How do you solve Adding Two Negabinary Numbers on LeetCode?

Adding Two Negabinary Numbers (LeetCode #1073) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Negabinary addition can be done directly without conversion to decimal.

What is the time complexity of Adding Two Negabinary Numbers?

The optimal solution for Adding Two Negabinary Numbers runs in O(n) time and uses O(n) space. The time complexity is O(n) because we process each bit of the input arrays once. The space complexity is O(n) for storing the result.

What is the brute force solution for Adding Two Negabinary Numbers?

The brute force approach for Adding Two Negabinary Numbers is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves converting both negabinary numbers to decimal, adding them, and then converting the result back to negabinary. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Adding Two Negabinary Numbers?

Adding Two Negabinary Numbers uses the following concepts: Array, Math. The recommended patterns to study are: Bit Manipulation, Array.

What are the interview tips for Adding Two Negabinary Numbers?

Always clarify the base system being used in the problem. Practice bit manipulation problems to get comfortable with carry operations. Explain your thought process clearly while coding; it helps the interviewer understand your approach.

What are common mistakes when solving Adding Two Negabinary Numbers?

Confusing the carry handling in negabinary with regular binary addition. Not reversing the result at the end.

#1073

Adding Two Negabinary Numbers

Medium

ArrayMathBit ManipulationArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal approach directly adds the two negabinary numbers without converting them to decimal. This is more efficient as it processes the bits in a single pass.

⚙️

Algorithm

7 steps

1Step 1: Initialize an empty result array and a carry variable set to 0.
2Step 2: Iterate from the end of both arrays until both are exhausted.
3Step 3: For each position, calculate the sum of the bits and the carry.
4Step 4: Determine the new bit and the new carry based on the sum.
5Step 5: Append the new bit to the result array.
6Step 6: If there's a carry left after the loop, append it to the result.
7Step 7: Reverse the result array to get the final answer.

solution.py17 lines

1# Full working Python code
2
3def add_negabinary(arr1, arr2):
4    result = []
5    carry = 0
6    i, j = len(arr1) - 1, len(arr2) - 1
7    while i >= 0 or j >= 0 or carry:
8        total = carry
9        if i >= 0:
10            total += arr1[i]
11            i -= 1
12        if j >= 0:
13            total += arr2[j]
14            j -= 1
15        result.append(total % 2)
16        carry = -(total // 2)
17    return result[::-1]

ℹ

Complexity note: The time complexity is O(n) because we process each bit of the input arrays once. The space complexity is O(n) for storing the result.

1Negabinary addition can be done directly without conversion to decimal.
2Understanding how to handle carries in negabinary is crucial.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.