g1901_2000.s1998_gcd_sort_of_an_array

Class Solution

java.lang.Object

g1901_2000.s1998_gcd_sort_of_an_array.Solution

public class Solution
extends Object

1998 - GCD Sort of an Array.

Hard

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

Constructor Summary

Constructors

Constructor and Description
Solution()

Method Summary

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

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

gcdSort

public boolean gcdSort(int[] nums)