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leetcode-problemset/leetcode-cn/problem (Chinese)/最短路径中的边 [find-edges-in-shortest-paths].html

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2024-04-30 10:04:49 +08:00
<p>给你一个 <code>n</code>&nbsp;个节点的无向带权图,节点编号为 <code>0</code>&nbsp;<code>n - 1</code>&nbsp;。图中总共有 <code>m</code>&nbsp;条边,用二维数组&nbsp;<code>edges</code>&nbsp;表示,其中&nbsp;<code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>, w<sub>i</sub>]</code>&nbsp;表示节点 <code>a<sub>i</sub></code>&nbsp;<code>b<sub>i</sub></code>&nbsp;之间有一条边权为&nbsp;<code>w<sub>i</sub></code>&nbsp;的边。</p>
<p>对于节点 <code>0</code>&nbsp;为出发点,节点 <code>n - 1</code>&nbsp;为结束点的所有最短路,你需要返回一个长度为 <code>m</code>&nbsp;<strong>boolean</strong>&nbsp;数组&nbsp;<code>answer</code>&nbsp;,如果&nbsp;<code>edges[i]</code>&nbsp;<strong>至少</strong>&nbsp;在其中一条最短路上,那么&nbsp;<code>answer[i]</code>&nbsp;&nbsp;<code>true</code>&nbsp;,否则&nbsp;<code>answer[i]</code>&nbsp;&nbsp;<code>false</code>&nbsp;</p>
<p>请你返回数组&nbsp;<code>answer</code>&nbsp;</p>
<p><b>注意</b>,图可能不连通。</p>
<p>&nbsp;</p>
<p><strong class="example">示例 1</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/03/05/graph35drawio-1.png" style="height: 129px; width: 250px;" /></p>
<div class="example-block">
<p><span class="example-io"><b>输入:</b>n = 6, edges = [[0,1,4],[0,2,1],[1,3,2],[1,4,3],[1,5,1],[2,3,1],[3,5,3],[4,5,2]]</span></p>
<p><span class="example-io"><b>输出:</b>[true,true,true,false,true,true,true,false]</span></p>
<p><strong>解释:</strong></p>
<p>以下为节点 0 出发到达节点 5 的 <strong>所有</strong>&nbsp;最短路:</p>
<ul>
<li>路径&nbsp;<code>0 -&gt; 1 -&gt; 5</code>&nbsp;:边权和为&nbsp;<code>4 + 1 = 5</code>&nbsp;</li>
<li>路径&nbsp;<code>0 -&gt; 2 -&gt; 3 -&gt; 5</code>&nbsp;:边权和为&nbsp;<code>1 + 1 + 3 = 5</code>&nbsp;</li>
<li>路径&nbsp;<code>0 -&gt; 2 -&gt; 3 -&gt; 1 -&gt; 5</code>&nbsp;:边权和为&nbsp;<code>1 + 1 + 2 + 1 = 5</code>&nbsp;</li>
</ul>
</div>
<p><strong class="example">示例 2</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/03/05/graphhhh.png" style="width: 185px; height: 136px;" /></p>
<div class="example-block">
<p><span class="example-io"><b>输入:</b>n = 4, edges = [[2,0,1],[0,1,1],[0,3,4],[3,2,2]]</span></p>
<p><span class="example-io"><b>输出:</b>[true,false,false,true]</span></p>
<p><strong>解释:</strong></p>
<p>只有一条从节点 0 出发到达节点 3 的最短路&nbsp;<code>0 -&gt; 2 -&gt; 3</code>&nbsp;,边权和为&nbsp;<code>1 + 2 = 3</code>&nbsp;</p>
</div>
<p>&nbsp;</p>
<p><strong>提示:</strong></p>
<ul>
<li><code>2 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>
<li><code>m == edges.length</code></li>
<li><code>1 &lt;= m &lt;= min(5 * 10<sup>4</sup>, n * (n - 1) / 2)</code></li>
<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>
<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
<li><code>1 &lt;= w<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
<li>图中没有重边。</li>
</ul>