perms

All possible permutations

Syntax

P = perms(v)

Description

P = perms(v) returns a matrix containing all permutations of the elements of vector v. Each row of P contains a different permutation of the n elements in v. Matrix P has the same data type as v, and it has n! rows and n columns.

Examples

All Permutations of Double Integers

v = [2 4 6];
P = perms(v)

P = 6×3

     6     4     2
     6     2     4
     4     6     2
     4     2     6
     2     6     4
     2     4     6

All Permutations of Unsigned Integers

v = uint16([1023 4095 65535]);
P = perms(v)

P = 6×3 uint16 matrix

   65535    4095    1023
   65535    1023    4095
    4095   65535    1023
    4095    1023   65535
    1023   65535    4095
    1023    4095   65535

All Permutations of Complex Numbers

v = [1+1i 2+1i 3+1i];
P = perms(v)

P = 6×3 complex

   3.0000 + 1.0000i   2.0000 + 1.0000i   1.0000 + 1.0000i
   3.0000 + 1.0000i   1.0000 + 1.0000i   2.0000 + 1.0000i
   2.0000 + 1.0000i   3.0000 + 1.0000i   1.0000 + 1.0000i
   2.0000 + 1.0000i   1.0000 + 1.0000i   3.0000 + 1.0000i
   1.0000 + 1.0000i   3.0000 + 1.0000i   2.0000 + 1.0000i
   1.0000 + 1.0000i   2.0000 + 1.0000i   3.0000 + 1.0000i

Input Arguments

v — Set of items

vector of numeric, logical, or char values

Set of items, specified as a vector of numeric, logical, or char values.

Example: [1 2 3 4]

Example: [1+1i 2+1i 3+1i 4+1i]

Example: int16([1 2 3 4])

Example: ['abcd']

Example: [true false true false]

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes

Limitations

perms(v) is practical when length(v) is less than about 10.

More About

Permutations

Permutations of a set are all possible arrangements of the elements of the set. P = perms(v) returns permutations of the elements of a vector v in reverse lexicographic order of the element indices in v. For example, for a vector v with 3 elements, P = perms(v) returns the same output as:

P = [v(3) v(2) v(1);
     v(3) v(1) v(2);
     v(2) v(3) v(1);
     v(2) v(1) v(3);
     v(1) v(3) v(2);
     v(1) v(2) v(3)]

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™. (since R2024b)

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The perms function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™. (since R2024b)

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a