leetcode-problemset/leetcode-cn/originData/number-of-possible-sets-of-closing-branches.json

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            "questionId": "3217",
            "questionFrontendId": "2959",
            "categoryTitle": "Algorithms",
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            "title": "Number of Possible Sets of Closing Branches",
            "titleSlug": "number-of-possible-sets-of-closing-branches",
            "content": "<p>There is a company with <code>n</code> branches across the country, some of which are connected by roads. Initially, all branches are reachable from each other by traveling some roads.</p>\n\n<p>The company has realized that they are spending an excessive amount of time traveling between their branches. As a result, they have decided to close down some of these branches (<strong>possibly none</strong>). However, they want to ensure that the remaining branches have a distance of at most <code>maxDistance</code> from each other.</p>\n\n<p>The <strong>distance</strong> between two branches is the <strong>minimum</strong> total traveled length needed to reach one branch from another.</p>\n\n<p>You are given integers <code>n</code>, <code>maxDistance</code>, and a <strong>0-indexed</strong> 2D array <code>roads</code>, where <code>roads[i] = [u<sub>i</sub>, v<sub>i</sub>, w<sub>i</sub>]</code> represents the <strong>undirected</strong> road between branches <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> with length <code>w<sub>i</sub></code>.</p>\n\n<p>Return <em>the number of possible sets of closing branches, so that any branch has a distance of at most </em><code>maxDistance</code><em> from any other</em>.</p>\n\n<p><strong>Note</strong> that, after closing a branch, the company will no longer have access to any roads connected to it.</p>\n\n<p><strong>Note</strong> that, multiple roads are allowed.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/08/example11.png\" style=\"width: 221px; height: 191px;\" />\n<pre>\n<strong>Input:</strong> n = 3, maxDistance = 5, roads = [[0,1,2],[1,2,10],[0,2,10]]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The possible sets of closing branches are:\n- The set [2], after closing, active branches are [0,1] and they are reachable to each other within distance 2.\n- The set [0,1], after closing, the active branch is [2].\n- The set [1,2], after closing, the active branch is [0].\n- The set [0,2], after closing, the active branch is [1].\n- The set [0,1,2], after closing, there are no active branches.\nIt can be proven, that there are only 5 possible sets of closing branches.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/08/example22.png\" style=\"width: 221px; height: 241px;\" />\n<pre>\n<strong>Input:</strong> n = 3, maxDistance = 5, roads = [[0,1,20],[0,1,10],[1,2,2],[0,2,2]]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> The possible sets of closing branches are:\n- The set [], after closing, active branches are [0,1,2] and they are reachable to each other within distance 4.\n- The set [0], after closing, active branches are [1,2] and they are reachable to each other within distance 2.\n- The set [1], after closing, active branches are [0,2] and they are reachable to each other within distance 2.\n- The set [0,1], after closing, the active branch is [2].\n- The set [1,2], after closing, the active branch is [0].\n- The set [0,2], after closing, the active branch is [1].\n- The set [0,1,2], after closing, there are no active branches.