mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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190 lines
23 KiB
JSON
190 lines
23 KiB
JSON
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"questionId": "2051",
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"questionFrontendId": "1923",
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"categoryTitle": "Algorithms",
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"boundTopicId": 851802,
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"title": "Longest Common Subpath",
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"titleSlug": "longest-common-subpath",
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"content": "<p>There is a country of <code>n</code> cities numbered from <code>0</code> to <code>n - 1</code>. In this country, there is a road connecting <b>every pair</b> of cities.</p>\n\n<p>There are <code>m</code> friends numbered from <code>0</code> to <code>m - 1</code> who are traveling through the country. Each one of them will take a path consisting of some cities. Each path is represented by an integer array that contains the visited cities in order. The path may contain a city <strong>more than once</strong>, but the same city will not be listed consecutively.</p>\n\n<p>Given an integer <code>n</code> and a 2D integer array <code>paths</code> where <code>paths[i]</code> is an integer array representing the path of the <code>i<sup>th</sup></code> friend, return <em>the length of the <strong>longest common subpath</strong> that is shared by <strong>every</strong> friend's path, or </em><code>0</code><em> if there is no common subpath at all</em>.</p>\n\n<p>A <strong>subpath</strong> of a path is a contiguous sequence of cities within that path.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, paths = [[0,1,<u>2,3</u>,4],\n [<u>2,3</u>,4],\n [4,0,1,<u>2,3</u>]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> The longest common subpath is [2,3].\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3, paths = [[0],[1],[2]]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There is no common subpath shared by the three paths.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, paths = [[<u>0</u>,1,2,3,4],\n [4,3,2,1,<u>0</u>]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> The possible longest common subpaths are [0], [1], [2], [3], and [4]. All have a length of 1.</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>m == paths.length</code></li>\n\t<li><code>2 <= m <= 10<sup>5</sup></code></li>\n\t<li><code>sum(paths[i].length) <= 10<sup>5</sup></code></li>\n\t<li><code>0 <= paths[i][j] < n</code></li>\n\t<li>The same city is not listed multiple times consecutively in <code>paths[i]</code>.</li>\n</ul>\n",
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"translatedTitle": "最长公共子路径",
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"translatedContent": "<p>一个国家由 <code>n</code> 个编号为 <code>0</code> 到 <code>n - 1</code> 的城市组成。在这个国家里，<strong>每两个</strong> 城市之间都有一条道路连接。</p>\n\n<p>总共有 <code>m</code> 个编号为 <code>0</code> 到 <code>m - 1</code> 的朋友想在这个国家旅游。他们每一个人的路径都会包含一些城市。每条路径都由一个整数数组表示，每个整数数组表示一个朋友按顺序访问过的城市序列。同一个城市在一条路径中可能 <strong>重复</strong> 出现，但同一个城市在一条路径中不会连续出现。</p>\n\n<p>给你一个整数 <code>n</code> 和二维数组 <code>paths</code> ，其中 <code>paths[i]</code> 是一个整数数组，表示第 <code>i</code> 个朋友走过的路径，请你返回 <strong>每一个</strong> 朋友都走过的 <strong>最长公共子路径</strong> 的长度，如果不存在公共子路径，请你返回 <code>0</code> 。</p>\n\n<p>一个 <strong>子路径</strong> 指的是一条路径中连续的城市序列。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>n = 5, paths = [[0,1,<strong>2,3</strong>,4],\n [<strong>2,3</strong>,4],\n [4,0,1,<strong>2,3</strong>]]\n<b>输出：</b>2\n<b>解释：</b>最长公共子路径为 [2,3] 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>n = 3, paths = [[0],[1],[2]]\n<b>输出：</b>0\n<b>解释：</b>三条路径没有公共子路径。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>n = 5, paths = [[<strong>0</strong>,1,2,3,4],\n [4,3,2,1,<strong>0</strong>]]\n<b>输出：</b>1\n<b>解释：</b>最长公共子路径为 [0]，[1]，[2]，[3] 和 [4] 。它们长度都为 1 。</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>m == paths.length</code></li>\n\t<li><code>2 <= m <= 10<sup>5</sup></code></li>\n\t<li><code>sum(paths[i].length) <= 10<sup>5</sup></code></li>\n\t<li><code>0 <= paths[i][j] < n</code></li>\n\t<li><code>paths[i]</code> 中同一个城市不会连续重复出现。</li>\n</ul>\n",
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"If there is a common path with length x, there is for sure a common path of length y where y < x.",
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"We can use binary search over the answer with the range [0, min(path[i].length)].",
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"Using binary search, we want to verify if we have a common path of length m. We can achieve this using hashing."
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