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56 lines
2.2 KiB
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56 lines
2.2 KiB
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<p>A <strong>0-indexed</strong> array <code>derived</code> with length <code>n</code> is derived by computing the <strong>bitwise XOR</strong> (⊕) of adjacent values in a <strong>binary array</strong> <code>original</code> of length <code>n</code>.</p>
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<p>Specifically, for each index <code>i</code> in the range <code>[0, n - 1]</code>:</p>
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<ul>
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<li>If <code>i = n - 1</code>, then <code>derived[i] = original[i] ⊕ original[0]</code>.</li>
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<li>Otherwise, <code>derived[i] = original[i] ⊕ original[i + 1]</code>.</li>
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</ul>
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<p>Given an array <code>derived</code>, your task is to determine whether there exists a <strong>valid binary array</strong> <code>original</code> that could have formed <code>derived</code>.</p>
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<p>Return <em><strong>true</strong> if such an array exists or <strong>false</strong> otherwise.</em></p>
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<ul>
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<li>A binary array is an array containing only <strong>0's</strong> and <strong>1's</strong></li>
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</ul>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> derived = [1,1,0]
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<strong>Output:</strong> true
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<strong>Explanation:</strong> A valid original array that gives derived is [0,1,0].
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derived[0] = original[0] ⊕ original[1] = 0 ⊕ 1 = 1
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derived[1] = original[1] ⊕ original[2] = 1 ⊕ 0 = 1
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derived[2] = original[2] ⊕ original[0] = 0 ⊕ 0 = 0
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> derived = [1,1]
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<strong>Output:</strong> true
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<strong>Explanation:</strong> A valid original array that gives derived is [0,1].
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derived[0] = original[0] ⊕ original[1] = 1
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derived[1] = original[1] ⊕ original[0] = 1
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> derived = [1,0]
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<strong>Output:</strong> false
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<strong>Explanation:</strong> There is no valid original array that gives derived.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == derived.length</code></li>
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<li><code>1 <= n <= 10<sup>5</sup></code></li>
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<li>The values in <code>derived</code> are either <strong>0's</strong> or <strong>1's</strong></li>
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</ul>
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