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| 1 | +<h2><a href="https://leetcode.com/problems/second-minimum-time-to-reach-destination/"><div id="big-omega-company-tags"><div id="big-omega-topbar"><div class="companyTagsContainer" style="overflow-x: scroll; flex-wrap: nowrap;"><div class="companyTagsContainer--tag">No companies found for this problem</div></div><div class="companyTagsContainer--chevron"><div><svg version="1.1" id="icon" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 32 32" fill="#4087F1" xml:space="preserve" style="width: 20px;"><polygon points="16,22 6,12 7.4,10.6 16,19.2 24.6,10.6 26,12 "></polygon><rect id="_x3C_Transparent_Rectangle_x3E_" class="st0" fill="none" width="32" height="32"></rect></svg></div></div></div></div>2045. Second Minimum Time to Reach Destination</a></h2><h3>Hard</h3><hr><div><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> |
| 2 | + |
| 3 | +<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> |
| 4 | + |
| 5 | +<p>The <strong>second minimum value</strong> is defined as the smallest value<strong> strictly larger </strong>than the minimum value.</p> |
| 6 | + |
| 7 | +<ul> |
| 8 | + <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> |
| 9 | +</ul> |
| 10 | + |
| 11 | +<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> |
| 12 | + |
| 13 | +<p><strong>Notes:</strong></p> |
| 14 | + |
| 15 | +<ul> |
| 16 | + <li>You can go through any vertex <strong>any</strong> number of times, <strong>including</strong> <code>1</code> and <code>n</code>.</li> |
| 17 | + <li>You can assume that when the journey <strong>starts</strong>, all signals have just turned <strong>green</strong>.</li> |
| 18 | +</ul> |
| 19 | + |
| 20 | +<p> </p> |
| 21 | +<p><strong class="example">Example 1:</strong></p> |
| 22 | +<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;"> |
| 23 | +<pre><strong>Input:</strong> n = 5, edges = [[1,2],[1,3],[1,4],[3,4],[4,5]], time = 3, change = 5 |
| 24 | +<strong>Output:</strong> 13 |
| 25 | +<strong>Explanation:</strong> |
| 26 | +The figure on the left shows the given graph. |
| 27 | +The blue path in the figure on the right is the minimum time path. |
| 28 | +The time taken is: |
| 29 | +- Start at 1, time elapsed=0 |
| 30 | +- 1 -> 4: 3 minutes, time elapsed=3 |
| 31 | +- 4 -> 5: 3 minutes, time elapsed=6 |
| 32 | +Hence the minimum time needed is 6 minutes. |
| 33 | + |
| 34 | +The red path shows the path to get the second minimum time. |
| 35 | +- Start at 1, time elapsed=0 |
| 36 | +- 1 -> 3: 3 minutes, time elapsed=3 |
| 37 | +- 3 -> 4: 3 minutes, time elapsed=6 |
| 38 | +- Wait at 4 for 4 minutes, time elapsed=10 |
| 39 | +- 4 -> 5: 3 minutes, time elapsed=13 |
| 40 | +Hence the second minimum time is 13 minutes. |
| 41 | +</pre> |
| 42 | + |
| 43 | +<p><strong class="example">Example 2:</strong></p> |
| 44 | +<img alt="" src="https://assets.leetcode.com/uploads/2021/09/29/eg2.png" style="width: 225px; height: 50px;"> |
| 45 | +<pre><strong>Input:</strong> n = 2, edges = [[1,2]], time = 3, change = 2 |
| 46 | +<strong>Output:</strong> 11 |
| 47 | +<strong>Explanation:</strong> |
| 48 | +The minimum time path is 1 -> 2 with time = 3 minutes. |
| 49 | +The second minimum time path is 1 -> 2 -> 1 -> 2 with time = 11 minutes.</pre> |
| 50 | + |
| 51 | +<p> </p> |
| 52 | +<p><strong>Constraints:</strong></p> |
| 53 | + |
| 54 | +<ul> |
| 55 | + <li><code>2 <= n <= 10<sup>4</sup></code></li> |
| 56 | + <li><code>n - 1 <= edges.length <= min(2 * 10<sup>4</sup>, n * (n - 1) / 2)</code></li> |
| 57 | + <li><code>edges[i].length == 2</code></li> |
| 58 | + <li><code>1 <= u<sub>i</sub>, v<sub>i</sub> <= n</code></li> |
| 59 | + <li><code>u<sub>i</sub> != v<sub>i</sub></code></li> |
| 60 | + <li>There are no duplicate edges.</li> |
| 61 | + <li>Each vertex can be reached directly or indirectly from every other vertex.</li> |
| 62 | + <li><code>1 <= time, change <= 10<sup>3</sup></code></li> |
| 63 | +</ul> |
| 64 | +</div> |
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