【C++】两个字符串相加

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

思路：对于两个string a，b从后往前取值，若取值为空则赋值为0.设置进制符号flag；
若a[i]+b[i]+flag == 3 则 c[i]=1 flag =1;若a[i]+b[i]+flag == 2 则 c[i]=0 flag =1;
若a[i]+b[i]+flag == 1 则 c[i]=1 flag =0;若a[i]+b[i]+flag == 0 则 c[i]=0 flag =0;

string addBinary(string a, string b) {
int lenA = a.size();
int lenB = b.size();
int lenC = lenA>lenB?lenA:lenB;
int flag = 0;

string c(lenC,'1');
//将a，b变成等长字符串，对短的字符串前面补'0'
if(lenA>lenB){
string temp(lenC-lenB,'0');
b=temp+b;
}
else if(lenA<lenB){
string temp(lenC-lenA,'0');
a=temp+a;
}
// 判断是否需要进位
for(int i=lenC-1;i>=0;--i){
if(a[i]-'0'+b[i]-'0'+flag==3){
c[i]='1';
flag =1;
}
else if(a[i]-'0'+b[i]-'0'+flag==2){
c[i]='0';
flag =1;
}
else if(a[i]-'0'+b[i]-'0'+flag==1){
c[i]='1';
flag =0;
}
else if(a[i]-'0'+b[i]-'0'+flag==0){
c[i]='0';
flag =0;
}

}
//如果溢出的话
if((a[0]-'0'+b[0]-'0'+flag)>=2){
c="1"+c;
}
return c;
}

if((a[0]-'0'+b[0]-'0'+flag)>=2){
c="1"+c;
}