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.<p>Hard</p> <p>We have <code>n</code> cities labeled from <code>1</code> to <code>n</code>. Two different cities with labels <code>x</code> and <code>y</code> are directly connected by a bidirectional road if and only if <code>x</code> and <code>y</code> share a common divisor <strong>strictly greater</strong> than some <code>threshold</code>. More formally, cities with labels <code>x</code> and <code>y</code> have a road between them if there exists an integer <code>z</code> such that all of the following are true:</p> <ul> <li><code>x % z == 0</code>,</li> <li><code>y % z == 0</code>, and</li> <li><code>z > threshold</code>.</li> </ul> <p>Given the two integers, <code>n</code> and <code>threshold</code>, and an array of <code>queries</code>, you must determine for each <code>queries[i] = [a_i, b_i]</code> if cities <code>a_i</code> and <code>b_i</code> are connected directly or indirectly. (i.e. there is some path between them).</p> <p>Return <em>an array</em> <code>answer</code><em>, where</em> <code>answer.length == queries.length</code> <em>and</em> <code>answer[i]</code> <em>is</em> <code>true</code> <em>if for the</em> <code>i^th</code> <em>query, there is a path between</em> <code>a_i</code> <em>and</em> <code>b_i</code><em>, or</em> <code>answer[i]</code> <em>is</em> <code>false</code> <em>if there is no path.</em></p> <p><strong>Example 1:</strong></p> <p><img src="https://assets.leetcode.com/uploads/2020/10/09/ex1.jpg" alt="" /></p> <p><strong>Input:</strong> n = 6, threshold = 2, queries = [[1,4],[2,5],[3,6]]</p> <p><strong>Output:</strong> [false,false,true]</p> <p><strong>Explanation:</strong> The divisors for each number:</p> <p>1: 1</p> <p>2: 1, 2</p> <p>3: 1, 3</p> <p>4: 1, 2, 4</p> <p>5: 1, 5</p> <p>6: 1, 2, 3, 6</p> <p>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:</p> <p>[1,4] 1 is not connected to 4</p> <p>[2,5] 2 is not connected to 5</p> <p>[3,6] 3 is connected to 6 through path 3&ndash;6</p> <p><strong>Example 2:</strong></p> <p><img src="https://assets.leetcode.com/uploads/2020/10/10/tmp.jpg" alt="" /></p> <p><strong>Input:</strong> n = 6, threshold = 0, queries = [[4,5],[3,4],[3,2],[2,6],[1,3]]</p> <p><strong>Output:</strong> [true,true,true,true,true]</p> <p><strong>Explanation:</strong> 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.</p> <p><strong>Example 3:</strong></p> <p><img src="https://assets.leetcode.com/uploads/2020/10/17/ex3.jpg" alt="" /></p> <p><strong>Input:</strong> n = 5, threshold = 1, queries = [[4,5],[4,5],[3,2],[2,3],[3,4]]</p> <p><strong>Output:</strong> [false,false,false,false,false]</p> <p><strong>Explanation:</strong> 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].</p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 <= n <= 10⁴</code></li> <li><code>0 <= threshold <= n</code></li> <li><code>1 <= queries.length <= 10⁵</code></li> <li><code>queries[i].length == 2</code></li> <li><code>1 <= a_i, b_i <= cities</code></li> <li><code>a_i != b_i</code></li> </ul>

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 Details

Solution

public Solution()

Method Details

areConnected

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