3587. Minimum Adjacent Swaps to Alternate Parity
You are given an array nums of distinct integers.
In one operation, you can swap any two adjacent elements in the array.
An arrangement of the array is considered valid if the parity of adjacent elements alternates, meaning every pair of neighboring elements consists of one even and one odd number.
Return the minimum number of adjacent swaps required to transform nums into any valid arrangement.
If it is impossible to rearrange nums such that no two adjacent elements have the same parity, return -1.
Example 1:
Input: nums = [2,4,6,5,7]
Output: 3
Explanation:
Swapping 5 and 6, the array becomes [2,4,5,6,7]
Swapping 5 and 4, the array becomes [2,5,4,6,7]
Swapping 6 and 7, the array becomes [2,5,4,7,6]. The array is now a valid arrangement. Thus, the answer is 3.
Example 2:
Input: nums = [2,4,5,7]
Output: 1
Explanation:
By swapping 4 and 5, the array becomes [2,5,4,7], which is a valid arrangement. Thus, the answer is 1.
Example 3:
Input: nums = [1,2,3]
Output: 0
Explanation:
The array is already a valid arrangement. Thus, no operations are needed.
Example 4:
Input: nums = [4,5,6,8]
Output: -1
Explanation:
No valid arrangement is possible. Thus, the answer is -1.
Constraints:
1 <= nums.length <= 1051 <= nums[i] <= 109- All elements in
numsare distinct.
Hints
Hint 1
evenCnt and oddCnt in nums. If abs(evenCnt - oddCnt) > 1, return -1 immediately.Hint 2
n = len(nums). You’ll try at most two target parity‐patterns: one starting with even at index 0, one with odd at index 0.Hint 3
n is odd, only the pattern whose starting parity matches the larger of evenCnt or oddCnt is feasible. If n is even, both starting‐even and starting‐odd patterns are possible—compute both and take the minimum.Hint 4
nums (or odd elements) and the indices where an even (or odd) should go in the pattern.