[LeetCode] 1073. Adding Two Negabinary Numbers 负二进制数相加
Given two numbers arr1
and arr2
in base -2, return the result of adding them together.
Each number is given in array format: as an array of 0s and 1s, from most significant bit to least significant bit. For example, arr = [1,1,0,1]
represents the number (-2)^3 + (-2)^2 + (-2)^0 = -3
. A number arr
in array, format is also guaranteed to have no leading zeros: either arr == [0]
or arr[0] == 1
.
Return the result of adding arr1
and arr2
in the same format: as an array of 0s and 1s with no leading zeros.
Example 1:
Input: arr1 = [1,1,1,1,1], arr2 = [1,0,1]
Output: [1,0,0,0,0]
Explanation: arr1 represents 11, arr2 represents 5, the output represents 16.
Example 2:
Input: arr1 = [0], arr2 = [0]
Output: [0]
Example 3:
Input: arr1 = [0], arr2 = [1]
Output: [1]
Constraints:
1 <= arr1.length, arr2.length <= 1000
arr1[i]
andarr2[i]
are0
or1
arr1
andarr2
have no leading zeros
这道题说是有两个负二进制数是用数组来表示的,现在让返回它们相加后的结果,还是放在数组中来表示。之前其实也遇到过负二进制的题 Convert to Base -2,所以博主自然而然想到的解法就是将其均转为十进制数,然后相加,再将其转为负二进制数。但是这种方法可能会整型溢出,因为给定的数组可能很长,从而表示的负二进制的数转为十进制后可能会越界,这也是之前那道 Add Binary 用字符串表示的二进制进行相加时,不直接转为十进制计算的原因。这道题其实利用的方法跟那道很像,都是一位一位的处理的,直接加到结果 res 数组中的。这里使用两个指针i和j,分别指向数组 arr1 和 arr2 的末尾,然后用个变量 carry 表示进位,当i大于等于0时,carry 加上i指向的数字,并且i自减1,同理,当j大于等于0时,carry 加上j指向的数字,并且j自减1。由于数组中当每位上只能放一个数字,所以让 carry ‘与’上1,并加入到结果 res 数组后。然后需要再填充更高一位上的数字,对于二进制来说,直接右移1位即可,这里由于是负二进制,所以右移1位之后再取负。之后要移除所有的 leading zeros,因为这里高位是加到了 res 的后面,所以要去除末尾的零,使用个 while 去除。最后别忘了将 res 翻转一下返回即可,参见代码如下:
class Solution {
public:
vector<int> addNegabinary(vector<int>& arr1, vector<int>& arr2) {
vector<int> res;
int carry = 0, i = (int)arr1.size() - 1, j = (int)arr2.size() - 1;
while (i >= 0 || j >= 0 || carry) {
if (i >= 0) carry += arr1[i--];
if (j >= 0) carry += arr2[j--];
res.push_back(carry & 1);
carry = -(carry >> 1);
}
while (res.size() > 1 && res.back() == 0) res.pop_back();
reverse(res.begin(), res.end());
return res;
}
};
Github 同步地址:
https://github.com/grandyang/leetcode/issues/1073
类似题目:
参考资料:
https://leetcode.com/problems/adding-two-negabinary-numbers/
https://leetcode.com/problems/adding-two-negabinary-numbers/discuss/303795/C%2B%2B-From-Wikipedia