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48 lines
3.1 KiB
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<p>You are given an undirected graph (the <strong>"original graph"</strong>) with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>. You decide to <strong>subdivide</strong> each edge in the graph into a chain of nodes, with the number of new nodes varying between each edge.</p>
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<p>The graph is given as a 2D array of <code>edges</code> where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>, cnt<sub>i</sub>]</code> indicates that there is an edge between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> in the original graph, and <code>cnt<sub>i</sub></code> is the total number of new nodes that you will <strong>subdivide</strong> the edge into. Note that <code>cnt<sub>i</sub> == 0</code> means you will not subdivide the edge.</p>
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<p>To <strong>subdivide</strong> the edge <code>[u<sub>i</sub>, v<sub>i</sub>]</code>, replace it with <code>(cnt<sub>i</sub> + 1)</code> new edges and <code>cnt<sub>i</sub></code> new nodes. The new nodes are <code>x<sub>1</sub></code>, <code>x<sub>2</sub></code>, ..., <code>x<sub>cnt<sub>i</sub></sub></code>, and the new edges are <code>[u<sub>i</sub>, x<sub>1</sub>]</code>, <code>[x<sub>1</sub>, x<sub>2</sub>]</code>, <code>[x<sub>2</sub>, x<sub>3</sub>]</code>, ..., <code>[x<sub>cnt<sub>i</sub>-1</sub>, x<sub>cnt<sub>i</sub></sub>]</code>, <code>[x<sub>cnt<sub>i</sub></sub>, v<sub>i</sub>]</code>.</p>
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<p>In this <strong>new graph</strong>, you want to know how many nodes are <strong>reachable</strong> from the node <code>0</code>, where a node is <strong>reachable</strong> if the distance is <code>maxMoves</code> or less.</p>
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<p>Given the original graph and <code>maxMoves</code>, return <em>the number of nodes that are <strong>reachable</strong> from node </em><code>0</code><em> in the new graph</em>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/01/origfinal.png" style="width: 600px; height: 247px;" />
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<pre>
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<strong>Input:</strong> edges = [[0,1,10],[0,2,1],[1,2,2]], maxMoves = 6, n = 3
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<strong>Output:</strong> 13
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<strong>Explanation:</strong> The edge subdivisions are shown in the image above.
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The nodes that are reachable are highlighted in yellow.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> edges = [[0,1,4],[1,2,6],[0,2,8],[1,3,1]], maxMoves = 10, n = 4
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<strong>Output:</strong> 23
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> edges = [[1,2,4],[1,4,5],[1,3,1],[2,3,4],[3,4,5]], maxMoves = 17, n = 5
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> Node 0 is disconnected from the rest of the graph, so only node 0 is reachable.
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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>0 <= edges.length <= min(n * (n - 1) / 2, 10<sup>4</sup>)</code></li>
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<li><code>edges[i].length == 3</code></li>
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<li><code>0 <= u<sub>i</sub> < v<sub>i</sub> < n</code></li>
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<li>There are <strong>no multiple edges</strong> in the graph.</li>
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<li><code>0 <= cnt<sub>i</sub> <= 10<sup>4</sup></code></li>
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<li><code>0 <= maxMoves <= 10<sup>9</sup></code></li>
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<li><code>1 <= n <= 3000</code></li>
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</ul>
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