\nIt can be proven, that there are only 7 possible sets of closing branches.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1, maxDistance = 10, roads = []\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> The possible sets of closing branches are:\n- The set [], after closing, the active branch is [0].\n- The set [0], after closing, there are no active branches.\nIt can be proven, that there are only 2 possible sets of closing branches.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10</code></li>\n\t<li><code>1 &lt;= maxDistance &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= roads.length &lt;= 1000</code></li>\n\t<li><code>roads[i].length == 3</code></li>\n\t<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt;= n - 1</code></li>\n\t<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>\n\t<li><code>1 &lt;= w<sub>i</sub> &lt;= 1000</code></li>\n\t<li>All branches are reachable from each other by traveling some roads.</li>\n</ul>\n",
            "translatedTitle": "关闭分部的可行集合数目",
            "translatedContent": "<p>一个公司在全国有 <code>n</code>&nbsp;个分部，它们之间有的有道路连接。一开始，所有分部通过这些道路两两之间互相可以到达。</p>\n\n<p>公司意识到在分部之间旅行花费了太多时间，所以它们决定关闭一些分部（<b>也可能不关闭任何分部</b>），同时保证剩下的分部之间两两互相可以到达且最远距离不超过&nbsp;<code>maxDistance</code>&nbsp;。</p>\n\n<p>两个分部之间的 <strong>距离</strong> 是通过道路长度之和的 <strong>最小值</strong>&nbsp;。</p>\n\n<p>给你整数&nbsp;<code>n</code>&nbsp;，<code>maxDistance</code>&nbsp;和下标从 <strong>0</strong>&nbsp;开始的二维整数数组&nbsp;<code>roads</code>&nbsp;，其中&nbsp;<code>roads[i] = [u<sub>i</sub>, v<sub>i</sub>, w<sub>i</sub>]</code>&nbsp;表示一条从&nbsp;<code>u<sub>i</sub></code>&nbsp;到&nbsp;<code>v<sub>i</sub></code>&nbsp;长度为&nbsp;<code>w<sub>i</sub></code>的&nbsp;<strong>无向</strong>&nbsp;道路。</p>\n\n<p>请你返回关闭分部的可行方案数目，满足每个方案里剩余分部之间的最远距离不超过<em>&nbsp;</em><code>maxDistance</code>。</p>\n\n<p><strong>注意</strong>，关闭一个分部后，与之相连的所有道路不可通行。</p>\n\n<p><b>注意</b>，两个分部之间可能会有多条道路。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/08/example11.png\" style=\"width: 221px; height: 191px;\" /></p>\n\n<pre>\n<b>输入：</b>n = 3, maxDistance = 5, roads = [[0,1,2],[1,2,10],[0,2,10]]\n<b>输出：</b>5\n<b>解释：</b>可行的关闭分部方案有：\n- 关闭分部集合 [2] ，剩余分部为 [0,1] ，它们之间的距离为 2 。\n- 关闭分部集合 [0,1] ，剩余分部为 [2] 。\n- 关闭分部集合 [1,2] ，剩余分部为 [0] 。\n- 关闭分部集合 [0,2] ，剩余分部为 [1] 。\n- 关闭分部集合 [0,1,2] ，关闭后没有剩余分部。\n总共有 5 种可行的关闭方案。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/08/example22.png\" style=\"width: 221px; height: 241px;\" /></p>\n\n<pre>\n<b>输入：</b>n = 3, maxDistance = 5, roads = [[0,1,20],[0,1,10],[1,2,2],[0,2,2]]\n<b>输出：</b>7\n<b>解释：</b>可行的关闭分部方案有：\n- 关闭分部集合 [] ，剩余分部为 [0,1,2] ，它们之间的最远距离为 4 。\n- 关闭分部集合 [0] ，剩余分部为 [1,2] ，它们之间的距离为 2 。\n- 关闭分部集合 [1] ，剩余分部为 [0,2] ，它们之间的距离为 2 。\n- 关闭分部集合 [0,1] ，剩余分部为 [2] 。\n- 关闭分部集合 [1,2] ，剩余分部为 [0] 。\n- 关闭分部集合 [0,2] ，剩余分部为 [1] 。\n- 关闭分部集合 [0,1,2] ，关闭后没有剩余分部。\n总共有 7 种可行的关闭方案。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>n = 1, maxDistance = 10, roads = []\n<b>输出：</b>2\n<b>解释：</b>可行的关闭分部方案有：\n- 关闭分部集合 [] ，剩余分部为 [0] 。\n- 关闭分部集合 [0] ，关闭后没有剩余分部。\n总共有 2 种可行的关闭方案。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10</code></li>\n\t<li><code>1 &lt;= maxDistance &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= roads.length &lt;= 1000</code></li>\n\t<li><code>roads[i].length == 3</code></li>\n\t<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt;= n - 1</code></li>\n\t<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>\n\t<li><code>1 &lt;= w<sub>i</sub> &lt;= 1000</code></li>\n\t<li>一开始所有分部之间通过道路互相可以到达。</li>\n</ul>\n",
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