Package g1601_1700.s1627_graph_connectivity_with_threshold

Class Solution

java.lang.Object

g1601_1700.s1627_graph_connectivity_with_threshold.Solution

public class Solution
extends Object

1627 - Graph Connectivity With Threshold\. Hard We have `n` cities labeled from `1` to `n`. Two different cities with labels `x` and `y` are directly connected by a bidirectional road if and only if `x` and `y` share a common divisor **strictly greater** than some `threshold`. More formally, cities with labels `x` and `y` have a road between them if there exists an integer `z` such that all of the following are true: * `x % z == 0`, * `y % z == 0`, and * `z > threshold`. Given the two integers, `n` and `threshold`, and an array of `queries`, you must determine for each queries[i] = [ai, bi] if cities ai and bi are connected directly or indirectly. (i.e. there is some path between them). Return _an array_ `answer`_, where_ `answer.length == queries.length` _and_ `answer[i]` _is_ `true` _if for the_ ith _query, there is a path between_ ai _and_ bi_, or_ `answer[i]` _is_ `false` _if there is no path._ **Example 1:**  **Input:** n = 6, threshold = 2, queries = \[\[1,4],[2,5],[3,6]] **Output:** [false,false,true] **Explanation:** The divisors for each number: 1: 1 2: 1, 2 3: 1, 3 4: 1, 2, 4 5: 1, 5 6: 1, 2, 3, 6 Using the underlined divisors above the threshold, only cities 3 and 6 share a common divisor, so they are the only ones directly connected. The result of each query: [1,4] 1 is not connected to 4 [2,5] 2 is not connected to 5 [3,6] 3 is connected to 6 through path 3--6 **Example 2:**  **Input:** n = 6, threshold = 0, queries = \[\[4,5],[3,4],[3,2],[2,6],[1,3]] **Output:** [true,true,true,true,true] **Explanation:** The divisors for each number are the same as the previous example. However, since the threshold is 0, all divisors can be used. Since all numbers share 1 as a divisor, all cities are connected. **Example 3:**  **Input:** n = 5, threshold = 1, queries = \[\[4,5],[4,5],[3,2],[2,3],[3,4]] **Output:** [false,false,false,false,false] **Explanation:** Only cities 2 and 4 share a common divisor 2 which is strictly greater than the threshold 1, so they are the only ones directly connected. Please notice that there can be multiple queries for the same pair of nodes [x, y], and that the query [x, y] is equivalent to the query [y, x]. **Constraints:** * 2 <= n <= 104 * `0 <= threshold <= n` * 1 <= queries.length <= 105 * `queries[i].length == 2` * 1 <= ai, bi <= cities * ai != bi

Constructor Summary

Constructors

Constructor	Description
Solution()

Method Summary

Modifier and Type	Method	Description
List<Boolean>	areConnected(int n, int threshold, int[][] queries)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Solution

public Solution()

Method Detail

areConnected

public List<Boolean> areConnected(int n,
                                  int threshold,
                                  int[][] queries)