67. 二进制求和

题目描述： 给定两个二进制字符串，返回他们的和（用二进制表示）。
输入为非空字符串且只包含数字 1 和 0。
示例 1:
输入: a = "11", b = "1"
输出: "100"
示例 2:
输入: a = "1010", b = "1011"
输出: "10101"

和66题类似，利用carry变量记录加1位

//C

//这里需要注意字符串数组默认最后一位应该为\0，分配内存的时候应该加1并手动添加结束符

#define max(a, b) ((a) > (b) ? (a) : (b))

char * addBinary(char * a, char * b){
	int lena = strlen(a), lenb = strlen(b), carry = 0, tmp = 0;
	int len = max(lena, lenb), i = lena - 1, j = lenb - 1;
	int idx = len - 1;
	char *p = (char *)malloc(sizeof(char)* (len + 1));
	p[len] = '\0';
	while (i >= 0 || j >= 0){
		if (i >= 0 && j >= 0)
			tmp = (a[i] - '0') + (b[j] - '0') + carry;
		else if (i >= 0)
			tmp = (a[i] - '0') + carry;
		else
			tmp = (b[j] - '0') + carry;

		if (tmp == 2) {
			p[idx--] = '0';
			carry = 1;
		}
		else if (tmp == 3){
			p[idx--] = '1';
			carry = 1;
		}
		else{
			carry = 0;
			p[idx--] = tmp + '0';
		}
		i--;
		j--;
	}
	
	if (carry == 1){
		char *q = (char *)malloc(sizeof(char)* (len + 2));
		q[0] = '1';
		for (i = 0; i < len + 1; i++) q[i + 1] = p[i];
		return q;
	}
	else{
		return p;
	}
}

另一种比较优美的写法。

//C

char * addBinary(char * a, char * b){
    int len1 = strlen(a),len2 = strlen(b),carry = 0,k = 0;
    int i,j;
    char *c = (char *)malloc(sizeof(char)*(len1 + len2));
    //核心代码，从右往左进行运算
    for(i = len1 - 1,j = len2 - 1;i >= 0 || j >= 0 || carry;--i,--j){
        //很可能有a,b数组长度不等的时候，所以会有i,j小于0的情况，这时直接把该位置为0即可
        int x = i < 0 ? 0 : a[i] - '0';
        int y = j < 0 ? 0 : b[j] - '0';

        int sum = (x + y + carry) % 2;  //存入数组中的值

        carry = (x + y + carry) / 2;    //进位
        c[k++] = sum + '0';
    }
    c[k] = '\0';    //结束字符

    //翻转字符串
    for(i = 0,j = k - 1;i < j;i++,j--){
        char cc = c[i];
        c[i] = c[j];
        c[j] = cc;
    }
    return c;
}

//JS
var addBinary = function(a, b) {
    let res = "", carry = 0, tmp = 0, lena = a.length, lenb = b.length;
    for(var i = lena - 1, j = lenb - 1; i >= 0 || j >= 0 || carry; i--, j--){
        let x = i >= 0 ? Number(a[i]) : 0,
        y = j >= 0 ? Number(b[j]) : 0;

        tmp = carry + x + y;

        if(tmp >= 2){
            carry = 1;
            res = tmp % 2 + res;
        }
        else{
            carry = 0;
            res = tmp + res;
        }
    }
    return res;
};

JS中的BigInt数据类型

//JS

var addBinary = function(a, b) {
  return (BigInt('0b' + a) + BigInt('0b' + b)).toString(2); //0b是二进制前缀
}