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84 lines
3.8 KiB
HTML
84 lines
3.8 KiB
HTML
<p>You are given an integer <code>n</code> and a <strong>directed</strong> graph with <code>n</code> nodes labeled from 0 to <code>n - 1</code>. This is represented by a 2D array <code>edges</code>, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>, start<sub>i</sub>, end<sub>i</sub>]</code> indicates an edge from node <code>u<sub>i</sub></code> to <code>v<sub>i</sub></code> that can <strong>only</strong> be used at any integer time <code>t</code> such that <code>start<sub>i</sub> <= t <= end<sub>i</sub></code>.</p>
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<p>You start at node 0 at time 0.</p>
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<p>In one unit of time, you can either:</p>
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<ul>
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<li>Wait at your current node without moving, or</li>
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<li>Travel along an outgoing edge from your current node if the current time <code>t</code> satisfies <code>start<sub>i</sub> <= t <= end<sub>i</sub></code>.</li>
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</ul>
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<p>Return the <strong>minimum</strong> time required to reach node <code>n - 1</code>. If it is impossible, return <code>-1</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 3, edges = [[0,1,0,1],[1,2,2,5]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">3</span></p>
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<p><strong>Explanation:</strong></p>
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<p><img src="https://assets.leetcode.com/uploads/2025/06/05/screenshot-2025-06-06-at-004535.png" style="width: 150px; height: 141px;" /></p>
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<p>The optimal path is:</p>
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<ul>
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<li>At time <code>t = 0</code>, take the edge <code>(0 → 1)</code> which is available from 0 to 1. You arrive at node 1 at time <code>t = 1</code>, then wait until <code>t = 2</code>.</li>
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<li>At time <code>t = <code>2</code></code>, take the edge <code>(1 → 2)</code> which is available from 2 to 5. You arrive at node 2 at time 3.</li>
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</ul>
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<p>Hence, the minimum time to reach node 2 is 3.</p>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 4, edges = [[0,1,0,3],[1,3,7,8],[0,2,1,5],[2,3,4,7]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">5</span></p>
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<p><strong>Explanation:</strong></p>
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<p><img src="https://assets.leetcode.com/uploads/2025/06/05/screenshot-2025-06-06-at-004757.png" style="width: 170px; height: 219px;" /></p>
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<p>The optimal path is:</p>
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<ul>
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<li>Wait at node 0 until time <code>t = 1</code>, then take the edge <code>(0 → 2)</code> which is available from 1 to 5. You arrive at node 2 at <code>t = 2</code>.</li>
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<li>Wait at node 2 until time <code>t = 4</code>, then take the edge <code>(2 → 3)</code> which is available from 4 to 7. You arrive at node 3 at <code>t = 5</code>.</li>
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</ul>
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<p>Hence, the minimum time to reach node 3 is 5.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 3, edges = [[1,0,1,3],[1,2,3,5]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">-1</span></p>
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<p><strong>Explanation:</strong></p>
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<p><img src="https://assets.leetcode.com/uploads/2025/06/05/screenshot-2025-06-06-at-004914.png" style="width: 150px; height: 145px;" /></p>
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<ul>
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<li>Since there is no outgoing edge from node 0, it is impossible to reach node 2. Hence, the output is -1.</li>
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</ul>
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</div>
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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<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] == [u<sub>i</sub>, v<sub>i</sub>, start<sub>i</sub>, end<sub>i</sub>]</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>0 <= start<sub>i</sub> <= end<sub>i</sub> <= 10<sup>9</sup></code></li>
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</ul>
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