Matlab生成所有可能的团队组合

Question

There's lots of questions that are similar to mine but I haven't found quite what I'm looking for yet. I'm working on a project to optimize teaming in a class, and am not sure how to generate all possible team combinations.

Say I have a vector that's a list of numbered people, like

<1,2,3,4,5....,n>

I want to generate all possible combinations of teams with k people per team, where k is smaller than n . The output should be matrices where the rows are the teams. Each matrix will have k columns, and n/k rows (corresponding to the number of teams).

For example, say my vector is <1,2,3,4> . I want all combinations of teams of 2. My possible output matrices would be [1,2;3,4] , [1,3;2,4] , and [1,4;2,3] . I'd like to know how to scale this up to any n and k value.

Answer 1

I have done only some incomplete testing, but this seems to work.

Code :

%// Data:
n = 6; %// number of people
k = 2; %// team size. Assumed to divide p

%// Let's go:
M = unique(perms(ceil((1:n)/k)), 'rows').'; %'// the transpose is for convenience
result = NaN(n/k, k, size(M,2)); %// preallocate
for t = 1:n/k
    [ii, ~] = find(M==t);
    result(t,:,:) = reshape(ii, k, []);
end
result = result(:,:,all(diff(result(:,1,:))>0, 1));

The result matrices are given by result(:,:,1) , result(:,:,2) etc.

Explanation :

The key steps are:

• Line M = unique(perms(ceil((1:n)/k)), 'rows').' : this assigns k different team numbers, one to each group of n/k people, and creates all different permutations of those numbers. So this includes all possible team groupings.

• for loop: this translates the above representation into the matrix format you want: each team is described by a row containing n/k labels from the set {1,2,..., n }, telling which people belong to that team. Within each row, those labels are always increasing.

• Line result = result(:,:,all(diff(result(:,1,:))>0, 1)) : this removes matrices that are row-permutations of others. It does so by keeping only matrices whose first column is increasing.

Examples :

For n=4; k=2 n=4; k=2 ,

>> result
result(:,:,1) =
     1     2
     3     4
result(:,:,2) =
     1     3
     2     4
result(:,:,3) =
     1     4
     2     3

For n=6; k=2 n=6; k=2 ,

>> result
result(:,:,1) =
     1     2
     3     4
     5     6
result(:,:,2) =
     1     2
     3     5
     4     6
result(:,:,3) =
     1     2
     3     6
     4     5
result(:,:,4) =
     1     3
     2     4
     5     6
...

Answer 2

It is quite overkilling, but it seems to work:

n = 4;
k = 2;

allCombinations = perms(1:n);

numComb = size(allCombinations,1);
selCombinations = zeros(size(allCombinations));
cellCombinations = cell(numComb,1);
for ii = 1:numComb
    candidate = sortrows(sort(reshape(allCombinations(ii,:),[],k),2));
    selCombinations(ii,:) = candidate(:);
    cellCombinations{ii} = candidate;
end

[~,idx] = unique(selCombinations, 'rows');
cellCombinations{idx}

I create all the possible combinations of n elements, and then I select the unique combinations that follow your criteria.