nth permutation of a vector in MATLAB

Question

Suppose I have a vector of integers like this:

A = [1 2 3]

What I need is nth permutation of vector A. As we now a vector of n numbers has n! permutation, For example some permutation of A is:

[1 2 3]
[1 3 2]
[2 1 3]
[2 3 1]
...

Is there any built-in function for calculating nth permutation? if not, can anyone please offer me a efficient algorithm for calculate it? Any suggestion would be highly appreciated

Answer 1

I found my answer from @Divakar comment (special thanks to @Divakar)
What I need is:

% this my vector 1, 2, 3 , ..., N
A = 1 : N;
P = perms(A);

% nth permutation of A is nth row of P
nthPerm = P(n, :);

Answer 2

If A is just the trivial sequence 1:N, as @Divakar said, the command

perms(1:N)

produces the permutations you need.

If A is an array whose content is generic and whose length is N, perms can be used to obtain the indices allowing the permutations, i.e.

A_permutations = A(perms(1:N)) 

Example:

given

A =

 3     7     9



  A(perms(1:3))

   9     7     3
   9     3     7
   7     9     3
   7     3     9
   3     7     9
   3     9     7

Answer 3

perms(v) works for the n! case,

http://www.mathworks.de/matlabcentral/fileexchange/11462-npermutek/content/npermutek.m works for the n^n or n^k case.

Answer 4

If you like doing stuff in less lines of code, you can also do:

A=1:N;
nthPerm=getfield(perms(A),{n,A})

Note that this is only valid if A=1,2,3,...,N. For different values of A, you would have to change this into:

A=1:N;
nthPerm=getfield(perms(A),{n,1:length(A)})