Im working on a problem where i have 2 variables
A= (1,2,3) B= (3,2,1)
I have to calculate the number of permutations, and the number of paths by swaping adjancent numbers until A becomes B
For permutations Im currently using the following function in python
nPr = (math.factorial(n))/(math.factorial(n-n))
This one works as intended and the result is ok (in this case nPr = 6), however how can I calculate the number of paths (swaps of pairs) until i get to B?
The combination formula
(n!)/((n-r!)*(r!))
doesnt seem to make the job since it always comes out as 1. (when r = n)
So there has to be another way to do this, I tried using the factorial of nPr however when 6! = 720, meaning theres 720 posible paths to get to B and thats not true.
this was just one example of 3 digits but A and B can be sets of numbers of 2,3,4,5... etc
For a list of size n my idea would be:
You need maximum n-1 swaps to put the first digit into its correct position, then you need maximum n-2 swaps to put the second digit into its correct position, n-3 for the third and so on untill 0 for the last.
Therefore maximum (1/2)(n-1)(n) swaps