construct-uniform-parity-array-ii

You are given an array nums1 of n distinct integers.

You want to construct another array nums2 of length n such that the elements in nums2 are either all odd or all even.

For each index i, you must choose exactly one of the following (in any order):

• nums2[i] = nums1[i]​​​​​​​


• nums2[i] = nums1[i] - nums1[j], for an index j != i, such that nums1[i] - nums1[j] >= 1

Return true if it is possible to construct such an array, otherwise return false.

Example 1:

Input: nums1 = [1,4,7]

Output: true

Explanation:​​​​​​​​​​​​​​

• Set nums2[0] = nums1[0] = 1.


• Set nums2[1] = nums1[1] - nums1[0] = 4 - 1 = 3.


• Set nums2[2] = nums1[2] = 7.


• nums2 = [1, 3, 7], and all elements are odd. Thus, the answer is true.

Example 2:

Input: nums1 = [2,3]

Output: false

Explanation:

It is not possible to construct nums2 such that all elements have the same parity. Thus, the answer is false.

Example 3:

Input: nums1 = [4,6]

Output: true

Explanation:

• Set nums2[0] = nums1[0] = 4.


• Set nums2[1] = nums1[1] = 6.


• nums2 = [4, 6], and all elements are even. Thus, the answer is true.

Constraints:

• 1 <= n == nums1.length <= 105


• 1 <= nums1[i] <= 109


• nums1 consists of distinct integers.