Add Binary

Given two binary strings, return their sum (also a binary string).

For example,
a = "11"
b = "1"
Return "100".

思路：逐位相加，进位保留在和的下一位中。

C++实现代码：

#include<iostream>
#include<string>
#include<vector>
using namespace std;class Solution
{
public:string addBinary(string a, string b){int size1=a.size()-1;int size2=b.size()-1;int size=max(size1,size2);string digits(size+1,'0');while(size1>=0&&size2>=0){if((a[size1]=='1')&&(b[size2]=='1')){digits[size-1]='1';if(size1==0&&size2==0)digits.insert(digits.begin(),'1');size1--;size2--;size--;}else if(((a[size1]=='1')||(b[size2]=='1'))&&(digits[size]=='0')){digits[size]='1';size1--;size2--;size--;}else if(((a[size1]=='1')||(b[size2]=='1'))&&(digits[size]=='1')){digits[size]='0';digits[size-1]='1';if(size1==0&&size2==0)digits.insert(digits.begin(),'1');size1--;size2--;size--;}else{digits[size]=digits[size];size1--;size2--;size--;}}cout<<digits<<endl;if(size1>=0){while(size1>=0&&size>=0){if((digits[size]=='1')&&(a[size1]=='1')){digits[size]='0';digits[size-1]='1';if(size==0)digits.insert(digits.begin(),'1');size1--;size--;}else if((digits[size]=='1')&&(a[size1]=='0')){size1--;size--;}else{digits[size]=a[size1];size--;size1--;}}}if(size2>=0){while(size2>=0&&size>=0){if((digits[size]=='1')&&(b[size2]=='1')){digits[size]='0';digits[size-1]='1';//最前面两个数相加需要进位的时候，在前面插入1if(size==0)digits.insert(digits.begin(),'1');size2--;size--;}else if((digits[size]=='1')&&(b[size2]=='0')){size2--;size--;}else{digits[size]=b[size2];size--;size2--;}}}return digits;}
};
int main()
{string b="100";string a="110010";Solution s;cout<<"digits: "<<s.addBinary(a,b)<<endl;
}

只能想到这么麻烦的方法，哎。。。

    string addBinary(string a, string b) {if(a.empty())return b;if(b.empty())return a;int carry=0;int i=a.size()-1;int j=b.size()-1;string res;int sum=0;while(i>=0&&j>=0){sum=a[i--]-'0'+b[j--]-'0'+carry;if(sum>=2){char c=sum%2+'0';res=c+res;carry=1;}else{char c=sum+'0';res=c+res;carry=0;}}while(i>=0){sum=carry+a[i--]-'0';if(sum>=2){char c=sum%2+'0';res=c+res;carry=sum/2;}else{char c=sum+'0';res=c+res;carry=0;}}while(j>=0){sum=carry+b[j--]-'0';if(sum>=2){char c=sum%2+'0';res=c+res;carry=sum/2;}else{char c=sum+'0';res=c+res;carry=0;}}if(carry==1)res.insert(0,"1");return res;}

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