mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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184 lines
25 KiB
JSON
184 lines
25 KiB
JSON
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"title": "Maximum Employees to Be Invited to a Meeting",
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"content": "<p>A company is organizing a meeting and has a list of <code>n</code> employees, waiting to be invited. They have arranged for a large <strong>circular</strong> table, capable of seating <strong>any number</strong> of employees.</p>\n\n<p>The employees are numbered from <code>0</code> to <code>n - 1</code>. Each employee has a <strong>favorite</strong> person and they will attend the meeting <strong>only if</strong> they can sit next to their favorite person at the table. The favorite person of an employee is <strong>not</strong> themself.</p>\n\n<p>Given a <strong>0-indexed</strong> integer array <code>favorite</code>, where <code>favorite[i]</code> denotes the favorite person of the <code>i<sup>th</sup></code> employee, return <em>the <strong>maximum number of employees</strong> that can be invited to the meeting</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/14/ex1.png\" style=\"width: 236px; height: 195px;\" />\n<pre>\n<strong>Input:</strong> favorite = [2,2,1,2]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong>\nThe above figure shows how the company can invite employees 0, 1, and 2, and seat them at the round table.\nAll employees cannot be invited because employee 2 cannot sit beside employees 0, 1, and 3, simultaneously.\nNote that the company can also invite employees 1, 2, and 3, and give them their desired seats.\nThe maximum number of employees that can be invited to the meeting is 3. \n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> favorite = [1,2,0]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> \nEach employee is the favorite person of at least one other employee, and the only way the company can invite them is if they invite every employee.\nThe seating arrangement will be the same as that in the figure given in example 1:\n- Employee 0 will sit between employees 2 and 1.\n- Employee 1 will sit between employees 0 and 2.\n- Employee 2 will sit between employees 1 and 0.\nThe maximum number of employees that can be invited to the meeting is 3.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/14/ex2.png\" style=\"width: 219px; height: 220px;\" />\n<pre>\n<strong>Input:</strong> favorite = [3,0,1,4,1]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong>\nThe above figure shows how the company will invite employees 0, 1, 3, and 4, and seat them at the round table.\nEmployee 2 cannot be invited because the two spots next to their favorite employee 1 are taken.\nSo the company leaves them out of the meeting.\nThe maximum number of employees that can be invited to the meeting is 4.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == favorite.length</code></li>\n\t<li><code>2 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>0 <= favorite[i] <= n - 1</code></li>\n\t<li><code>favorite[i] != i</code></li>\n</ul>\n",
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"translatedTitle": "参加会议的最多员工数",
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"translatedContent": "<p>一个公司准备组织一场会议，邀请名单上有 <code>n</code> 位员工。公司准备了一张 <strong>圆形</strong> 的桌子，可以坐下 <strong>任意数目</strong> 的员工。</p>\n\n<p>员工编号为 <code>0</code> 到 <code>n - 1</code> 。每位员工都有一位 <strong>喜欢</strong> 的员工，每位员工 <strong>当且仅当</strong> 他被安排在喜欢员工的旁边，他才会参加会议。每位员工喜欢的员工 <strong>不会</strong> 是他自己。</p>\n\n<p>给你一个下标从 <strong>0</strong> 开始的整数数组 <code>favorite</code> ，其中 <code>favorite[i]</code> 表示第 <code>i</code> 位员工喜欢的员工。请你返回参加会议的 <strong>最多员工数目</strong> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/14/ex1.png\" style=\"width: 236px; height: 195px;\" /></p>\n\n<pre>\n<b>输入：</b>favorite = [2,2,1,2]\n<b>输出：</b>3\n<strong>解释：</strong>\n上图展示了公司邀请员工 0，1 和 2 参加会议以及他们在圆桌上的座位。\n没办法邀请所有员工参与会议，因为员工 2 没办法同时坐在 0，1 和 3 员工的旁边。\n注意，公司也可以邀请员工 1，2 和 3 参加会议。\n所以最多参加会议的员工数目为 3 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>favorite = [1,2,0]\n<b>输出：</b>3\n<b>解释：</b>\n每个员工都至少是另一个员工喜欢的员工。所以公司邀请他们所有人参加会议的前提是所有人都参加了会议。\n座位安排同图 1 所示：\n- 员工 0 坐在员工 2 和 1 之间。\n- 员工 1 坐在员工 0 和 2 之间。\n- 员工 2 坐在员工 1 和 0 之间。\n参与会议的最多员工数目为 3 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/14/ex2.png\" style=\"width: 219px; height: 220px;\" /></p>\n\n<pre>\n<b>输入：</b>favorite = [3,0,1,4,1]\n<b>输出：</b>4\n<b>解释：</b>\n上图展示了公司可以邀请员工 0，1，3 和 4 参加会议以及他们在圆桌上的座位。\n员工 2 无法参加，因为他喜欢的员工 1 旁边的座位已经被占领了。\n所以公司只能不邀请员工 2 。\n参加会议的最多员工数目为 4 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == favorite.length</code></li>\n\t<li><code>2 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>0 <= favorite[i] <= n - 1</code></li>\n\t<li><code>favorite[i] != i</code></li>\n</ul>\n",
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"From the given array favorite, create a graph where for every index i, there is a directed edge from favorite[i] to i. The graph will be a combination of cycles and chains of acyclic edges. Now, what are the ways in which we can choose employees to sit at the table?",
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"The first way by which we can choose employees is by selecting a cycle of the graph. It can be proven that in this case, the employees that do not lie in the cycle can never be seated at the table.",
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"The second way is by combining acyclic chains. At most two chains can be combined by a cycle of length 2, where each chain ends on one of the employees in the cycle."
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