package leetcode;
/* Given two binary strings, return their sum (also a binary string).
 * For example,
 * a = "11"
 * b = "1"
 * Return "100".
 */
import java.lang.Math;

public class AddBinary {
	public String addBinary(String a, String b) {    
		if (a == null || a.length() == 0) //如果a為空，則返回b；反之則返回a
			return
 
 b;
		if (b == null || b.length() == 0)
			return a;
		int i = a.length() - 1; //獲取a,b的長
		int j = b.length() - 1;
		int carry = 0;     //進位標誌，初始化為0
		StringBuilder res = new StringBuilder();
		while (i >= 0 && j >= 0) {   // a，b都不為空時，從後往前遍歷，從低位開始相加
			int digit = (int) (a.charAt(i) - '0' + b.charAt
 
(j) - '0') + carry;
			carry = digit / 2;  //儲存下一個carry位：逢2進位
			digit %= 2;         //取餘，儲存當前位（進位後）的值
			res.insert(0, digit);   //插入到res中
			i--;  
			j--;
		}
		//a更長時，處理a餘下的數位
		while (i >= 0) {   
			int digit = (int) (a.charAt(i) - '0') + carry;
			carry = digit / 2;
			digit %= 2;
			res.insert(0, digit)
 
;
			i--;
		}
		//b更長時，處理b餘下的數位
		while (j >= 0) {
			int digit = (int) (b.charAt(j) - '0') + carry;
			carry = digit / 2;
			digit %= 2;
			res.insert(0, digit);
			j--;
		}
		//加完之後，第一位也需進位
		if (carry > 0) {
			res.insert(0, carry);
		}
		return res.toString();
	}
}