How to find the minimum number of permutations?

Question

C++ / C#

Let's call uniform a set of natural numbers in which even and odd numbers alternate: even-odd-even-odd... or odd-even-odd... Given a set of 2N natural numbers, of which exactly N are even and N are odd . It is necessary to determine for what MINIMUM number of permutations it can be made uniform. By permutation we consider the exchange of places of two e-comrade. Are there any formulas for this?
I need to write a program to calculate. I will write the program myself, the question is how to calculate the minimum number of permutations? even for a person, manually, it is difficult to say what is the minimum .. are there any formulas for this?

Answer 1

Consider the order even-odd-even-odd...
We count how many even ones are not in their places (=a).
And how many odd ones are out of place (=b).
If a≠b, we do not have N even and N odd - we output "invalid data set".
And if they are equal, then a substitutions are needed for the even-odd order. For the opposite - Na.
So the answer is min(a, N−a).