LeetCode-in-Java

3532. Path Existence Queries in a Graph I

Medium

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 sorted in non-decreasing order, 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], determine whether there exists a path between nodes ui and vi.

Return a boolean array answer, where answer[i] is true if there exists a path between ui and vi in the ith query and false otherwise.

Example 1:

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

Output: [true,false]

Explanation:

• Query [0,0]: Node 0 has a trivial path to itself.
• Query [0,1]: There is no edge between Node 0 and Node 1 because |nums[0] - nums[1]| = |1 - 3| = 2, which is greater than maxDiff.
• Thus, the final answer after processing all the queries is [true, false].

Example 2:

Input: n = 4, nums = [2,5,6,8], maxDiff = 2, queries = [[0,1],[0,2],[1,3],[2,3]]

Output: [false,false,true,true]

Explanation:

The resulting graph is:

• Query [0,1]: There is no edge between Node 0 and Node 1 because |nums[0] - nums[1]| = |2 - 5| = 3, which is greater than maxDiff.
• Query [0,2]: There is no edge between Node 0 and Node 2 because |nums[0] - nums[2]| = |2 - 6| = 4, which is greater than maxDiff.
• Query [1,3]: There is a path between Node 1 and Node 3 through Node 2 since |nums[1] - nums[2]| = |5 - 6| = 1 and |nums[2] - nums[3]| = |6 - 8| = 2, both of which are within maxDiff.
• Query [2,3]: There is an edge between Node 2 and Node 3 because |nums[2] - nums[3]| = |6 - 8| = 2, which is equal to maxDiff.
• Thus, the final answer after processing all the queries is [false, false, true, true].

Constraints:

• 1 <= n == nums.length <= 105
• 0 <= nums[i] <= 105
• nums is sorted in non-decreasing order.
• 0 <= maxDiff <= 105
• 1 <= queries.length <= 105
• queries[i] == [ui, vi]
• 0 <= ui, vi < n

Solution

public class Solution {
    public boolean[] pathExistenceQueries(int n, int[] nums, int maxDiff, int[][] queries) {
        int[] comp = new int[n];
        int compId = 0;
        comp[0] = compId;
        for (int i = 1; i < n; i++) {
            if (nums[i] - nums[i - 1] <= maxDiff) {
                comp[i] = compId;
            } else {
                compId++;
                comp[i] = compId;
            }
        }
        boolean[] ans = new boolean[queries.length];
        for (int i = 0; i < queries.length; i++) {
            int x = queries[i][0];
            int y = queries[i][1];
            ans[i] = (comp[x] == comp[y]);
        }
        return ans;
    }
}

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