leetcode-problemset/leetcode-cn/originData/maximum-and-sum-of-array.json

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        "question": {
            "questionId": "2291",
            "questionFrontendId": "2172",
            "categoryTitle": "Algorithms",
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            "title": "Maximum AND Sum of Array",
            "titleSlug": "maximum-and-sum-of-array",
            "content": "<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 &gt;= n</code>. There are <code>numSlots</code> slots numbered from <code>1</code> to <code>numSlots</code>.</p>\n\n<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>\n\n<ul>\n\t<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>\n</ul>\n\n<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>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4,5,6], numSlots = 3\n<strong>Output:</strong> 9\n<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>. \nThis 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.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,3,10,4,7,1], numSlots = 9\n<strong>Output:</strong> 24\n<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>.\nThis 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.\nNote that slots 2, 5, 6, and 8 are empty which is permitted.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>1 &lt;= numSlots &lt;= 9</code></li>\n\t<li><code>1 &lt;= n &lt;= 2 * numSlots</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 15</code></li>\n</ul>\n",
            "translatedTitle": "数组的最大与和",
            "translatedContent": "<p>给你一个长度为&nbsp;<code>n</code>&nbsp;的整数数组&nbsp;<code>nums</code>&nbsp;和一个整数&nbsp;<code>numSlots</code>&nbsp;，满足<code>2 * numSlots &gt;= n</code>&nbsp;。总共有&nbsp;<code>numSlots</code>&nbsp;个篮子，编号为&nbsp;<code>1</code>&nbsp;到&nbsp;<code>numSlots</code>&nbsp;。</p>\n\n<p>你需要把所有&nbsp;<code>n</code>&nbsp;个整数分到这些篮子中，且每个篮子 <strong>至多</strong>&nbsp;有 2 个整数。一种分配方案的 <strong>与和</strong>&nbsp;定义为每个数与它所在篮子编号的 <strong>按位与运算</strong>&nbsp;结果之和。</p>\n\n<ul>\n\t<li>比方说，将数字&nbsp;<code>[1, 3]</code>&nbsp;放入篮子&nbsp;<strong><em><code>1</code></em></strong>&nbsp;中，<code>[4, 6]</code> 放入篮子&nbsp;<strong><em><code>2</code></em></strong>&nbsp;中，这个方案的与和为&nbsp;<code>(1 AND <strong><em>1</em></strong>) + (3 AND <strong><em>1</em></strong>) + (4 AND <em><strong>2</strong></em>) + (6 AND <em><strong>2</strong></em>) = 1 + 1 + 0 + 2 = 4</code>&nbsp;。</li>\n</ul>\n\n<p>请你返回将 <code>nums</code>&nbsp;中所有数放入<em>&nbsp;</em><code>numSlots</code>&nbsp;个篮子中的最大与和。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>nums = [1,2,3,4,5,6], numSlots = 3\n<b>输出：</b>9\n<b>解释：</b>一个可行的方案是 [1, 4] 放入篮子 <em><strong>1</strong></em>&nbsp;中，[2, 6] 放入篮子 <strong><em>2</em></strong>&nbsp;中，[3, 5] 放入篮子 <strong><em>3</em></strong> 中。\n最大与和为 (1 AND <strong><em>1</em></strong>) + (4 AND <strong><em>1</em></strong>) + (2 AND <strong><em>2</em></strong>) + (6 AND <strong><em>2</em></strong>) + (3 AND <strong><em>3</em></strong>) + (5 AND <em><strong>3</strong></em>) = 1 + 0 + 2 + 2 + 3 + 1 = 9 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>nums = [1,3,10,4,7,1], numSlots = 9\n<b>输出：</b>24\n<b>解释：</b>一个可行的方案是 [1, 1] 放入篮子 <em><strong>1</strong></em> 中，[3] 放入篮子 <em><strong>3</strong></em> 中，[4] 放入篮子 <strong><em>4</em></strong> 中，[7] 放入篮子 <strong><em>7</em></strong> 中，[10] 放入篮子 <strong><em>9</em></strong>&nbsp;中。\n最大与和为 (1 AND <strong><em>1</em></strong>) + (1 AND <strong><em>1</em></strong>) + (3 AND <strong><em>3</em></strong>) + (4 AND <strong><em>4</em></strong>) + (7 AND <strong><em>7</em></strong>) + (10 AND <strong><em>9</em></strong>) = 1 + 1 + 3 + 4 + 7 + 8 = 24 。\n注意，篮子 2 ，5 ，6 和 8 是空的，这是允许的。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>1 &lt;= numSlots &lt;= 9</code></li>\n\t<li><code>1 &lt;= n &lt;= 2 * numSlots</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 15</code></li>\n</ul>\n",
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