67. Add Binary

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

For example,
a = "11"
b = "1"

Return "100".

二进制相加，使用数组存下每一位带carry的相加，最长长度不会超过a.length+b.length

取较短的位数相加，较短到较长的位数，长的串和carry相加，较长到a.length+b.length这段区间，和carry相加直到进位为0

 public static String addBinary(String a, String b)
	{
		int alen=a.length();
		int blen=b.length();
		int minlen=alen<blen?alen:blen;
		int maxlen=alen==minlen?blen:alen;
		int len=alen+blen;
		int[] num=new int[len];
		int carry=0;
		for(int i=0;i<minlen;i++)
			{
				num[len-1-i]=a.charAt(alen-1-i)-'0'+b.charAt(blen-1-i)-'0'+carry;
				carry=num[len-1-i]/2;
				num[len-1-i]%=2;
			}
		
		for(int i=minlen;i<maxlen;i++)
		{
			if(alen==maxlen)
				num[len-1-i]=a.charAt(alen-1-i)-'0'+carry;
			else {
				num[len-1-i]=b.charAt(blen-1-i)-'0'+carry;
			}
			carry=num[len-1-i]/2;
			num[len-1-i]%=2;
		}
		
		for(int i=maxlen;i<len;i++)
		{
			num[len-1-i]+=carry;
			carry=num[len-1-i]/2;
			if(carry==0)
				break;
			num[len-1-i]%=2;
		}
		
		
		int start=-1;
		for(int i=0;i<len;i++)
			if(num[i]!=0)
			{
				start=i;
				break;
			}
		
		if(start==-1)
			return "0";
		
		StringBuilder sb=new StringBuilder();
		for(int i=start;i<len;i++)
			sb.append(num[i]);
		
		return sb.toString();
	}