Complete set of combinations combining 3 set

Question

I need to generate the complete set of combinations obtained combining three different subset:

• Set 1: choosing any 4 numbers from a vector of

Answer 1

I guess this could be further optimized but this generates you AllComb:

H=3;
L=4;
a = combnk(1:H+L-1, H);
b = cumsum([a(:,1)  diff(a,[],2) - 1],2);
H=2;
L=3;
c = combnk(1:H+L-1, H);
d = cumsum([c(:,1)  diff(c,[],2) - 1],2);
H=2;
L=4;
e = combnk(1:H+L-1, H);
f = cumsum([e(:,1)  diff(e,[],2) - 1],2);
u=[];
for k=1:10
u=vertcat(u,d);
end
u=sortrows(u,[1 2]);
v=[];
for k=1:6
v= vertcat(v,f);
end
w= [u,v];
v=[];
for k=1:20
 v= vertcat(v,w);
end
u=[];
for k=1:60
 u = vertcat(u,b);
end
u=sortrows(u,[1 2 3]);
AllComb= [u,v];

Here b,d and f are your 3 sets. Then i loop over the numbers of permutation in d and f and replicate them so that all possibilities are constructed. One of them is sorted and then i write them in a new matrix w. THis process is repeated with Set A (b) and this new constructed matrix. Resulting in the end in AllComb.

Answer 2

You basically need to find

1. Combinations with repetition for each set;
2. "Multi-variations" (I don't know the correct name for this) of the results of stage 1.

Both stages can be solved with more or less the same logic, taken from here.

%// Stage 1, set A
LA = 4;
HA = 3;
SetA = cell(1,HA);
[SetA{:}] = ndgrid(1:LA);
SetA = cat(HA+1, SetA{:});
SetA = reshape(SetA,[],HA);
SetA = unique(sort(SetA(:,1:HA),2),'rows');

%// Stage 1, set B
LB = 3;
HB = 2;
SetB = cell(1,HB);
[SetB{:}] = ndgrid(1:LB);
SetB = cat(HB+1, SetB{:});
SetB = reshape(SetB,[],HB);
SetB = unique(sort(SetB(:,1:HB),2),'rows');

%// Stage 1, set C
LC = 4;
HC = 2;
SetC = cell(1,HC);
[SetC{:}] = ndgrid(1:LC);
SetC = cat(HC+1, SetC{:});
SetC = reshape(SetC,[],HC);
SetC = unique(sort(SetC(:,1:HC),2),'rows');

%// Stage 2
L = 3; %// number of sets
result = cell(1,L);
[result{:}] = ndgrid(1:size(SetA,1),1:size(SetB,1),1:size(SetC,1));
result = cat(L+1, result{:});
result = reshape(result,[],L);
result = [ SetA(result(:,1),:) SetB(result(:,2),:) SetC(result(:,3),:) ];
result = flipud(sortrows(result)); %// put into desired order

This gives

result =
     4     4     4     3     3     4     4
     4     4     4     3     3     3     4
     4     4     4     3     3     3     3
     4     4     4     3     3     2     4
     4     4     4     3     3     2     3
     4     4     4     3     3     2     2
     4     4     4     3     3     1     4
     4     4     4     3     3     1     3
     4     4     4     3     3     1     2
     4     4     4     3     3     1     1
     4     4     4     2     3     4     4
     4     4     4     2     3     3     4
     4     4     4     2     3     3     3
     4     4     4     2     3     2     4
     4     4     4     2     3     2     3
     4     4     4     2     3     2     2
     4     4     4     2     3     1     4
     4     4     4     2     3     1     3
     4     4     4     2     3     1     2
     ...