Determine whether an array can be transformed into nondecreasing order under a bit-based swap restriction.
Problem
You are given an integer array nums. You may reorder the array only if the elements you need to swap satisfy a specific bit-manipulation rule derived from their values.
Your task is to determine whether it is possible to sort the array in nondecreasing order using only the allowed reordering operations.
Return true if the array can be sorted under the rule, otherwise return false.
Intuition
This problem is about checking whether the array can be globally sorted while respecting a local constraint based on the binary structure of the numbers. A direct full sort is not enough; you need to reason about which values can move past each other under the restriction.
Input Format
- A single integer array
nums. - The array contains one or more integers.
Output Format
- Return
trueifnumscan be sorted in nondecreasing order under the given restriction. - Otherwise return
false.
Constraints
1 <= nums.length- Values are integers within a typical 32-bit signed range.
- The exact operation rule is problem-specific and should be inferred from the statement.
Example 1
Input
nums = [8,4,2,30,15]
Output
true
Explanation
The array can be arranged into nondecreasing order while respecting the constraint, so the answer is true.
Example 2
Input
nums = [1,2,3,4,5]
Output
true
Explanation
The array is already sorted, so it is trivially sortable.
Show 1 more example
Example 3
Input
nums = [3,16,8,4,2]
Output
false
Explanation
The constrained reordering is not sufficient to place all values into nondecreasing order.
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