c++ - Difference between permutations -

this question has answer here:

• counting adjacent swaps required convert 1 permutation another 6 answers

is there way compute quantitatively distance between 2 permutations?

suppose have following 2 sequences of elements:

a = {0, 1, 2, 3} b = {0, 3, 2, 1} 

i permutation b differs a because:

• i require 1 swap operation in order transform b a
• there 2 elements within b have index different same elements in a

are there other ways compare , describe difference between two?

the main goal define algorithm able approach second permutation b first 1 a, such if steps of procedure applied outcome permutation a itself. in order to think should best define first sensible procedure describes how b differs a.

is there known algorithm allows approach on permutation another?

there few different ways define difference between 2 sequences. name few:

hamming distance: number of positions @ elements differ.

hamming(a, b)   b[1] different a[1] , b[3] different a[3] => 2 

levenshtein distance: minimum number of modifications necessary 1 sequence another.

levenshtein(a, b)   replace b[1] a[1] , replace b[3] a[3] => 2 

damerau–levenshtein distance: extension of former takes account transpositions.

damerau_levenshtein(a, b)   transpose b[3] b[1] => 1 

based upon given example, interested in tracking transpositions , therefore damerau–levenshtein distance best bet.