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40 lines
2.3 KiB
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40 lines
2.3 KiB
HTML
<p>You are given an integer array <code>nums</code> of length <code>n</code> and an integer <code>numSlots</code> such that <code>2 * numSlots >= n</code>. There are <code>numSlots</code> slots numbered from <code>1</code> to <code>numSlots</code>.</p>
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<p>You have to place all <code>n</code> integers into the slots such that each slot contains at <strong>most</strong> two numbers. The <strong>AND sum</strong> of a given placement is the sum of the <strong>bitwise</strong> <code>AND</code> of every number with its respective slot number.</p>
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<ul>
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<li>For example, the <strong>AND sum</strong> of placing the numbers <code>[1, 3]</code> into slot <u><code>1</code></u> and <code>[4, 6]</code> into slot <u><code>2</code></u> is equal to <code>(1 AND <u>1</u>) + (3 AND <u>1</u>) + (4 AND <u>2</u>) + (6 AND <u>2</u>) = 1 + 1 + 0 + 2 = 4</code>.</li>
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</ul>
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<p>Return <em>the maximum possible <strong>AND sum</strong> of </em><code>nums</code><em> given </em><code>numSlots</code><em> slots.</em></p>
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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> nums = [1,2,3,4,5,6], numSlots = 3
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<strong>Output:</strong> 9
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<strong>Explanation:</strong> One possible placement is [1, 4] into slot <u>1</u>, [2, 6] into slot <u>2</u>, and [3, 5] into slot <u>3</u>.
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This gives the maximum AND sum of (1 AND <u>1</u>) + (4 AND <u>1</u>) + (2 AND <u>2</u>) + (6 AND <u>2</u>) + (3 AND <u>3</u>) + (5 AND <u>3</u>) = 1 + 0 + 2 + 2 + 3 + 1 = 9.
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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> nums = [1,3,10,4,7,1], numSlots = 9
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<strong>Output:</strong> 24
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<strong>Explanation:</strong> One possible placement is [1, 1] into slot <u>1</u>, [3] into slot <u>3</u>, [4] into slot <u>4</u>, [7] into slot <u>7</u>, and [10] into slot <u>9</u>.
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This gives the maximum AND sum of (1 AND <u>1</u>) + (1 AND <u>1</u>) + (3 AND <u>3</u>) + (4 AND <u>4</u>) + (7 AND <u>7</u>) + (10 AND <u>9</u>) = 1 + 1 + 3 + 4 + 7 + 8 = 24.
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Note that slots 2, 5, 6, and 8 are empty which is permitted.
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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 == nums.length</code></li>
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<li><code>1 <= numSlots <= 9</code></li>
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<li><code>1 <= n <= 2 * numSlots</code></li>
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<li><code>1 <= nums[i] <= 15</code></li>
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</ul>
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