Class Solution

  • All Implemented Interfaces:

    
    public final class Solution
    
                        

    2709 - Greatest Common Divisor Traversal\.

    Hard

    You are given a 0-indexed integer array nums, and you are allowed to traverse between its indices. You can traverse between index i and index j, i != j, if and only if gcd(nums[i], nums[j]) > 1, where gcd is the greatest common divisor.

    Your task is to determine if for every pair of indices i and j in nums, where i < j, there exists a sequence of traversals that can take us from i to j.

    Return true if it is possible to traverse between all such pairs of indices, or false otherwise.

    Example 1:

    Input: nums = 2,3,6

    Output: true

    Explanation: 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(nums0, nums2) = gcd(2, 6) = 2 > 1, and then move from index 2 to index 1 because gcd(nums2, nums1) = gcd(6, 3) = 3 > 1. To go from index 0 to index 2, we can just go directly because gcd(nums0, nums2) = gcd(2, 6) = 2 > 1. Likewise, to go from index 1 to index 2, we can just go directly because gcd(nums1, nums2) = gcd(3, 6) = 3 > 1.

    Example 2:

    Input: nums = 3,9,5

    Output: false

    Explanation: No sequence of traversals can take us from index 0 to index 2 in this example. So, we return false.

    Example 3:

    Input: nums = 4,3,12,8

    Output: true

    Explanation: 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.

    Constraints:

    • <code>1 <= nums.length <= 10<sup>5</sup></code>

    • <code>1 <= numsi<= 10<sup>5</sup></code>

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description
    • Field Summary

      Fields 
      Modifier and Type Field Description
    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()
    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description
    • Method Summary

      Modifier and Type Method Description
      final Boolean canTraverseAllPairs(IntArray nums)
      • Methods inherited from class java.lang.Object

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