perms

All permutations of the elements of a vector.

Category: Mathematics > Elementary Math

Syntax

P = perms(v)

Description

The rows come out in reverse lexicographic order of the positions: the first row is v reversed and the last is v itself. The number of rows grows as n!, so perms(1:10) already has 3,628,800 rows and perms(1:12) is too large for memory.

Because repeated values count as different, perms([1 1 2]) has 6 rows with duplicates; apply unique(..., 'rows') to remove them.

Input arguments

v

Vector of numbers, characters or other values. Repeated values are treated as distinct.

Output arguments

P

Matrix with factorial(numel(v)) rows and numel(v) columns, of the same class as v. A char vector gives a char matrix.

Example

Numbers and characters

perms([1 2 3])
perms('abc')

ans = 6×3

     3     2     1
     3     1     2
     2     3     1
     2     1     3
     1     3     2
     1     2     3
ans = 6×3 char array

    'cba'
    'cab'
    'bca'
    'bac'
    'acb'
    'abc'

See also

nchoosek factorial randperm unique sortrows