leetcode-problemset/leetcode-cn/originData/find-edges-in-shortest-paths.json

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        "question": {
            "questionId": "3386",
            "questionFrontendId": "3123",
            "categoryTitle": "Algorithms",
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            "title": "Find Edges in Shortest Paths",
            "titleSlug": "find-edges-in-shortest-paths",
            "content": "<p>You are given an undirected weighted graph of <code>n</code> nodes numbered from 0 to <code>n - 1</code>. The graph consists of <code>m</code> edges represented by a 2D 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>\n\n<p>Consider all the shortest paths from node 0 to node <code>n - 1</code> in the graph. You need to find a <strong>boolean</strong> array <code>answer</code> where <code>answer[i]</code> is <code>true</code> if the edge <code>edges[i]</code> is part of <strong>at least</strong> one shortest path. Otherwise, <code>answer[i]</code> is <code>false</code>.</p>\n\n<p>Return the array <code>answer</code>.</p>\n\n<p><strong>Note</strong> that the graph may not be connected.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/03/05/graph35drawio-1.png\" style=\"height: 129px; width: 250px;\" />\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">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>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[true,true,true,false,true,true,true,false]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The following are <strong>all</strong> the shortest paths between nodes 0 and 5:</p>\n\n<ul>\n\t<li>The path <code>0 -&gt; 1 -&gt; 5</code>: The sum of weights is <code>4 + 1 = 5</code>.</li>\n\t<li>The path <code>0 -&gt; 2 -&gt; 3 -&gt; 5</code>: The sum of weights is <code>1 + 1 + 3 = 5</code>.</li>\n\t<li>The path <code>0 -&gt; 2 -&gt; 3 -&gt; 1 -&gt; 5</code>: The sum of weights is <code>1 + 1 + 2 + 1 = 5</code>.</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/03/05/graphhhh.png\" style=\"width: 185px; height: 136px;\" />\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">n = 4, edges = [[2,0,1],[0,1,1],[0,3,4],[3,2,2]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[true,false,false,true]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>There is one shortest path between nodes 0 and 3, which is the path <code>0 -&gt; 2 -&gt; 3</code> with the sum of weights <code>1 + 2 = 3</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>m == edges.length</code></li>\n\t<li><code>1 &lt;= m &lt;= min(5 * 10<sup>4</sup>, n * (n - 1) / 2)</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>1 &lt;= w<sub>i</sub> &lt;= 10<sup>5</sup></code></li>\n\t<li>There are no repeated edges.</li>\n</ul>\n",
            "translatedTitle": "最短路径中的边",
            "translatedContent": "<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;到 <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> 和&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>\n\n<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;的 <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;为&nbsp;<code>true</code>&nbsp;，否则&nbsp;<code>answer[i]</code>&nbsp;为&nbsp;<code>false</code>&nbsp;。</p>\n\n<p>请你返回数组&nbsp;<code>answer</code>&nbsp;。</p>\n\n<p><b>注意</b>，图可能不连通。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/03/05/graph35drawio-1.png\" style=\"height: 129px; width: 250px;\" /></p>\n\n<div class=\"example-block\">\n<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>\n\n<p><span class=\"example-io\"><b>输出：</b>[true,true,true,false,true,true,true,false]</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>以下为节点 0 出发到达节点 5 的 <strong>所有</strong>&nbsp;最短路：</p>\n\n<ul>\n\t<li>路径&nbsp;<code>0 -&gt; 1 -&gt; 5</code>&nbsp;：边权和为&nbsp;<code>4 + 1 = 5</code>&nbsp;。</li>\n\t<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>\n\t<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>\n</ul>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/03/05/graphhhh.png\" style=\"width: 185px; height: 136px;\" /></p>\n\n<div class=\"example-block\">\n<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>\n\n<p><span class=\"example-io\"><b>输出：</b>[true,false,false,true]</span></p>\n\n<p><strong>解释：</strong></p>\n\n<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>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>m == edges.length</code></li>\n\t<li><code>1 &lt;= m &lt;= min(5 * 10<sup>4</sup>, n * (n - 1) / 2)</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>1 &lt;= w<sub>i</sub> &lt;= 10<sup>5</sup></code></li>\n\t<li>图中没有重边。</li>\n</ul>\n",
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target=\\\"_blank\\\">Apple\\u653e\\u51fa\\u7684\\u6700\\u65b0\\u7248Swift<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u53d1\\u73b0Swift\\u4e0d\\u662f\\u6700\\u65b0\\u7248\\u7684\\uff0c\\u8bf7\\u8054\\u7cfb\\u6211\\u4eec\\uff01\\u6211\\u4eec\\u5c06\\u5c3d\\u5feb\\u66f4\\u65b0\\u3002<\\/p>\"],\"golang\":[\"Go\",\"<p>\\u7248\\u672c\\uff1a<code>Go 1.21<\\/code><\\/p>\\r\\n\\r\\n<p>\\u652f\\u6301 <a href=\\\"https:\\/\\/pkg.go.dev\\/github.com\\/emirpasic\\/gods@v1.18.1\\\" target=\\\"_blank\\\">https:\\/\\/pkg.go.dev\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u548c <a href=\\\"https:\\/\\/pkg.go.dev\\/github.com\\/emirpasic\\/gods\\/v2@v2.0.0-alpha\\\" target=\\\"_blank\\\">https:\\/\\/pkg.go.dev\\/github.com\\/emirpasic\\/gods\\/v2@v2.0.0-alpha<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 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