3534 - Path Existence Queries in a Graph II.

Hard

You are given an integer n representing the number of nodes in a graph, labeled from 0 to n - 1.

You are also given an integer array nums of length n and an integer maxDiff.

An undirected edge exists between nodes i and j if the absolute difference between nums[i] and nums[j] is at most maxDiff (i.e., |nums[i] - nums[j]| <= maxDiff).

You are also given a 2D integer array queries. For each <code>queriesi = u_i, v_i</code>, find the minimum distance between nodes <code>u_i</code> and <code>v_i</code>_. If no path exists between the two nodes, return -1 for that query.

Return an array answer, where answer[i] is the result of the <code>i^th</code> query.

Note: The edges between the nodes are unweighted.

Example 1:

Input: n = 5, nums = 1,8,3,4,2, maxDiff = 3, queries = [0,3,2,4]

Output: 1,1

Explanation:

The resulting graph is:

Thus, the output is [1, 1].

Example 2:

Input: n = 5, nums = 5,3,1,9,10, maxDiff = 2, queries = [0,1,0,2,2,3,4,3]

Output: 1,2,-1,1

Explanation:

The resulting graph is:

Here is the equivalent Markdown for the given HTML table:

Thus, the output is [1, 2, -1, 1].

Example 3:

Input: n = 3, nums = 3,6,1, maxDiff = 1, queries = [0,0,0,1,1,2]

Output: 0,-1,-1

Explanation:

There are no edges between any two nodes because:

• Nodes 0 and 1: |nums[0] - nums[1]| = |3 - 6| = 3 > 1

• Nodes 0 and 2: |nums[0] - nums[2]| = |3 - 1| = 2 > 1

• Nodes 1 and 2: |nums[1] - nums[2]| = |6 - 1| = 5 > 1

Thus, no node can reach any other node, and the output is [0, -1, -1].

Constraints:

• <code>1 <= n == nums.length <= 10⁵</code>

• <code>0 <= numsi<= 10⁵</code>

• <code>0 <= maxDiff <= 10⁵</code>

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

• <code>queriesi == u_i, v_i</code>

• <code>0 <= u_i, v_i< n</code>