Is Neighboring Bitwise XOR easy or hard?

Neighboring Bitwise XOR is classified as Medium difficulty. The implementation is simple, but recognizing that all original elements cancel out in the XOR cycle requires understanding of XOR algebra and circular array relationships.

Neighboring Bitwise XOR Python/Java solution

In Python or Java, the optimal implementation iterates through the array and XORs every value into a variable. After the loop, return true if the XOR equals 0. The implementation is typically fewer than 10 lines and runs in O(n) time.

How to solve Neighboring Bitwise XOR in O(n)?

Iterate through the derived array and maintain a running XOR of all elements. Because every original value appears twice in the circular XOR equations, they cancel out. If the final XOR of the derived array equals 0, a valid original array exists; otherwise it does not.

What is the best approach for Neighboring Bitwise XOR?

The most efficient approach is the XOR cycle check. XOR all values in the derived array and verify that the result equals 0. If the total XOR is zero, a valid original binary array exists. This solution runs in O(n) time with O(1) space.

Is Neighboring Bitwise XOR asked at Google/Amazon/Meta?

Bit manipulation and XOR reasoning problems similar to Neighboring Bitwise XOR frequently appear in interviews at companies like Amazon, Google, and Meta. The question tests understanding of XOR properties and circular array constraints.

What data structure is used in Neighboring Bitwise XOR?

The problem mainly relies on arrays and bit manipulation. The optimal solution does not require additional data structures; it only computes a cumulative XOR while iterating through the array.

What is the time complexity of Neighboring Bitwise XOR?

The optimal algorithm runs in O(n) time because it performs a single pass through the derived array to compute the cumulative XOR. Space complexity is O(1) since only a single variable is needed to track the XOR sum.

Description Hints 2 Solution Video 47:01

2683. Neighboring Bitwise XOR

Medium79.8% acceptance2 companies

A 0-indexed array derived with length n is derived by computing the bitwise XOR (⊕) of adjacent values in a binary array original of length n.

Specifically, for each index i in the range [0, n - 1]:

If i = n - 1, then derived[i] = original[i] ⊕ original[0].
Otherwise, derived[i] = original[i] ⊕ original[i + 1].

Given an array derived, your task is to determine whether there exists a valid binary array original that could have formed derived.

Return true if such an array exists or false otherwise.

A binary array is an array containing only 0's and 1's

Example 1:

Input: derived = [1,1,0]
Output: true
Explanation: A valid original array that gives derived is [0,1,0].
derived[0] = original[0] ⊕ original[1] = 0 ⊕ 1 = 1 
derived[1] = original[1] ⊕ original[2] = 1 ⊕ 0 = 1
derived[2] = original[2] ⊕ original[0] = 0 ⊕ 0 = 0

Example 2:

Input: derived = [1,1]
Output: true
Explanation: A valid original array that gives derived is [0,1].
derived[0] = original[0] ⊕ original[1] = 1
derived[1] = original[1] ⊕ original[0] = 1

Example 3:

Input: derived = [1,0]
Output: false
Explanation: There is no valid original array that gives derived.

Constraints:

n == derived.length
1 <= n <= 10⁵
The values in derived are either 0's or 1's

Asked at 2 companies

Google Amazon

Topics

Array Bit Manipulation

Hints open one at a time

Hint 1

Understand that from the original element, we are using each element twice to construct the derived array

Hint 2

The xor-sum of the derived array should be 0 since there is always a duplicate occurrence of each element.

47:01

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