 && lenb>=0)
        {
            sum=std::to_string((a[lena]-'0' + b[lenb] - '0' + increase)%2) + sum;
            increase=(a[lena]-'0' + b[lenb] - '0' + increase)/2;
            lena--;
            lenb--;
        }
        while(lena>=0)
        {
            sum=std::to_string((increase+a[lena]-'0')%2)+sum;
            increase=(a[lena]-'0'+increase)/2;
            lena--;
        }
        while(lenb>=0)
        {
            sum=std::to_string((increase+b[lenb]-'0')%2)+sum;
            increase=(b[lenb]-'0'+increase)/2;
            lenb--;
        }
       if(increase==1)
            sum="1"+sum;
        return sum;
    }
};