<p>Given two numbers <code>arr1</code> and <code>arr2</code> in base <strong>-2</strong>, return the result of adding them together.</p>

<p>Each number is given in <em>array format</em>:&nbsp; as an array of 0s and 1s, from most significant bit to least significant bit.&nbsp; For example, <code>arr = [1,1,0,1]</code> represents the number <code>(-2)^3&nbsp;+ (-2)^2 + (-2)^0 = -3</code>.&nbsp; A number <code>arr</code> in <em>array, format</em> is also guaranteed to have no leading zeros: either&nbsp;<code>arr == [0]</code> or <code>arr[0] == 1</code>.</p>

<p>Return the result of adding <code>arr1</code> and <code>arr2</code> in the same format: as an array of 0s and 1s with no leading zeros.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,1,1,1,1], arr2 = [1,0,1]
<strong>Output:</strong> [1,0,0,0,0]
<strong>Explanation: </strong>arr1 represents 11, arr2 represents 5, the output represents 16.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [0], arr2 = [0]
<strong>Output:</strong> [0]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [0], arr2 = [1]
<strong>Output:</strong> [1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr1.length,&nbsp;arr2.length &lt;= 1000</code></li>
	<li><code>arr1[i]</code>&nbsp;and <code>arr2[i]</code> are&nbsp;<code>0</code> or <code>1</code></li>
	<li><code>arr1</code> and <code>arr2</code> have no leading zeros</li>
</ul>

// 2024/09/15
// Similar to regular binary addition
// But alternate + and - between digits
// So the carry acts as a negative

class Solution {
public:
    vector<int> addNegabinary(vector<int>& arr1, vector<int>& arr2) {
        int i = 0;
        int carry = 0;
        vector<int> res{};
        while (i < arr1.size() || i < arr2.size()) {
            int a = 0; int b = 0;
            if (i < arr1.size()) { 
                a = arr1[arr1.size() - i - 1];
            }
            if (i < arr2.size()) { 
                b = arr2[arr2.size() - i - 1];
            }
            int sum = a + b + carry;
            res.push_back(sum == -1 ? 1 : sum % 2);
            carry = sum == -1 ? 1 : - sum / 2;
            ++i;
        }
        if (carry != 0) { 
            res.push_back(1);
            res.push_back(1);
        }
        while (res.size() > 1 && res.back() == 0) { 
            res.pop_back();
        }
        reverse(res.begin(), res.end());
        return res;
    }
};
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