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g2601_2700.s2683_neighboring_bitwise_xor.readme.md Maven / Gradle / Ivy

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]. 

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**