mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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175 lines
18 KiB
JSON
175 lines
18 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>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>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>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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"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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