Assume I want to change [1,2,...,n] to anthor order, say [n,n-1,...,2,1].
In the exmaple, I know I can do like this
[1,2,...,n] $\rightarrow$ [2,1...,n]$\rightarrow$ [2,3,1,...,n]$\rightarrow \cdots \rightarrow$ [2,...,n,1]
$\rightarrow$ [3,...,n,2,1]$\rightarrow \cdots$ $\rightarrow$ [n,n-1,...,2,1],
so I need to swap adjacent elements $\frac{(0+n-1)n}{2}$ times.
The above process depends on my observation, but if the aim order of the numbers is more complicated, it won't be this easy to know by observation.
I wonder if there is any genral method to know that if the permutation is even or odd?