3123 - Find Edges in Shortest Paths\.

Hard

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 <code>edgesi = a_i, b_i, w_i</code> indicates that there is an edge between nodes <code>a_i</code> and <code>b_i</code> with weight <code>w_i</code>.

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

Explanation:

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

• The path 0 -> 1 -> 5: The sum of weights is 4 + 1 = 5.

• The path 0 -> 2 -> 3 -> 5: The sum of weights is 1 + 1 + 3 = 5.

• The path 0 -> 2 -> 3 -> 1 -> 5: The sum of weights is 1 + 1 + 2 + 1 = 5.

Example 2:

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

Output: true,false,false,true

Explanation:

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.

Constraints:

• <code>2 <= n <= 5 * 10⁴</code>

• m == edges.length

• <code>1 <= m <= min(5 * 10⁴, n * (n - 1) / 2)</code>

• <code>0 <= a_i, b_i< n</code>

• <code>a_i != b_i</code>

• <code>1 <= w_i<= 10⁵</code>

• There are no repeated edges.