mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-11 02:58:13 +08:00
57 lines
4.1 KiB
HTML
57 lines
4.1 KiB
HTML
|
<p>You are given an <strong>undirected weighted</strong> <strong>connected</strong> graph containing <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and an integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>, w<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> with weight <code>w<sub>i</sub></code>.</p>
|
||
|
|
|
||
|
|
<p>Some edges have a weight of <code>-1</code> (<code>w<sub>i</sub> = -1</code>), while others have a <strong>positive</strong> weight (<code>w<sub>i</sub> > 0</code>).</p>
|
||
|
|
|
||
|
|
<p>Your task is to modify <strong>all edges</strong> with a weight of <code>-1</code> by assigning them <strong>positive integer values </strong>in the range <code>[1, 2 * 10<sup>9</sup>]</code> so that the <strong>shortest distance</strong> between the nodes <code>source</code> and <code>destination</code> becomes equal to an integer <code>target</code>. If there are <strong>multiple</strong> <strong>modifications</strong> that make the shortest distance between <code>source</code> and <code>destination</code> equal to <code>target</code>, any of them will be considered correct.</p>
|
||
|
|
|
||
|
|
<p>Return <em>an array containing all edges (even unmodified ones) in any order if it is possible to make the shortest distance from </em><code>source</code><em> to </em><code>destination</code><em> equal to </em><code>target</code><em>, or an <strong>empty array</strong> if it's impossible.</em></p>
|
||
|
|
|
||
|
|
<p><strong>Note:</strong> You are not allowed to modify the weights of edges with initial positive weights.</p>
|
||
|
|
|
||
|
|
<p> </p>
|
||
|
|
<p><strong class="example">Example 1:</strong></p>
|
||
|
|
|
||
|
|
<p><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2023/04/18/graph.png" style="width: 300px; height: 300px;" /></strong></p>
|
||
|
|
|
||
|
|
<pre>
|
||
|
|
<strong>Input:</strong> n = 5, edges = [[4,1,-1],[2,0,-1],[0,3,-1],[4,3,-1]], source = 0, destination = 1, target = 5
|
||
|
|
<strong>Output:</strong> [[4,1,1],[2,0,1],[0,3,3],[4,3,1]]
|
||
|
|
<strong>Explanation:</strong> The graph above shows a possible modification to the edges, making the distance from 0 to 1 equal to 5.
|
||
|
|
</pre>
|
||
|
|
|
||
|
|
<p><strong class="example">Example 2:</strong></p>
|
||
|
|
|
||
|
|
<p><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2023/04/18/graph-2.png" style="width: 300px; height: 300px;" /></strong></p>
|
||
|
|
|
||
|
|
<pre>
|
||
|
|
<strong>Input:</strong> n = 3, edges = [[0,1,-1],[0,2,5]], source = 0, destination = 2, target = 6
|
||
|
|
<strong>Output:</strong> []
|
||
|
|
<strong>Explanation:</strong> The graph above contains the initial edges. It is not possible to make the distance from 0 to 2 equal to 6 by modifying the edge with weight -1. So, an empty array is returned.
|
||
|
|
</pre>
|
||
|
|
|
||
|
|
<p><strong class="example">Example 3:</strong></p>
|
||
|
|
|
||
|
|
<p><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2023/04/19/graph-3.png" style="width: 300px; height: 300px;" /></strong></p>
|
||
|
|
|
||
|
|
<pre>
|
||
|
|
<strong>Input:</strong> n = 4, edges = [[1,0,4],[1,2,3],[2,3,5],[0,3,-1]], source = 0, destination = 2, target = 6
|
||
|
|
<strong>Output:</strong> [[1,0,4],[1,2,3],[2,3,5],[0,3,1]]
|
||
|
|
<strong>Explanation:</strong> The graph above shows a modified graph having the shortest distance from 0 to 2 as 6.
|
||
|
|
</pre>
|
||
|
|
|
||
|
|
<p> </p>
|
||
|
|
<p><strong>Constraints:</strong></p>
|
||
|
|
|
||
|
|
<ul>
|
||
|
|
<li><code>1 <= n <= 100</code></li>
|
||
|
|
<li><code><font face="monospace">1 <= edges.length <= n * (n - 1) / 2</font></code></li>
|
||
|
|
<li><code>edges[i].length == 3</code></li>
|
||
|
|
<li><code>0 <= a<sub>i</sub>, b<sub>i </sub>< n</code></li>
|
||
|
|
<li><code><font face="monospace">w<sub>i</sub> = -1 </font></code>or <code><font face="monospace">1 <= w<sub>i </sub><= 10<sup><span style="font-size: 10.8333px;">7</span></sup></font></code></li>
|
||
|
|
<li><code>a<sub>i </sub>!= b<sub>i</sub></code></li>
|
||
|
|
<li><code>0 <= source, destination < n</code></li>
|
||
|
|
<li><code>source != destination</code></li>
|
||
|
|
<li><code><font face="monospace">1 <= target <= 10<sup>9</sup></font></code></li>
|
||
|
|
<li>The graph is connected, and there are no self-loops or repeated edges</li>
|
||
|
|
</ul>
|