1998. GCD Sort of an Array

https://leetcode.com/problems/gcd-sort-of-an-array

Description

You are given an integer array nums, and you can perform the following operation any number of times on nums:

• Swap the positions of two elements nums[i] and nums[j] if gcd(nums[i], nums[j]) > 1 where gcd(nums[i], nums[j]) is the greatest common divisor of nums[i] and nums[j].

Return true if it is possible to sort nums in non-decreasing order using the above swap method, or false otherwise.

Example 1:

**Input:** nums = [7,21,3]
**Output:** true
**Explanation:** We can sort [7,21,3] by performing the following operations:
- Swap 7 and 21 because gcd(7,21) = 7. nums = [**21**,**7**,3]
- Swap 21 and 3 because gcd(21,3) = 3. nums = [**3**,7,**21**]

Example 2:

**Input:** nums = [5,2,6,2]
**Output:** false
**Explanation:** It is impossible to sort the array because 5 cannot be swapped with any other element.

Example 3:

**Input:** nums = [10,5,9,3,15]
**Output:** true
We can sort [10,5,9,3,15] by performing the following operations:
- Swap 10 and 15 because gcd(10,15) = 5. nums = [**15**,5,9,3,**10**]
- Swap 15 and 3 because gcd(15,3) = 3. nums = [**3**,5,9,**15**,10]
- Swap 10 and 15 because gcd(10,15) = 5. nums = [3,5,9,**10**,**15**]

Constraints:

• 1 <= nums.length <= 3 * 104

• 2 <= nums[i] <= 105

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