Permutation with repeating elements.

Hello, greetings! I have the following array, A= 1:7. I want to get all the possible permutations of seven elements and I am trying to get my answer like this

ans =

1 2 3 4 5 6 7

1 2 5 3 4 7 6

2 3 4 5 1 7 6...... etc

It should be easy. But in the 'A' matrix, 1 and 2 indicates the simillar thing; 3 and 4 indicates the simillar thing; 5, 6, and 7 indicates the simillar thing. So, in the 'ans' 1 2 3 4 5 6 7 and 2 1 4 3 7 6 5 will be same. I want the code to return the values without repitating it. Is there any way to do this?

note: I want this code to do linear indexing. So, I can't replace A with any other matrix. It has to be 1:7.

Answer 1

[Bruno Luong]

Just brute force of filter out what is considered as duplicated

g = [1 1 2 2 3 3 3];
x = 1:7;

p = perms(x);
[~,i] = unique(perms(g),'rows');
p = p(i,:);

p

p = 210×7

2 1 4 3 7 6 5 2 1 4 7 3 6 5 2 1 4 7 6 3 5 2 1 4 7 6 5 3 2 1 7 4 3 6 5 2 1 7 4 6 3 5 2 1 7 4 6 5 3 2 1 7 6 4 3 5 2 1 7 6 4 5 3 2 1 7 6 5 4 3

[Sourov Kumar Mondal]

Thanks a lot. This works just fine. Appreciate your effort.

[Sourov Kumar Mondal]

Hi, if I want to use only 4 out of this 7 to make my permutations what modifications needed to be done in the code? ( same conditions as before: 1,2 are same; 3,4 are same; 5,6,7 same). The answer will be like this:

1 3 5 7

4 6 7 2 etc....

[Bruno Luong]

Please don't change your problem (even when you think its minor) in the future, it is count productive and induce waste of time for people who are trying to help you.

g = [1 1 2 2 3 3 3];
x = 1:7;
k = 4;

p = lperms(x,k);
[~,i] = unique(lperms(g,k),'rows');
p = p(i,:);

p

p = 62×4

2 1 4 3 2 1 3 5 2 1 5 3 2 1 6 5 2 4 1 3 2 3 1 5 2 4 3 1 1 4 3 5 2 3 5 1 1 4 5 3

function p = lperms(x, k)
p = nchoosek(x,k);
q = perms(1:k);
n = size(p,1);
[I,J] = ndgrid(1:n,q-1);
p = reshape(p(I + n*J),[],k);
end

[Sourov Kumar Mondal]

Thanks again for the answer!

[Bruno Luong]

Simplify lperms

function p = lperms(x, k)
p = nchoosek(x,k);
p = reshape(p(:,perms(1:k)),[],k);
end

Answer 2

[KSSV]

 A = {[1 2], [3 4], [5 6 7]} ;
 iwant = perms(A)

iwant = 6×3 cell array
    {[5 6 7]}    {[  3 4]}    {[  1 2]}
    {[5 6 7]}    {[  1 2]}    {[  3 4]}
    {[  3 4]}    {[5 6 7]}    {[  1 2]}
    {[  3 4]}    {[  1 2]}    {[5 6 7]}
    {[  1 2]}    {[5 6 7]}    {[  3 4]}
    {[  1 2]}    {[  3 4]}    {[5 6 7]}

[Sourov Kumar Mondal]

Thanks for the answer. But this is keeping 1 and 2; 3 and 4; 5, 6, and 7 together always. The output I am looking for is just like normal permutations of 7 elements. but 1 and 2; 3 and 4; and 5,6 and 7 will behave like simillar elements. The no. of expected permutations would be (7! / (2! * 2! * 3!)). Is there any solution to this? thanks is advanced.

[Sourov Kumar Mondal]

Some expected outputs would be like this

1 3 5 7 6 4 2

1 4 3 5 6 2 7.... etc

But there won't be 2 3 5 7 6 1 because 1 and 2 are simillar