3011 - Find if Array Can Be Sorted.

Medium

You are given a 0-indexed array of positive integers nums.

In one operation , you can swap any two adjacent elements if they have the same number of set bits. You are allowed to do this operation any number of times ( including zero ).

Return true if you can sort the array, else return false.

Example 1:

Input: nums = 8,4,2,30,15

Output: true

Explanation: Let's look at the binary representation of every element. The numbers 2, 4, and 8 have one set bit each with binary representation "10", "100", and "1000" respectively. The numbers 15 and 30 have four set bits each with binary representation "1111" and "11110". We can sort the array using 4 operations:

• Swap nums0 with nums1. This operation is valid because 8 and 4 have one set bit each. The array becomes 4,8,2,30,15.

• Swap nums1 with nums2. This operation is valid because 8 and 2 have one set bit each. The array becomes 4,2,8,30,15.

• Swap nums0 with nums1. This operation is valid because 4 and 2 have one set bit each. The array becomes 2,4,8,30,15.

• Swap nums3 with nums4. This operation is valid because 30 and 15 have four set bits each. The array becomes 2,4,8,15,30.

The array has become sorted, hence we return true. Note that there may be other sequences of operations which also sort the array.

Example 2:

Input: nums = 1,2,3,4,5

Output: true

Explanation: The array is already sorted, hence we return true.

Example 3:

Input: nums = 3,16,8,4,2

Output: false

Explanation: It can be shown that it is not possible to sort the input array using any number of operations.

Constraints:

• 1 <= nums.length <= 100

• <code>1 <= numsi<= 2⁸</code>