To generate all possible combinations of selecting one combination from each period, you can use the concept of Cartesian products. In your context, you want to select one row from each period's combinations. Here's how you can achieve this in MATLAB:Step-by-Step Solution
- Generate the Initial Combinations: You've already done this part, where you have the matrix C with all possible combinations for each period.
- Group by Period: For each period, extract its corresponding combinations.
- Generate All Possible Selections: Use a nested loop or a more efficient approach to generate all possible selections of one combination per period.
Here's how you can implement this:
n = 2; % number of candidates
sp = 4; % number of periods
% Generate all combinations for one period
M = dec2bin(0:(2^n)-1) - '0';
% Prepare matrix C with all combinations for each period
A = repmat((1:sp)', size(M, 1), 1);
B = repmat(M, sp, 1);
C = [A, B];
% Initialize a cell array to hold combinations for each period
periodCombinations = cell(sp, 1);
% Group combinations by period
for i = 1:sp
periodCombinations{i} = C(C(:, 1) == i, :);
end
% Generate all possible selections
allSelections = cell(1, sp);
[allSelections{:}] = ndgrid(1:size(M, 1));
allSelections = cellfun(@(x) x(:), allSelections, 'UniformOutput', false);
allSelections = [allSelections{:}];
% Build the final matrix with all possible selections
finalCombinations = zeros(size(allSelections, 1), sp * (n + 1));
for i = 1:size(allSelections, 1)
for j = 1:sp
rowIdx = allSelections(i, j);
finalCombinations(i, (j-1)*(n+1)+1:j*(n+1)) = periodCombinations{j}(rowIdx, :);
end
end
% Display the result
disp(finalCombinations);
