Partitions_opt_4.m

function [set_part, time_part, time_opt] = Partitions_opt_4(value_opt, init_state, targets, sub_nu)
    tic;
    nu = double(targets);
    time_opt=[];
    time_part = [];
    sub_n_c_ag = [];
    sub_nu_l = cellfun('length',sub_nu);
    cover_time_opt = -value_opt;
    time = cover_time_opt(init_state,:);
    for i=1:size(sub_nu,1)
        rem_l_j = length(nu) - sub_nu_l(i);
        to_sub_j = find(sub_nu_l<=rem_l_j);
        for c_j=1:length(to_sub_j)        
            j = to_sub_j(c_j);
            rem_l_k = length(nu) - sub_nu_l(i) - sub_nu_l(j);
            to_sub_k = find(sub_nu_l<=rem_l_k);
            for c_k=1:length(to_sub_k)        
                k = to_sub_k(c_k);
                rem_l_l = length(nu) - sub_nu_l(i) - sub_nu_l(j) - sub_nu_l(k);
                to_sub_l = find(sub_nu_l==rem_l_l);
                for c_l=1:length(to_sub_l)
                    l = to_sub_l(c_l);
                    if(length(unique([sub_nu{i,1}(1:sub_nu_l(i)),sub_nu{j,1}(1:sub_nu_l(j)),sub_nu{k,1}(1:sub_nu_l(k)),sub_nu{l,1}(1:sub_nu_l(l))]))==length(nu))
                        if(isempty(time_opt))
                            time_opt = max([time(i),time(j),time(k),time(l)]);
                            time_part = [time(i),time(j),time(k),time(l)];
                            set_part_1 = sub_nu{i,1}(1:sub_nu_l(i));
                            set_part_2 = sub_nu{j,1}(1:sub_nu_l(j));
                            set_part_3 = sub_nu{k,1}(1:sub_nu_l(k));
                            set_part_4 = sub_nu{l,1}(1:sub_nu_l(l));
                        elseif(max([time(i),time(j),time(k)]) < time_opt)
                            time_opt = max([time(i),time(j),time(k),time(l)]);
                            time_part = [time(i),time(j),time(k),time(l)];
                            set_part_1 = sub_nu{i,1}(1:sub_nu_l(i));
                            set_part_2 = sub_nu{j,1}(1:sub_nu_l(j));
                            set_part_3 = sub_nu{k,1}(1:sub_nu_l(k));
                            set_part_4 = sub_nu{l,1}(1:sub_nu_l(l));
                        end
                    end
                end
            end
        end
    end
    set_part = {set_part_1; set_part_2; set_part_3; set_part_4};
    toc;
end