stepwise sort combvec result by its sum over one dimension

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FirefoxMetzger
FirefoxMetzger on 14 Aug 2016
Answered: Balavignesh on 2 Jul 2024
Take this code, which works for small lists:
% generate a small list (only works for small randi)
list = cell(1,7);
for idx = 1:7
list{idx} = randi(100,1,randi(10,1));
end
%generate all possible combinations and sort them based on their sum
all_combinations = combvec(list{:});
[~, sorted_idx] = sort(sum(all_combinations, 1),'descend');
all_combinations_sorted = all_combinations(:,sorted_idx);
%do some work with the generated list
for idx = 1:size(all_combinations_sorted, 2)
combination = all_combinations_sorted(:,idx);
% do more stuff
if some_criteria
break;
end
end
So first I am generating all possible combinations of elements from the 7 lists. Then I calculate the sum of each generated element, e.g. the combination a = [1; 1; 1; 1; 1; 1; 1] has sum(a) == 7. Based on this sum I sort all combinations. Afterwards I iterate over this sorted list and do my work until a stopping criteria is met.
The problem is that, contrary to my example the lists I am dealing with are in the range 100 < size(list{idx}) < 5000 . Thus there are to many combinations to generate all of them, let alone sorting the result. I usually don't need to go through the entire list, but rather the first 1000 or so entries. My question is:
How can I generate this sorted list sequentially, so that I start with the biggest element and then gradually step down to the smallest?

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Answers (1)

Balavignesh
Balavignesh on 2 Jul 2024
Ran in:
Hi FirefoxMetzger,
It is computationally infeasible to generate and sort all possible combinations of elements from large lists due to the combinatorial explosion. I suggest you use a priority queue (max-heap) to generate the combinations sequentially, starting with the largest sum and gradually stepping down. In this case, you could avoid generating all combinations at once and stop when your criteria are met.
The following MATLAB code might help you better understand this:
function largest_combinations = generate_largest_combinations(list, num_combinations, sum_threshold)
% Initialize priority queue (max-heap)
pq = {};
% Initial combination (largest elements of each list)
initial_combination = cellfun(@(x) max(x), list);
pq{end+1} = initial_combination;
% Set to keep track of visited combinations
visited = containers.Map('KeyType', 'char', 'ValueType', 'logical');
visited(mat2str(initial_combination)) = true;
largest_combinations = zeros(length(list), num_combinations);
for k = 1:num_combinations
if isempty(pq)
break;
end
% Extract maximum sum combination
[~, max_idx] = max(cellfun(@(x) sum(x), pq));
combination = pq{max_idx};
pq(max_idx) = []; % Remove the max element
largest_combinations(:, k) = combination;
% Check stopping criteria
if sum(combination) <= sum_threshold
break;
end
% Generate neighboring combinations
for i = 1:length(list)
if combination(i) > min(list{i})
new_combination = combination;
new_combination(i) = max(list{i}(list{i} < combination(i)));
key = mat2str(new_combination);
if ~isKey(visited, key)
pq{end+1} = new_combination;
visited(key) = true;
end
end
end
% Maintain the priority queue order
pq = sort_priority_queue(pq);
end
end
function pq = sort_priority_queue(pq)
% Sort the priority queue based on the sum of combinations in descending order
[~, sorted_idx] = sort(cellfun(@(x) sum(x), pq), 'descend');
pq = pq(sorted_idx);
end
% Example usage
list = cell(1, 7);
for idx = 1:7
list{idx} = randi([100, 5000], 1, randi([100, 5000], 1));
end
num_combinations = 1000;
sum_threshold = 20000; % Example threshold for stopping criteria
largest_combinations = generate_largest_combinations(list, num_combinations, sum_threshold);
% Process the largest combinations
for idx = 1:size(largest_combinations, 2)
combination = largest_combinations(:, idx);
% Replace with your actual processing code
disp(combination);
% Example stopping criteria: sum of combination less than or equal to threshold
if sum(combination) <= sum_threshold
break;
end
end
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The sum_threshold parameter is introduced to demonstrate a stopping condition. The loop will break if the sum of the current combination is less than or equal to this threshold. Replace the sum_threshold and the processing logic with your actual criteria and code as needed. This example demonstrates how to incorporate a stopping condition into the process.
Kindly have a look at the following documentation links to have more information on:
Hope that helps!
Balavignesh

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