Merge cell that has common element

I have

A ={[1,2; 1,3; 2,4; 3,4; 2,5],[72,73],[5,6; 6,7],[36,39],[71,80;72,80],[27,70;28,71],[39,51],[21,29]};

I want to merge each cell that have common element.

for example:

[1,2; 1,3; 2,4; 3,4; 2,5] and [5,6; 6,7] have 5 in common ---> [1,2; 1,3; 2,4; 3,4; 2,5; 5,6; 6,7]
[71,80;72,80] and [27,70;28,71] have 71 in common ---> [71,80; 72,80; 27,70;28,71]
[71,80; 72,80; 27,70;28,71] and [72,73] have 72 in common ---> [71,80; 72,80; 27,70;28,71;72,73] 
[36,39] and [39,51] ---> [36,39;39,51]
[21,29] does not have any common element to others ---> [21,29]

result should be

A_new ={[1,2; 1,3; 2,4; 3,4; 2,5; 5,6; 6,7],[71,80; 72,80; 27,70;28,71;72,73] ,[36,39;39,51],[21,29]};

[Stephen23]

Can each matrix only be used once in the output, or can the be used multiple times?

[NA]

Should be used one time.

If [1,2; 1,3; 2,4; 3,4; 2,5] and [5,6; 6,7] are merged to [1,2; 1,3; 2,4; 3,4; 2,5; 5,6; 6,7] I only want to keep [1,2; 1,3; 2,4; 3,4; 2,5; 5,6; 6,7] and remove the [1,2; 1,3; 2,4; 3,4; 2,5] and [5,6; 6,7].

And compare [1,2; 1,3; 2,4; 3,4; 2,5; 5,6; 6,7] with others.

but for [21,29] as it dose not merge to others, I want to keep it.

Answer 1

[Tommy]

I'm not sure if this is the best way to do it, but I believe it will work.

It starts by setting A_new to A. It then loops through each pair of cells in A_new, and if it finds a pair of cells which share a common element, the two cells are concatenated and put in place of one of the cells. The other cell is removed from A_new. It then restarts at the beginning, again looping through pairs of cells. This continues until no two pairs of cells share any elements.

A ={[1,2; 1,3; 2,4; 3,4; 2,5],[72,73],[5,6; 6,7],[36,39],[71,80;72,80],[27,70;28,71],[39,51],[21,29]};

A_new = A;
done = false;
while ~done
    next = false;
    for i=1:numel(A_new)
        for j=i+1:numel(A_new)
            if any(any(ismember(A_new{i},A_new{j})))
                A_new{i} = [A_new{i};A_new{j}];
                A_new = A_new(1:end ~= j);
                next = true;
                break
            end
        end
        if next
            continue
        end
        if i == numel(A_new)
            done = true;
        end
    end
end

Answer 2

[Stephen23]

Simpler:

A = {[1,2;1,3;2,4;3,4;2,5],[72,73],[5,6;6,7],[36,39],[71,80;72,80],[27,70;28,71],[39,51],[21,29]};
ii = 1;
while ii<=numel(A)
    kk = [];
    for jj = ii+1:numel(A)
        if numel(intersect(A{ii}(:),A{jj}(:)))
            A{ii} = [A{ii};A{jj}];
            kk = [kk,jj];
        end
    end
    A(kk) = []; % remove cells
    ii = ii+1;
end