2683 - Neighboring Bitwise XOR.

Medium

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.

derived0 = original0 ⊕ original1 = 0 ⊕ 1 = 1

derived1 = original1 ⊕ original2 = 1 ⊕ 0 = 1

derived2 = original2 ⊕ original0 = 0 ⊕ 0 = 0

Example 2:

Input: derived = 1,1

Output: true

Explanation: A valid original array that gives derived is 0,1.

derived0 = original0 ⊕ original1 = 1

derived1 = original1 ⊕ original0 = 1

Example 3:

Input: derived = 1,0

Output: false

Explanation: There is no valid original array that gives derived.

Constraints:

• n == derived.length

• <code>1 <= n <= 10⁵</code>

• The values in derived are either 0's or 1's