题目

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

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

分析

计算两个二进制数之和，思路和代码类似于大整数相加，只是十进制改为二进制，对应位数字相加，将进位进上去。
需要注意的是""+"",""+"0","0"+"1"几个特殊的情况。

char* addBinary(char* a, char* b) {
    int alength=0,blength=0;
    while(a[alength]!='\0')
        alength++;
    while(b[blength]!='\0')
        blength++;
    if(alength==0&&blength==0)
    {
        return "0";
    }
    char *ans=(char *)malloc(sizeof(char)*(alength+blength+1));
    
    int anslength=0;
    int temp=0,i=0;
    while(i<alength&&i<blength)
    {
        temp=temp+a[alength-i-1]-'0'+b[blength-i-1]-'0';
        if(temp>1)
        {
            ans[alength+blength-1-anslength]=temp%2+'0';
            temp=temp/2;
        }
        else
        {
            ans[alength+blength-1-anslength]=temp+'0';
            temp=0;
        }
        anslength++;
        i++;
    }
    while(i<alength)
    {
        temp=temp+a[alength-i-1]-'0';
        if(temp>1)
        {
            ans[alength+blength-1-anslength]=temp%2+'0';
            temp=temp/2;
        }
        else
        {
            ans[alength+blength-1-anslength]=temp+'0';
            temp=0;
        }
        anslength++;
        i++;
    }
    while(i<blength)
    {
        temp=temp+b[blength-i-1]-'0';
        if(temp>1)
        {
            ans[alength+blength-1-anslength]=temp%2+'0';
            temp=temp/2;
        }
        else
        {
            ans[alength+blength-1-anslength]=temp+'0';
            temp=0;
        }
        anslength++;
        i++;
    }
    if(temp>0)
    {
        ans[alength+blength-1-anslength]=temp+'0';
        anslength++;
    }
    printf("%d %d %d\n",alength,blength,anslength);
    ans[alength+blength]='\0';
    return ans+alength+blength-anslength;
}