{ "data": { "question": { "questionId": "3386", "questionFrontendId": "3123", "categoryTitle": "Algorithms", "boundTopicId": 2746491, "title": "Find Edges in Shortest Paths", "titleSlug": "find-edges-in-shortest-paths", "content": "

You are given an undirected weighted graph of n nodes numbered from 0 to n - 1. The graph consists of m edges represented by a 2D array edges, where edges[i] = [ai, bi, wi] indicates that there is an edge between nodes ai and bi with weight wi.

\n\n

Consider all the shortest paths from node 0 to node n - 1 in the graph. You need to find a boolean array answer where answer[i] is true if the edge edges[i] is part of at least one shortest path. Otherwise, answer[i] is false.

\n\n

Return the array answer.

\n\n

Note that the graph may not be connected.

\n\n

 

\n

Example 1:

\n\"\"\n
\n

Input: 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]]

\n\n

Output: [true,true,true,false,true,true,true,false]

\n\n

Explanation:

\n\n

The following are all the shortest paths between nodes 0 and 5:

\n\n\n
\n\n

Example 2:

\n\"\"\n
\n

Input: n = 4, edges = [[2,0,1],[0,1,1],[0,3,4],[3,2,2]]

\n\n

Output: [true,false,false,true]

\n\n

Explanation:

\n\n

There is one shortest path between nodes 0 and 3, which is the path 0 -> 2 -> 3 with the sum of weights 1 + 2 = 3.

\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "最短路径中的边", "translatedContent": "

给你一个 n 个节点的无向带权图,节点编号为 0 到 n - 1 。图中总共有 m 条边,用二维数组 edges 表示,其中 edges[i] = [ai, bi, wi] 表示节点 ai 和 bi 之间有一条边权为 wi 的边。

\n\n

对于节点 0 为出发点,节点 n - 1 为结束点的所有最短路,你需要返回一个长度为 m 的 boolean 数组 answer ,如果 edges[i] 至少 在其中一条最短路上,那么 answer[i] 为 true ,否则 answer[i] 为 false 。

\n\n

请你返回数组 answer 。

\n\n

注意,图可能不连通。

\n\n

 

\n\n

示例 1:

\n\n

\"\"

\n\n
\n

输入: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]]

\n\n

输出:[true,true,true,false,true,true,true,false]

\n\n

解释:

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以下为节点 0 出发到达节点 5 的 所有 最短路:

\n\n\n
\n\n

示例 2:

\n\n

\"\"

\n\n
\n

输入:n = 4, edges = [[2,0,1],[0,1,1],[0,3,4],[3,2,2]]

\n\n

输出:[true,false,false,true]

\n\n

解释:

\n\n

只有一条从节点 0 出发到达节点 3 的最短路 0 -> 2 -> 3 ,边权和为 1 + 2 = 3 。

\n
\n\n

 

\n\n

提示:

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