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Re: generation of random multiset permutation with restrictions
Posted:
Jan 30, 2013 3:34 AM
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Dynamic programming:
function p= allpc(a, s)
s = cellfun(@sort, s, 'unif', 0);
[u, ~, J] = unique(a);
n = accumarray(J(:), 1);
p = fliplr(allpc_engine(s, u, n));
end % allpc
%%
function p = allpc_engine(s, u, n)
s1 = s{1};
[b, loc] = ismember(s1, u);
s1 = s1(b);
s = s(2:end);
if isempty(s)
p = s1;
return
end
loc = loc(b);
p = [];
for i = 1:length(s1)
j = loc(i);
n(j) = n(j)-1;
old = u(j);
if n(j) <= 0
u(j) = Inf;
end
q = allpc_engine(s, u, n);
if ~isempty(q)
q(:,end+1) = s1(i);
p = [p; q];
end
u(j) = old;
n(j) = n(j)+1;
end
end % allpc_engine
%% Test
>> a = [1,1,1,2,2,3,3,3]
a =
1 1 1 2 2 3 3 3
>> s = {[3],[1,2],[1,2,3],[1,2,3],[1,2,3],[1,2,3],[2,3],[2,3]};
>> p = allpc(a,s)
p =
3 1 1 1 2 2 3 3
3 1 1 1 2 3 2 3
3 1 1 1 2 3 3 2
3 1 1 1 3 2 2 3
3 1 1 1 3 2 3 2
3 1 1 1 3 3 2 2
3 1 1 2 1 2 3 3
3 1 1 2 1 3 2 3
3 1 1 2 1 3 3 2
3 1 1 2 2 1 3 3
3 1 1 2 3 1 2 3
3 1 1 2 3 1 3 2
3 1 1 3 1 2 2 3
3 1 1 3 1 2 3 2
3 1 1 3 1 3 2 2
3 1 1 3 2 1 2 3
3 1 1 3 2 1 3 2
3 1 1 3 3 1 2 2
3 1 2 1 1 2 3 3
3 1 2 1 1 3 2 3
3 1 2 1 1 3 3 2
3 1 2 1 2 1 3 3
3 1 2 1 3 1 2 3
3 1 2 1 3 1 3 2
3 1 2 2 1 1 3 3
3 1 2 3 1 1 2 3
3 1 2 3 1 1 3 2
3 1 3 1 1 2 2 3
3 1 3 1 1 2 3 2
3 1 3 1 1 3 2 2
3 1 3 1 2 1 2 3
3 1 3 1 2 1 3 2
3 1 3 1 3 1 2 2
3 1 3 2 1 1 2 3
3 1 3 2 1 1 3 2
3 1 3 3 1 1 2 2
3 2 1 1 1 2 3 3
3 2 1 1 1 3 2 3
3 2 1 1 1 3 3 2
3 2 1 1 2 1 3 3
3 2 1 1 3 1 2 3
3 2 1 1 3 1 3 2
3 2 1 2 1 1 3 3
3 2 1 3 1 1 2 3
3 2 1 3 1 1 3 2
3 2 2 1 1 1 3 3
3 2 3 1 1 1 2 3
3 2 3 1 1 1 3 2
% Bruno
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