Question

我有一个像A={{1} {2 3 4} {5}}这样的单元格分区。我应该发现可以通过将某些单元格合并为一个单元格或将一个单元格拆分为某些单元格来从该分区访问所有分区。

对于分区A，结果分区为：

分区通过合并单元格获得：
{{1 2 3 4}{5}}, {{1 5}{2 3 4}}, {{1} {2 3 4 5}} {{1 2 3 4 5}}
分区通过拆分单元格获得：
{{1}{2}{3 4}{5}}, {{1}{3}{2 4}{5}}, {1}{4}{2 3}{5}},{{1}{2 3}{4}{5}}, {{1}{2 4}{3}{5}},{{1}{2}{3 4}{5}}

我知道要通过合并操作找到可访问的分区，我应该找到| A |的所有组合k。的单元格，其中2<=k<=|A|。

但是，我不知道如何找到所有可以通过分割形成的分区。

我该怎么做？谢谢

Answer 1

            function Acc_Parts=Merge_Split(in_part)
            %Returns all partitions can be accessed from the input partition


            si_part=size(in_part,2);              %number of cells in the input partition
            Bell_Number=ceil(sum((1:2*N).^N./cumprod(1:2*N))/exp(1)); %N is the number of elements in in_part partitions 
            Acc_Parts=cell(Bell_Number,1);

            %% merge some cells to form new cell
            %should find any combination k of si_part, where 2<=k<=si_part, and combine the selected cells to form a new cell

            l=1;                                % count the new partitions
            for k=2:si_part                     % choose k cells of si_part cells to merge them into one cell

                V=nchoosek(in_part,k);      %A MATLAB function gives a matrix containing all possible combinations of the elements of input vector taken k at a time
                s_V=nchoosek(si_part,k);    %Number of rows of comb. (Number of the possible combinations)
                celldisp(V)

                for i=1:s_V
                    cp_part=in_part;
                    b1=V{i,1};

                    for h=1:si_part         %delete this cell from cp_part
                        f=0;
                        if(b1==cell2mat(in_part(h)))
                            cp_part(h)=[];
                            f=1;
                            break;
                        else
                        end
                    end

                    for j=2:k
                        b2=V{i,j};
                        si_cpart=size(cp_part,2);
                        for h=1:si_cpart            %delete this cell from cp_part
                            f=0;
                            if(b2==cell2mat(cp_part(h)))
                                cp_part(h)=[];
                                f=1;
                                break;
                            else
                            end
                        end
                        celldisp(cp_part)

                        b1=[b1 b2];         %merge cells
                    end

                    new_coal={b1};

                    if(isempty(cp_part)==0)
                        Acc_Parts{l}=[new_coal,cp_part];
                    else
                        Acc_Parts{l}=[new_coal];
                    end
                    l=l+1;
                end

            end

            %% split a cell to some cells
            for i=1:si_part 
                cp_part=in_part;
                cp_coal=in_part{i};
                si_coal=size(cp_coal,2);    

                if (si_coal>=2)                 %check all cells to find cells with 2 or more elements
                    cp_part(i)=[];

                    parts=partitions(in_part{i});
                    si_parts=size(parts,1);

                    for k=2:si_parts
                        if(isempty(cp_part)==0)
                            Acc_Parts{l}=[parts{k},cp_part];
                        else
                            Acc_Parts{l}=[parts{k}];
                        end
                        l=l+1;
                    end

                else ;
                end
            end

            Acc_Parts(all(cellfun('isempty',Acc_Parts),2),:) = [];

            Acc_Parts
            celldisp(in_part)
            celldisp(Acc_Parts)

            end

如何找到可以从MATLAB中的分区访问的单元格分区？

1 个答案: