loto0.m

%    #######################  loto0.m DRAFT  #######################
%
%    Author      : Senol Korkmaz <senol.korkmaz@gmail.com>
%    Filename    : loto0.m
%    Description : A MATLAB script to calculate n/m\k
%    Usage       : Run script and follow instructions.
%    Version     : 0 (Draft)
%
%    License     : GNU/GPL v3
%    This program is free software: you can redistribute it and/or modify
%    it under the terms of the GNU General Public License as published by
%    the Free Software Foundation, either version 3 of the License, or
%    (at your option) any later version.
%    This program is distributed in the hope that it will be useful,
%    but WITHOUT ANY WARRANTY; without even the implied warranty of
%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%    GNU General Public License for more details.
%    You should have received a copy of the GNU General Public License
%    along with this program.  If not, see <http://www.gnu.org/licenses/>.

%% Clear all variables and screen
clear;
clc;

%% Get user inputs n,m,k and validate
n = input(' n : ');
if ~(n>1)
    error(' n must be greater than 1 (n=%d)',n);
end;

m = input(' m : ');
if ~(m>n)
    error(' m must be greater than n (m=%d , n=%d)',m,n);
end;

k = input(' k : ');
if (k>n)
    error(' k cannot be greater than n (k=%d , n=%d)',k,n)
end;

%% Generate variables
tmp = 0;    % Temporary variable
flg = false;    % Flag variable
covered = false;    % Is selections covered target_pool in scope k ?
sub_combinations = 0;    % 

i = 0;    % index to be used within loops
j = 0;    % index to be used within loops
l = 0;    % index to be used within loops
z = 0;    % index to be used within loops

target_pool = combnk(1:m,n);    % One of these combinations will be selected in loto
source_pool = target_pool;    % Min of these combinations should be selected to cover target_pool at scope k
selections = zeros(1,n);    % Current selections to test
selections_scope = [];
show_info = 0;

%% cycle throught combinations
while ~(covered)    % Main loop 
 i = i + 1;    % It is not enought, increase i
 sub_combinations = combnk(1:size(source_pool,1),i);    % Generate subcombinations
 j=0;
 z=size(sub_combinations,1);
 show_info_period = z/100;

    while ( (j < z) && ~(covered)) % #######
     j = j+1;
     selections = source_pool(sub_combinations(j,:),:);
     show_info = show_info+1;

     if (show_info > show_info_period)
         disp(sprintf('is %d enought ? sub-Combination %d/%d , Completed = %d %%',i,j,z,fix(j/show_info_period)));
         show_info = 0;
     end;
  
     selections_scope = selections(1,1:k);    % ###################
  
     for l=1:i    % Prepare k scope to test target_pool ########
         selections_scope = union(selections_scope,combnk(selections(l,:),k),'rows');
     end;

     for l=1:size(target_pool,1)
         if (size(intersect(combnk(target_pool(l,:),k),selections_scope,'rows'),1)==0)
             break;
         end;
         if (l==size(target_pool,1))
             covered = true;
         end;
     end;
    end;
end;

%% Show results
disp(sprintf('Answer = %d',i));