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"question": {
"questionId": "2359",
"questionFrontendId": "2271",
"categoryTitle": "Algorithms",
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"title": "Maximum White Tiles Covered by a Carpet",
"titleSlug": "maximum-white-tiles-covered-by-a-carpet",
"content": "<p>You are given a 2D integer array <code>tiles</code> where <code>tiles[i] = [l<sub>i</sub>, r<sub>i</sub>]</code> represents that every tile <code>j</code> in the range <code>l<sub>i</sub> &lt;= j &lt;= r<sub>i</sub></code> is colored white.</p>\n\n<p>You are also given an integer <code>carpetLen</code>, the length of a single carpet that can be placed <strong>anywhere</strong>.</p>\n\n<p>Return <em>the <strong>maximum</strong> number of white tiles that can be covered by the carpet</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/03/25/example1drawio3.png\" style=\"width: 644px; height: 158px;\" />\n<pre>\n<strong>Input:</strong> tiles = [[1,5],[10,11],[12,18],[20,25],[30,32]], carpetLen = 10\n<strong>Output:</strong> 9\n<strong>Explanation:</strong> Place the carpet starting on tile 10. \nIt covers 9 white tiles, so we return 9.\nNote that there may be other places where the carpet covers 9 white tiles.\nIt can be shown that the carpet cannot cover more than 9 white tiles.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/03/24/example2drawio.png\" style=\"width: 231px; height: 168px;\" />\n<pre>\n<strong>Input:</strong> tiles = [[10,11],[1,1]], carpetLen = 2\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> Place the carpet starting on tile 10. \nIt covers 2 white tiles, so we return 2.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= tiles.length &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>tiles[i].length == 2</code></li>\n\t<li><code>1 &lt;= l<sub>i</sub> &lt;= r<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= carpetLen &lt;= 10<sup>9</sup></code></li>\n\t<li>The <code>tiles</code> are <strong>non-overlapping</strong>.</li>\n</ul>\n",
"translatedTitle": "毯子覆盖的最多白色砖块数",
"translatedContent": "<p>给你一个二维整数数组&nbsp;<code>tiles</code>&nbsp;,其中&nbsp;<code>tiles[i] = [l<sub>i</sub>, r<sub>i</sub>]</code>&nbsp;,表示所有在&nbsp;<code>l<sub>i</sub> &lt;= j &lt;= r<sub>i</sub></code>&nbsp;之间的每个瓷砖位置 <code>j</code>&nbsp;都被涂成了白色。</p>\n\n<p>同时给你一个整数&nbsp;<code>carpetLen</code>&nbsp;,表示可以放在&nbsp;<strong>任何位置</strong>&nbsp;的一块毯子的长度。</p>\n\n<p>请你返回使用这块毯子,<strong>最多</strong>&nbsp;可以盖住多少块瓷砖。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/03/25/example1drawio3.png\" style=\"width: 644px; height: 158px;\" /></p>\n\n<pre>\n<b>输入:</b>tiles = [[1,5],[10,11],[12,18],[20,25],[30,32]], carpetLen = 10\n<b>输出:</b>9\n<b>解释:</b>将毯子从瓷砖 10 开始放置。\n总共覆盖 9 块瓷砖,所以返回 9 。\n注意可能有其他方案也可以覆盖 9 块瓷砖。\n可以看出瓷砖无法覆盖超过 9 块瓷砖。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/03/24/example2drawio.png\" style=\"width: 231px; height: 168px;\" /></p>\n\n<pre>\n<strong>输入:</strong>tiles = [[10,11],[1,1]], carpetLen = 2\n<b>输出:</b>2\n<b>解释:</b>将毯子从瓷砖 10 开始放置。\n总共覆盖 2 块瓷砖,所以我们返回 2 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= tiles.length &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>tiles[i].length == 2</code></li>\n\t<li><code>1 &lt;= l<sub>i</sub> &lt;= r<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= carpetLen &lt;= 10<sup>9</sup></code></li>\n\t<li><code>tiles</code>&nbsp;互相 <strong>不会重叠</strong>&nbsp;。</li>\n</ul>\n",
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"Think about the potential placements of the carpet in an optimal solution.",
"Can we use Prefix Sum and Binary Search to determine how many tiles are covered for a given placement?"
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