Creating possible addition of a number

I have a set of array A

A= [1 2 4 8 16]

For example I want a set of number that make up total of 4 (from A), it would be

B=[1 1 1 1] *total in array B would be 4*
B=[1 1 2]
B=[2 2]
B=[4]

Is it possible to do it in Matlab?

[Rik]

It is possible to this in Matlab. How would you try to solve it?

Answer 1

[John D'Errico]

Trivial, if you download my partitions function from the File Exchange.

A = [1 2 4 8 16];

partitions(4,A)
ans =
     4     0     0     0     0
     2     1     0     0     0
     0     2     0     0     0
     0     0     1     0     0

Each row of the result tells you how many times that element appears in the target sum.

Find it here:

https://www.mathworks.com/matlabcentral/fileexchange/12009-partitions-of-an-integer

Note that the number of such partitions can be immense for some problems. You can easily overwhelm such a tool. For example, I have another utiility that will count the number of partitions of an integer.

numberOfPartitions(1000)

ans =

24061467864032622473692149727991

Thus as the sum of numbers in the set [1:1000]. It gets big, and does so pretty fast.

Answer 2

[Stephen23]

Download John D'Errico's excellent partitions:

https://www.mathworks.com/matlabcentral/fileexchange/12009-partitions-of-an-integer

and use it like this:

>> A = [1,2,4,8,16];
>> M = partitions(4,A);
>> F = @(v)repelem(A,v);
>> C = cellfun(F,num2cell(M,2),'uni',0);
>> C{:}
ans =
     1     1     1     1
ans =
     1     1     2
ans =
     2     2
ans =
     4

[John D'Errico]

One of the things I should have added as an option, was the ability to return the partitions in an expanded form, something much like Stephen did here. You can never have too many options in an interface. Well, at least not until you do. ;-)

[fyza affandi]

Thank you very much :)