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3534. Path Existence Queries in a Graph II

Description

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 queries[i] = [ui, vi], find the minimum distance between nodes ui and vi. 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 ith 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:

Query Shortest Path Minimum Distance
[0, 3] 0 → 3 1
[2, 4] 2 → 4 1

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:

Query Shortest Path Minimum Distance
[0, 1] 0 → 1 1
[0, 2] 0 → 1 → 2 2
[2, 3] None -1
[4, 3] 3 → 4 1

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:

  • 1 <= n == nums.length <= 105
  • 0 <= nums[i] <= 105
  • 0 <= maxDiff <= 105
  • 1 <= queries.length <= 105
  • queries[i] == [ui, vi]
  • 0 <= ui, vi < n

Solutions

Solution 1

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