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86 lines
2.8 KiB
HTML
86 lines
2.8 KiB
HTML
<p>You are given an integer array <code>nums</code>.</p>
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<p>Partition the array into <strong>three</strong> (possibly empty) <span data-keyword="subsequence-array">subsequences</span> <code>A</code>, <code>B</code>, and <code>C</code> such that every element of <code>nums</code> belongs to <strong>exactly</strong> one subsequence.</p>
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<p>Your goal is to <strong>maximize</strong> the value of: <code>XOR(A) + AND(B) + XOR(C)</code></p>
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<p>where:</p>
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<ul>
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<li><code>XOR(arr)</code> denotes the bitwise XOR of all elements in <code>arr</code>. If <code>arr</code> is empty, its value is defined as 0.</li>
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<li><code>AND(arr)</code> denotes the bitwise AND of all elements in <code>arr</code>. If <code>arr</code> is empty, its value is defined as 0.</li>
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</ul>
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<p>Return the <strong>maximum</strong> value achievable.</p>
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<p><strong>Note:</strong> If multiple partitions result in the same <strong>maximum</strong> sum, you can consider any one of them.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">nums = [2,3]</span></p>
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<p><strong>Output:</strong> <span class="example-io">5</span></p>
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<p><strong>Explanation:</strong></p>
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<p>One optimal partition is:</p>
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<ul>
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<li><code>A = [3], XOR(A) = 3</code></li>
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<li><code>B = [2], AND(B) = 2</code></li>
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<li><code>C = [], XOR(C) = 0</code></li>
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</ul>
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<p>The maximum value of: <code>XOR(A) + AND(B) + XOR(C) = 3 + 2 + 0 = 5</code>. Thus, the answer is 5.</p>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">nums = [1,3,2]</span></p>
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<p><strong>Output:</strong> <span class="example-io">6</span></p>
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<p><strong>Explanation:</strong></p>
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<p>One optimal partition is:</p>
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<ul>
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<li><code>A = [1], XOR(A) = 1</code></li>
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<li><code>B = [2], AND(B) = 2</code></li>
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<li><code>C = [3], XOR(C) = 3</code></li>
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</ul>
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<p>The maximum value of: <code>XOR(A) + AND(B) + XOR(C) = 1 + 2 + 3 = 6</code>. Thus, the answer is 6.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">nums = [2,3,6,7]</span></p>
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<p><strong>Output:</strong> <span class="example-io">15</span></p>
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<p><strong>Explanation:</strong></p>
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<p>One optimal partition is:</p>
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<ul>
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<li><code>A = [7], XOR(A) = 7</code></li>
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<li><code>B = [2,3], AND(B) = 2</code></li>
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<li><code>C = [6], XOR(C) = 6</code></li>
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</ul>
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<p>The maximum value of: <code>XOR(A) + AND(B) + XOR(C) = 7 + 2 + 6 = 15</code>. Thus, the answer is 15.</p>
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</div>
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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>1 <= nums.length <= 19</code></li>
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<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>
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</ul>
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