Add Binary 算法详解

算法题目：Given two binary strings, return their sum (also a binary string).

For example,
a = “11”
b = “1”
Return “100”

大致意思：二进制字符串的加法

解题思路：可以用循环与递归来求解

循环版本：

    string addBinary(string a, string b) {
        int c=0;
        int len1=a.size();
        int len2=b.size();
        string ret(max(len1,len2),'0');
        int i=a.size()-1;
        int j=b.size()-1;
        int k=ret.size()-1;

        int m=0;        
        while(k>=0)
        {
            m+=c;
            if(i>=0)
            {
                m+=(a[i]-'0');
            }
            if(j>=0)
            {
                m+=(b[j]-'0');
            }

            c=m/2;
            ret[k]+=m%2;
            m=0;

            i--;
            j--;
            k--;
        }
        return c>0?string(1,c+'0')+ret:ret;
    }

递归版本：

    string addBinaryCore(string a,string b,int c)
    {
        if(a.size()==0&&b.size()==0&&c==0)return "";
        string substra("");
        string substrb("");
        int ca=0;
        int cb=0;
        if(a.size()!=0)
        {
           substra=a.substr(0,a.size()-1); 
           ca=a[a.size()-1]-'0';
        }
        if(b.size()!=0)
        {
            substrb=b.substr(0,b.size()-1);
            cb=b[b.size()-1]-'0';
        }

        int m=(ca+cb+c)%2;
        c=(ca+cb+c)/2;

        return addBinaryCore(substra,substrb,c)+string(1,m+'0');
    }
    string addBinary(string a, string b) {
        return addBinaryCore(a,b,0);
    }