1697 - Checking Existence of Edge Length Limited Paths\.

Hard

An undirected graph of n nodes is defined by edgeList, where <code>edgeListi = u_i, v_i, dis_i</code> denotes an edge between nodes <code>u_i</code> and <code>v_i</code> with distance <code>dis_i</code>. Note that there may be multiple edges between two nodes.

Given an array queries, where <code>queriesj = p_j, q_j, limit_j</code>, your task is to determine for each queries[j] whether there is a path between <code>p_j</code> and <code>q_j</code> such that each edge on the path has a distance strictly less than <code>limit_j</code> .

Return a boolean array answer, where answer.length == queries.length and the <code>j^th</code> value of answer is true if there is a path for queries[j] is true, and false otherwise.

Example 1:

Input: n = 3, edgeList = \[\[0,1,2],1,2,4,2,0,8,1,0,16], queries = \[\[0,1,2],0,2,5]

Output: false,true

Explanation: The above figure shows the given graph. Note that there are two overlapping edges between 0 and 1 with distances 2 and 16.

For the first query, between 0 and 1 there is no path where each distance is less than 2, thus we return false for this query.

For the second query, there is a path (0 -> 1 -> 2) of two edges with distances less than 5, thus we return true for this query.

Example 2:

Input: n = 5, edgeList = \[\[0,1,10],1,2,5,2,3,9,3,4,13], queries = \[\[0,4,14],1,4,13]

Output: true,false Exaplanation: The above figure shows the given graph.

Constraints:

• <code>2 <= n <= 10⁵</code>

• <code>1 <= edgeList.length, queries.length <= 10⁵</code>

• edgeList[i].length == 3

• queries[j].length == 3

• <code>0 <= u_i, v_i, p_j, q_j<= n - 1</code>

• <code>u_i != v_i</code>

• <code>p_j != q_j</code>

• <code>1 <= dis_i, limit_j<= 10⁹</code>

• There may be multiple edges between two nodes.