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45 lines
2.8 KiB
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45 lines
2.8 KiB
HTML
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<p>You are given an integer <code>n</code> denoting the number of nodes of a <strong>weighted directed</strong> graph. The nodes are numbered from <code>0</code> to <code>n - 1</code>.</p>
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<p>You are also given a 2D integer array <code>edges</code> where <code>edges[i] = [from<sub>i</sub>, to<sub>i</sub>, weight<sub>i</sub>]</code> denotes that there exists a <strong>directed</strong> edge from <code>from<sub>i</sub></code> to <code>to<sub>i</sub></code> with weight <code>weight<sub>i</sub></code>.</p>
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<p>Lastly, you are given three <strong>distinct</strong> integers <code>src1</code>, <code>src2</code>, and <code>dest</code> denoting three distinct nodes of the graph.</p>
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<p>Return <em>the <strong>minimum weight</strong> of a subgraph of the graph such that it is <strong>possible</strong> to reach</em> <code>dest</code> <em>from both</em> <code>src1</code> <em>and</em> <code>src2</code> <em>via a set of edges of this subgraph</em>. In case such a subgraph does not exist, return <code>-1</code>.</p>
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<p>A <strong>subgraph</strong> is a graph whose vertices and edges are subsets of the original graph. The <strong>weight</strong> of a subgraph is the sum of weights of its constituent edges.</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://assets.leetcode.com/uploads/2022/02/17/example1drawio.png" style="width: 263px; height: 250px;" />
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<pre>
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<strong>Input:</strong> n = 6, edges = [[0,2,2],[0,5,6],[1,0,3],[1,4,5],[2,1,1],[2,3,3],[2,3,4],[3,4,2],[4,5,1]], src1 = 0, src2 = 1, dest = 5
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<strong>Output:</strong> 9
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<strong>Explanation:</strong>
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The above figure represents the input graph.
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The blue edges represent one of the subgraphs that yield the optimal answer.
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Note that the subgraph [[1,0,3],[0,5,6]] also yields the optimal answer. It is not possible to get a subgraph with less weight satisfying all the constraints.
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</pre>
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<p><strong>Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2022/02/17/example2-1drawio.png" style="width: 350px; height: 51px;" />
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<pre>
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<strong>Input:</strong> n = 3, edges = [[0,1,1],[2,1,1]], src1 = 0, src2 = 1, dest = 2
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<strong>Output:</strong> -1
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<strong>Explanation:</strong>
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The above figure represents the input graph.
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It can be seen that there does not exist any path from node 1 to node 2, hence there are no subgraphs satisfying all the constraints.
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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>3 <= n <= 10<sup>5</sup></code></li>
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<li><code>0 <= edges.length <= 10<sup>5</sup></code></li>
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<li><code>edges[i].length == 3</code></li>
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<li><code>0 <= from<sub>i</sub>, to<sub>i</sub>, src1, src2, dest <= n - 1</code></li>
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<li><code>from<sub>i</sub> != to<sub>i</sub></code></li>
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<li><code>src1</code>, <code>src2</code>, and <code>dest</code> are pairwise distinct.</li>
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<li><code>1 <= weight[i] <= 10<sup>5</sup></code></li>
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</ul>
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