Leetcode #1073: Adding Two Negabinary Numbers
In this guide, we solve Leetcode #1073 Adding Two Negabinary Numbers in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Math
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
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
The time complexity is O(n) or O(1). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.