Adding Two Negabinary Numbers — LeetCode 1073 Python Solution

The problem

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.

Example

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.

Python solution

class Solution:
    def addNegabinary(self, arr1: List[int], arr2: List[int]) -> List[int]:
        i, j = len(arr1) - 1, len(arr2) - 1
        c = 0
        ans = []
        while i >= 0 or j >= 0 or c:
            a = 0 if i < 0 else arr1[i]
            b = 0 if j < 0 else arr2[j]
            x = a + b + c
            c = 0
            if x >= 2:
                x -= 2
                c -= 1
            elif x == -1:
                x = 1
                c += 1
            ans.append(x)
            i, j = i - 1, j - 1
        while len(ans) > 1 and ans[-1] == 0:
            ans.pop()
        return ans[::-1]

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1073. Adding Two Negabinary Numbers is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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