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70 lines
4.1 KiB
HTML
70 lines
4.1 KiB
HTML
<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>
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<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>
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<p>The <strong>distance</strong> between two branches is the <strong>minimum</strong> total traveled length needed to reach one branch from another.</p>
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<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>
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<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>
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<p><strong>Note</strong> that, after closing a branch, the company will no longer have access to any roads connected to it.</p>
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<p><strong>Note</strong> that, multiple roads are allowed.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2023/11/08/example11.png" style="width: 221px; height: 191px;" />
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<pre>
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<strong>Input:</strong> n = 3, maxDistance = 5, roads = [[0,1,2],[1,2,10],[0,2,10]]
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<strong>Output:</strong> 5
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<strong>Explanation:</strong> The possible sets of closing branches are:
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- The set [2], after closing, active branches are [0,1] and they are reachable to each other within distance 2.
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- The set [0,1], after closing, the active branch is [2].
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- The set [1,2], after closing, the active branch is [0].
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- The set [0,2], after closing, the active branch is [1].
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- The set [0,1,2], after closing, there are no active branches.
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It can be proven, that there are only 5 possible sets of closing branches.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2023/11/08/example22.png" style="width: 221px; height: 241px;" />
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<pre>
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<strong>Input:</strong> n = 3, maxDistance = 5, roads = [[0,1,20],[0,1,10],[1,2,2],[0,2,2]]
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<strong>Output:</strong> 7
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<strong>Explanation:</strong> The possible sets of closing branches are:
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- The set [], after closing, active branches are [0,1,2] and they are reachable to each other within distance 4.
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- The set [0], after closing, active branches are [1,2] and they are reachable to each other within distance 2.
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- The set [1], after closing, active branches are [0,2] and they are reachable to each other within distance 2.
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- The set [0,1], after closing, the active branch is [2].
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- The set [1,2], after closing, the active branch is [0].
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- The set [0,2], after closing, the active branch is [1].
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- The set [0,1,2], after closing, there are no active branches.
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It can be proven, that there are only 7 possible sets of closing branches.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> n = 1, maxDistance = 10, roads = []
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> The possible sets of closing branches are:
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- The set [], after closing, the active branch is [0].
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- The set [0], after closing, there are no active branches.
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It can be proven, that there are only 2 possible sets of closing branches.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= n <= 10</code></li>
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<li><code>1 <= maxDistance <= 10<sup>5</sup></code></li>
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<li><code>0 <= roads.length <= 1000</code></li>
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<li><code>roads[i].length == 3</code></li>
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<li><code>0 <= u<sub>i</sub>, v<sub>i</sub> <= n - 1</code></li>
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<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>
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<li><code>1 <= w<sub>i</sub> <= 1000</code></li>
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<li>All branches are reachable from each other by traveling some roads.</li>
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</ul>
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