how to create an array of all permutations

Hi there,

I have a question about how to create the following array in a simple, concise way (for any permutations).

Think of a 4 digit lock, but numbers allowed are not 0-9, but 1-6 or 0-17 (or any other range).

For 0-9 there are 10^4 permutations, which should be a 10000 x 4 array, each row showing one of the permutations.

I thought of building the array from 4 vectors (thousand, hundred, tens, ones), but that is also cumbersome when looking at a 7digit lock with 11 possible numbers for each digit.

example:

4 digits, possible numbers for each digit 1 - 6 (1296 permutations)

unity_ones = [1;6];

which means that the ones vector can be created by:

n = 1296/6;

ones_vector = [];

for i=1:n

ones_vector = [ones_vector,ones];

end

Then one can do the same for the tens_vector, hundreds_vector and thousands_vector... This seems not very efficient. I am sure there is an easier, one or two liner out there.... :-)

Answer 1

[James Tursa]

If you want all of them in an array (which might be too large if the number of digits is too large), you can use

n = number of digits
b = range of the digits (0 to b)
result = dec2base(0:(b+1)^n-1,b+1);

This will give you a character array since the digits might be bigger than 9.

If b is 9 or less, you can turn this into numeric with

result = dec2base(0:(b+1)^n-1,b+1) - '0';

Otherwise, you would need code to convert the letters 'A' - whatever into numbers.

[antifreund]

Thanks for the answer James...

That works well for any number below 9, but still requires an additional conversion

n = 4

b = 5 %(6 digits)

result = dec2base(0:(b+1)^n-1,b+1);

yields:

result=

'0000'

'0001'

'0002'

'0003'

'0004'

'0005'

'0010'

'0011'

....

'6666'

How is that converted into an 1296 x 4 array with numbers?

Thanks for your help, much appreciated!

[antifreund]

Yes, I know it is str2num to convert a string into a number, but ideally each row needs to be mae into 4 columns with one digit in each, then converting into a number ( or if it is a letter for a range being beyond 0-9, first replacing and then converting to a number...)

[James Tursa]

I already posted that. You simply do the - '0' operation at the end.

Answer 2

[madhan ravi]

 doc randperm

[antifreund]

this seems to generate only one permutation without repeats... But for a 4 digit lock with permissible numbers 1-6 one would have 1296 permutation from:

0 0 0 0

to

6 6 6 6

The question is how to populate that array with 1296 unique rows?