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66 lines
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66 lines
3.9 KiB
HTML
<p>A city is represented as a <strong>bi-directional connected</strong> graph with <code>n</code> vertices where each vertex is labeled from <code>1</code> to <code>n</code> (<strong>inclusive</strong>). The edges in the graph are represented as a 2D integer array <code>edges</code>, where each <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> denotes a bi-directional edge between vertex <code>u<sub>i</sub></code> and vertex <code>v<sub>i</sub></code>. Every vertex pair is connected by <strong>at most one</strong> edge, and no vertex has an edge to itself. The time taken to traverse any edge is <code>time</code> minutes.</p>
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<p>Each vertex has a traffic signal which changes its color from <strong>green</strong> to <strong>red</strong> and vice versa every <code>change</code> minutes. All signals change <strong>at the same time</strong>. You can enter a vertex at <strong>any time</strong>, but can leave a vertex <strong>only when the signal is green</strong>. You <strong>cannot wait </strong>at a vertex if the signal is <strong>green</strong>.</p>
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<p>The <strong>second minimum value</strong> is defined as the smallest value<strong> strictly larger </strong>than the minimum value.</p>
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<ul>
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<li>For example the second minimum value of <code>[2, 3, 4]</code> is <code>3</code>, and the second minimum value of <code>[2, 2, 4]</code> is <code>4</code>.</li>
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</ul>
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<p>Given <code>n</code>, <code>edges</code>, <code>time</code>, and <code>change</code>, return <em>the <strong>second minimum time</strong> it will take to go from vertex </em><code>1</code><em> to vertex </em><code>n</code>.</p>
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<p><strong>Notes:</strong></p>
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<ul>
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<li>You can go through any vertex <strong>any</strong> number of times, <strong>including</strong> <code>1</code> and <code>n</code>.</li>
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<li>You can assume that when the journey <strong>starts</strong>, all signals have just turned <strong>green</strong>.</li>
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</ul>
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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/2021/09/29/e1.png" style="width: 200px; height: 250px;" />        <img alt="" src="https://assets.leetcode.com/uploads/2021/09/29/e2.png" style="width: 200px; height: 250px;" />
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<pre>
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<strong>Input:</strong> n = 5, edges = [[1,2],[1,3],[1,4],[3,4],[4,5]], time = 3, change = 5
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<strong>Output:</strong> 13
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<strong>Explanation:</strong>
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The figure on the left shows the given graph.
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The blue path in the figure on the right is the minimum time path.
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The time taken is:
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- Start at 1, time elapsed=0
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- 1 -> 4: 3 minutes, time elapsed=3
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- 4 -> 5: 3 minutes, time elapsed=6
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Hence the minimum time needed is 6 minutes.
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The red path shows the path to get the second minimum time.
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- Start at 1, time elapsed=0
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- 1 -> 3: 3 minutes, time elapsed=3
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- 3 -> 4: 3 minutes, time elapsed=6
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- Wait at 4 for 4 minutes, time elapsed=10
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- 4 -> 5: 3 minutes, time elapsed=13
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Hence the second minimum time is 13 minutes.
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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/2021/09/29/eg2.png" style="width: 225px; height: 50px;" />
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<pre>
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<strong>Input:</strong> n = 2, edges = [[1,2]], time = 3, change = 2
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<strong>Output:</strong> 11
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<strong>Explanation:</strong>
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The minimum time path is 1 -> 2 with time = 3 minutes.
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The second minimum time path is 1 -> 2 -> 1 -> 2 with time = 11 minutes.</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>2 <= n <= 10<sup>4</sup></code></li>
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<li><code>n - 1 <= edges.length <= min(2 * 10<sup>4</sup>, n * (n - 1) / 2)</code></li>
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<li><code>edges[i].length == 2</code></li>
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<li><code>1 <= u<sub>i</sub>, v<sub>i</sub> <= n</code></li>
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<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>
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<li>There are no duplicate edges.</li>
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<li>Each vertex can be reached directly or indirectly from every other vertex.</li>
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<li><code>1 <= time, change <= 10<sup>3</sup></code></li>
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</ul>
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