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package g2601_2700.s2683_neighboring_bitwise_xor;

// #Medium #Array #Bit_Manipulation #2023_09_12_Time_2_ms_(100.00%)_Space_59.9_MB_(62.03%)

/**
 * 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**
**/
public class Solution {
    public boolean doesValidArrayExist(int[] derived) {
        int xor = 0;
        for (int j : derived) {
            xor = xor ^ j;
        }
        return xor == 0;
    }
}




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