2683. Neighboring Bitwise XOR
Medium
199
6

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`.
• 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 = original ⊕ original = 0 ⊕ 1 = 1
derived = original ⊕ original = 1 ⊕ 0 = 1
derived = original ⊕ original = 0 ⊕ 0 = 0
```

Example 2:

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