leetcode-problemset/leetcode-cn/originData/maximum-beauty-of-an-array-after-applying-operation.json

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            "categoryTitle": "Algorithms",
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            "title": "Maximum Beauty of an Array After Applying Operation",
            "titleSlug": "maximum-beauty-of-an-array-after-applying-operation",
            "content": "<p>You are given a <strong>0-indexed</strong> array <code>nums</code> and a <strong>non-negative</strong> integer <code>k</code>.</p>\n\n<p>In one operation, you can do the following:</p>\n\n<ul>\n\t<li>Choose an index <code>i</code> that <strong>hasn&#39;t been chosen before</strong> from the range <code>[0, nums.length - 1]</code>.</li>\n\t<li>Replace <code>nums[i]</code> with any integer from the range <code>[nums[i] - k, nums[i] + k]</code>.</li>\n</ul>\n\n<p>The <strong>beauty</strong> of the array is the length of the longest subsequence consisting of equal elements.</p>\n\n<p>Return <em>the <strong>maximum</strong> possible beauty of the array </em><code>nums</code><em> after applying the operation any number of times.</em></p>\n\n<p><strong>Note</strong> that you can apply the operation to each index <strong>only once</strong>.</p>\n\n<p>A&nbsp;<strong>subsequence</strong> of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the order of the remaining elements.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [4,6,1,2], k = 2\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> In this example, we apply the following operations:\n- Choose index 1, replace it with 4 (from range [4,8]), nums = [4,4,1,2].\n- Choose index 3, replace it with 4 (from range [0,4]), nums = [4,4,1,4].\nAfter the applied operations, the beauty of the array nums is 3 (subsequence consisting of indices 0, 1, and 3).\nIt can be proven that 3 is the maximum possible length we can achieve.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,1,1,1], k = 10\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> In this example we don&#39;t have to apply any operations.\nThe beauty of the array nums is 4 (whole array).\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i], k &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "数组的最大美丽值",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的整数数组 <code>nums</code> 和一个 <strong>非负</strong> 整数 <code>k</code> 。</p>\n\n<p>在一步操作中，你可以执行下述指令：</p>\n\n<ul>\n\t<li>在范围&nbsp;<code>[0, nums.length - 1]</code> 中选择一个 <strong>此前没有选过</strong> 的下标 <code>i</code> 。</li>\n\t<li>将 <code>nums[i]</code> 替换为范围 <code>[nums[i] - k, nums[i] + k]</code> 内的任一整数。</li>\n</ul>\n\n<p>数组的 <strong>美丽值</strong> 定义为数组中由相等元素组成的最长子序列的长度。</p>\n\n<p>对数组 <code>nums</code> 执行上述操作任意次后，返回数组可能取得的 <strong>最大</strong> 美丽值。</p>\n\n<p><strong>注意：</strong>你 <strong>只</strong> 能对每个下标执行 <strong>一次</strong> 此操作。</p>\n\n<p>数组的 <strong>子序列</strong> 定义是：经由原数组删除一些元素（也可能不删除）得到的一个新数组，且在此过程中剩余元素的顺序不发生改变。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [4,6,1,2], k = 2\n<strong>输出：</strong>3\n<strong>解释：</strong>在这个示例中，我们执行下述操作：\n- 选择下标 1 ，将其替换为 4（从范围 [4,8] 中选出），此时 nums = [4,4,1,2] 。\n- 选择下标 3 ，将其替换为 4（从范围 [0,4] 中选出），此时 nums = [4,4,1,4] 。\n执行上述操作后，数组的美丽值是 3（子序列由下标 0 、1 、3 对应的元素组成）。\n可以证明 3 是我们可以得到的由相等元素组成的最长子序列长度。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,1,1,1], k = 10\n<strong>输出：</strong>4\n<strong>解释：</strong>在这个示例中，我们无需执行任何操作。\n数组 nums 的美丽值是 4（整个数组）。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i], k &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                "Sort the array.",
                "The problem becomes the following: find maximum subarray A[i … j] such that A[j] - A[i] ≤ 2 * k."
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