Find Edges in Shortest Paths
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.
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.
Return the array answer.
Note that the graph may not be connected.
Example 1
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]]Output
[true,true,true,false,true,true,true,false]The shortest paths from node 0 to node 5 have total weight 5, and exactly the marked edges appear in at least one of those shortest paths.
Example 2
Input
n = 4, edges = [[2,0,1],[0,1,1],[0,3,4],[3,2,2]]Output
[true,false,false,true]The only shortest path from node 0 to node 3 is 0 -> 2 -> 3 with total weight 3.
Constraints
- 2 <= n <= 5 * 10^4
- m == edges.length
- 1 <= m <= min(5 * 10^4, n * (n - 1) / 2)
- 0 <= ai, bi < n
- ai != bi
- 1 <= wi <= 10^5
- There are no repeated edges.