all possible combination between matrices

I have 3 matrices with 2 columns but different number of lines, for example;

A=[[2,1],[0,6],[4,2]]

B = [[0,2],[1,1],[3,4],[0,5]

C = [[0,1],[5,4]]

i want to do all the combinations between,each pairs A/B and B/C for a difference of +1 or -1 between the sum of each pair, and they must have a number in common. For example if we take [2,1] from A, the sum is 3=2+1 now i have to find the next pair in B (if exist), see that [0,2] the sum is 2=0+2 and there is a number in common with [2,1] from A so i keep this pair and i dont keep [1,1] cause there is no common number, now if i go to C i will take [0,1] cause the sum is 1=0+1 and there is number in common with [1,1], passing from A to B, B to C respecting -1 sum difference and having always a number in common between the previous pair and the chosen one.

So the result in this case must be

[2,1], [0,2], [0,1]

[Bruno Luong]

"dont keep [1,1] cause there is no common number"

Why you said that? It has 1 in common with [2,1] from A.

Answer 1

[Akira Agata]

Seems to be an interesting 'puzzle'.

Though this is not so smart, how about the following?

%% Data
A = {[2,1],[0,6],[4,2]};
B = {[0,2],[1,1],[3,4],[0,5]};
C = {[0,1],[5,4]};

%% Compare A and B
sumA = cellfun(@sum,A);
sumB = cellfun(@sum,B);

idx1 = abs(sumA - sumB') == 1;

c1 = cellfun(@intersect,repmat(A,4,1),repmat(B',1,3),'UniformOutput',false);
idx2 = cellfun(@(x) ~isempty(x),c1);

idxAll = idx1 & idx2;

[row,col] = find(idxAll);

T1 = table(cell2mat(A(col)'),cell2mat(B(row)'),'VariableNames',{'A','B'});

%% Compare B and C
sumC = cellfun(@sum,C);

idx1 = abs(sumB - sumC') == 1;

c2 = cellfun(@intersect,repmat(B,2,1),repmat(C',1,4),'UniformOutput',false);
idx2 = cellfun(@(x) ~isempty(x),c2);

idxAll = idx1 & idx2;

[row,col] = find(idxAll);

T2 = table(cell2mat(B(col)'),cell2mat(C(row)'),'VariableNames',{'B','C'});

%% Apply innerjoin to obtain the final result
Tall = innerjoin(T1,T2,'Keys','B');

Result:

There seems to be two comtinations:

>> Tall

Tall =

2×3 table

A B C

______ ______ ______

2 1 0 2 0 1

2 1 1 1 0 1