Package g2701_2800.s2709_greatest_common_divisor_traversal

Class Solution

java.lang.Object

g2701_2800.s2709_greatest_common_divisor_traversal.Solution

public class Solution
extends Object

2709 - Greatest Common Divisor Traversal.<p>Hard</p> <p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>, and you are allowed to <strong>traverse</strong> between its indices. You can traverse between index <code>i</code> and index <code>j</code>, <code>i != j</code>, if and only if <code>gcd(nums[i], nums[j]) > 1</code>, where <code>gcd</code> is the <strong>greatest common divisor</strong>.</p> <p>Your task is to determine if for <strong>every pair</strong> of indices <code>i</code> and <code>j</code> in nums, where <code>i < j</code>, there exists a <strong>sequence of traversals</strong> that can take us from <code>i</code> to <code>j</code>.</p> <p>Return <code>true</code> <em>if it is possible to traverse between all such pairs of indices,</em> <em>or</em> <code>false</code> <em>otherwise.</em></p> <p><strong>Example 1:</strong></p> <p><strong>Input:</strong> nums = [2,3,6]</p> <p><strong>Output:</strong> true</p> <p><strong>Explanation:</strong> In this example, there are 3 possible pairs of indices: (0, 1), (0, 2), and (1, 2). To go from index 0 to index 1, we can use the sequence of traversals 0 -> 2 -> 1, where we move from index 0 to index 2 because gcd(nums[0], nums[2]) = gcd(2, 6) = 2 > 1, and then move from index 2 to index 1 because gcd(nums[2], nums[1]) = gcd(6, 3) = 3 > 1. To go from index 0 to index 2, we can just go directly because gcd(nums[0], nums[2]) = gcd(2, 6) = 2 > 1. Likewise, to go from index 1 to index 2, we can just go directly because gcd(nums[1], nums[2]) = gcd(3, 6) = 3 > 1.</p> <p><strong>Example 2:</strong></p> <p><strong>Input:</strong> nums = [3,9,5]</p> <p><strong>Output:</strong> false</p> <p><strong>Explanation:</strong> No sequence of traversals can take us from index 0 to index 2 in this example. So, we return false.</p> <p><strong>Example 3:</strong></p> <p><strong>Input:</strong> nums = [4,3,12,8]</p> <p><strong>Output:</strong> true</p> <p><strong>Explanation:</strong> There are 6 possible pairs of indices to traverse between: (0, 1), (0, 2), (0, 3), (1, 2), (1, 3), and (2, 3). A valid sequence of traversals exists for each pair, so we return true.</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= nums.length <= 10⁵</code></li> <li><code>1 <= nums[i] <= 10⁵</code></li> </ul>

Constructor Summary

Constructors

Constructor	Description
Solution()

Method Summary

Modifier and Type	Method	Description
boolean	canTraverseAllPairs(int[] nums)

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

canTraverseAllPairs

public boolean canTraverseAllPairs(int[] nums)