Update the array - Count minimum number of operations required such that 2 given conditions are met (Hard)

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Problem
Given an array A of N integers and an integer K. You can perform the following operation any number of times on the given array :

Choose an integer x such that 
Choose any index i such that 
Update A[i] = x
In different operations, different value of x and i can be chosen.

Task

Your task is to count minimum number of operations required such that following conditions are met:

All elements in array A becomes pairwise distinct.
Count of array elements with odd value is equal to count of array elements with even value.
If the above conditions cannot be met after any number of operations, return -1.

Note:

Assume 1 Based Indexing is followed.
Array A is said to have pairwise distinct elements if and only if the value of all the elements in array A is distinct.
Example 

Assumptions:

N = 4
A = [1, 4, 4, 1]
K = 5
Approach:

Initial array A is [1, 4, 4, 1]
Update A[2] = 2, choose x = 2, i = 2.
Update A[4] = 5, choose x = 5, i = 4.
Updated array A is [1, 2, 4, 5]
Now, array A have all distinct elements and count of array elements with odd value is equal to count of array elements with even value.
Therefore, minimum 2 operations are required.
Note, there can be other possible selections of x and i, at each step but the minimum number of operations remains the same. 

Function description 

Complete the minUpdates function provided in the editor. This function takes the following 3 parameters and returns an integer.

N: Represents the number of elements in array A
A: Represents the elements of array A.
K: Represents the value of K
Input Format 

Note: This is the input format that you must use to provide custom input (available above the Compile and Test button).

The first line contains a single integer T, which denotes the number of test cases. T also specifies the number of times you have to run the minUpdates function on a different set of inputs.
For each test case:-
First line contains an integer N.
Next line contains N space-separated integers denoting the elements of array A.
Next line contains an integer K.
Output Format 

For each test case in a new line, print an integer denoting the minimum number of operations required or print -1, if the conditions cannot be met.

Constraints 


Code snippets (also called starter code/boilerplate code) 

This question has code snippets for C, CPP, Java, and Python.

Sample Input
2
6
4 1 5 5 6 8
3
4
1 2 3 1
2
 
Sample Output
1
-1
 
Time Limit: 1.5
Memory Limit: 256
Source Limit:
Explanation
First line denotes number of test cases T = 2.

For first test case:

N = 6
A = [4, 1, 5, 5, 6, 8]
K = 3
Approach:

Either update element at index 3 or index 4 with value 3.
Either A[3] = 3 or A[4] = 3
Array A becomes [4, 1, 3, 5, 6, 8] or [4, 1, 5, 3, 6, 8]
In both the cases number of operations required is 1, which is minimum possible.
For second test case:

N = 4
A = [1, 2, 3, 1]
K = 2
Approach:

Number of array elements with even value must be 2.
Since, number of elements with even value in range [1,K] is only 1 i.e. 2 which is already present in array A.
Thus, above conditions cannot be met. 
Therefore, print -1.


Brainstorming... Initial Thoughts
1. We need to ensure that all elements in the array are pairwise distinct and that the count of odd and even elements is equal.
2. We can use a set to keep track of the distinct elements in the array and count the number of odd and even elements.
3. We can iterate through the array and for each duplicatete element, we can try to replace it with a new value that is not already in the set and that helps us achieve the balance of odd and even elements.
4. We can keep track of the number of operations required to achieve the desired conditions and return that count at the end. If it's not possible to achieve the conditions, we can return -1.

The problem is: it is possible that array elements are unique but the counts of odd and even elements are not equal. In such cases, we need to perform operations to balance the counts while ensuring uniqueness.


Could not solve the problem -- even with ChatGPT's help