leetcode-problemset/leetcode-cn/originData/minimum-increment-operations-to-make-array-beautiful.json

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            "questionId": "3178",
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            "title": "Minimum Increment Operations to Make Array Beautiful",
            "titleSlug": "minimum-increment-operations-to-make-array-beautiful",
            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> having length <code>n</code>, and an integer <code>k</code>.</p>\n\n<p>You can perform the following <strong>increment</strong> operation <strong>any</strong> number of times (<strong>including zero</strong>):</p>\n\n<ul>\n\t<li>Choose an index <code>i</code> in the range <code>[0, n - 1]</code>, and increase <code>nums[i]</code> by <code>1</code>.</li>\n</ul>\n\n<p>An array is considered <strong>beautiful</strong> if, for any <strong>subarray</strong> with a size of <code>3</code> or <strong>more</strong>, its <strong>maximum</strong> element is <strong>greater than or equal</strong> to <code>k</code>.</p>\n\n<p>Return <em>an integer denoting the <strong>minimum</strong> number of increment operations needed to make </em><code>nums</code><em> <strong>beautiful</strong>.</em></p>\n\n<p>A subarray is a contiguous <strong>non-empty</strong> sequence of elements within an array.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,3,0,0,2], k = 4\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> We can perform the following increment operations to make nums beautiful:\nChoose index i = 1 and increase nums[1] by 1 -&gt; [2,4,0,0,2].\nChoose index i = 4 and increase nums[4] by 1 -&gt; [2,4,0,0,3].\nChoose index i = 4 and increase nums[4] by 1 -&gt; [2,4,0,0,4].\nThe subarrays with a size of 3 or more are: [2,4,0], [4,0,0], [0,0,4], [2,4,0,0], [4,0,0,4], [2,4,0,0,4].\nIn all the subarrays, the maximum element is equal to k = 4, so nums is now beautiful.\nIt can be shown that nums cannot be made beautiful with fewer than 3 increment operations.\nHence, the answer is 3.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [0,1,3,3], k = 5\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We can perform the following increment operations to make nums beautiful:\nChoose index i = 2 and increase nums[2] by 1 -&gt; [0,1,4,3].\nChoose index i = 2 and increase nums[2] by 1 -&gt; [0,1,5,3].\nThe subarrays with a size of 3 or more are: [0,1,5], [1,5,3], [0,1,5,3].\nIn all the subarrays, the maximum element is equal to k = 5, so nums is now beautiful.\nIt can be shown that nums cannot be made beautiful with fewer than 2 increment operations.\nHence, the answer is 2.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,1,2], k = 1\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> The only subarray with a size of 3 or more in this example is [1,1,2].\nThe maximum element, 2, is already greater than k = 1, so we don&#39;t need any increment operation.\nHence, the answer is 0.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= n == nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "使数组变美的最小增量运算数",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始、长度为 <code>n</code> 的整数数组 <code>nums</code> ，和一个整数 <code>k</code> 。</p>\n\n<p>你可以执行下述 <strong>递增</strong> 运算 <strong>任意</strong> 次（可以是 <strong>0</strong> 次）：</p>\n\n<ul>\n\t<li>从范围&nbsp;<code>[0, n - 1]</code> 中选择一个下标 <code>i</code> ，并将 <code>nums[i]</code> 的值加 <code>1</code> 。</li>\n</ul>\n\n<p>如果数组中任何长度 <strong>大于或等于 3</strong> 的子数组，其 <strong>最大</strong> 元素都大于或等于 <code>k</code> ，则认为数组是一个 <strong>美丽数组</strong> 。</p>\n\n<p>以整数形式返回使数组变为 <strong>美丽数组</strong> 需要执行的 <strong>最小</strong> 递增运算数。</p>\n\n<p>子数组是数组中的一个连续 <strong>非空</strong> 元素序列。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [2,3,0,0,2], k = 4\n<strong>输出：</strong>3\n<strong>解释：</strong>可以执行下述递增运算，使 nums 变为美丽数组：\n选择下标 i = 1 ，并且将 nums[1] 的值加 1 -&gt; [2,4,0,0,2] 。\n选择下标 i = 4 ，并且将 nums[4] 的值加 1 -&gt; [2,4,0,0,3] 。\n选择下标 i = 4 ，并且将 nums[4] 的值加 1 -&gt; [2,4,0,0,4] 。\n长度大于或等于 3 的子数组为 [2,4,0], [4,0,0], [0,0,4], [2,4,0,0], [4,0,0,4], [2,4,0,0,4] 。\n在所有子数组中，最大元素都等于 k = 4 ，所以 nums 现在是美丽数组。\n可以证明无法用少于 3 次递增运算使 nums 变为美丽数组。\n因此，答案为 3 。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [0,1,3,3], k = 5\n<strong>输出：</strong>2\n<strong>解释：</strong>可以执行下述递增运算，使 nums 变为美丽数组：\n选择下标 i = 2 ，并且将 nums[2] 的值加 1 -&gt; [0,1,4,3] 。\n选择下标 i = 2 ，并且将 nums[2] 的值加 1 -&gt; [0,1,5,3] 。\n长度大于或等于 3 的子数组为 [0,1,5]、[1,5,3]、[0,1,5,3] 。\n在所有子数组中，最大元素都等于 k = 5 ，所以 nums 现在是美丽数组。\n可以证明无法用少于 2 次递增运算使 nums 变为美丽数组。 \n因此，答案为 2 。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,1,2], k = 1\n<strong>输出：</strong>0\n<strong>解释：</strong>在这个示例中，只有一个长度大于或等于 3 的子数组 [1,1,2] 。\n其最大元素 2 已经大于 k = 1 ，所以无需执行任何增量运算。\n因此，答案为 0 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= n == nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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                "There needs to be at least one value among <code>3</code> consecutive values in the array that is greater than or equal to <code>k</code>.",
                "The problem can be solved using dynamic programming.",
                "Let <code>dp[i]</code> be the minimum number of increment operations required to make the subarray consisting of the first <code>i</code> values beautiful, while also having the value at <code>nums[i] >= k</code>.",
                "<code>dp[0] = max(0, k - nums[0])</code>, <code>dp[1] = max(0, k - nums[1])</code>, and <code>dp[2] = max(0, k - nums[2])</code>.",
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href=\\\"https:\\/\\/github.com\\/emirpasic\\/gods\\/tree\\/v1.18.1\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap 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