Iterate one vector through another in Matlab Part 2 - matlab

Question

This is a similar request to my post at Iterate one vector through another in Matlab
I am using Luis' suggestion with the following code:
E=[1 2 3 4 5 6 7 8 9 10];
A = [1 2];
s = size(E,2);
t = numel(A);
C = cell(1,s);
[C{:}] = ndgrid(A);
C = cat(s+1, C{:});
C = fliplr(reshape(C, t^s, s));
This produces a good result for C as a 1024x10 matrix with all possible permutations of 1 and 2 to a length of 10 columns. What I want to do is remove any rows that are not in increasing order. For example now I get:
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 2
1 1 1 1 1 1 1 1 2 1
1 1 1 1 1 1 1 1 2 2
All are valid except for the third row since it goes from 2 to back to 1.
I have code to get the desired result, but it is very slow and inefficient.
E=[1 2 3 4 5 6 7 8 9 10];
A = [1 2];
s = size(E,2);
t = numel(A);
C = cell(1,s);
[C{:}] = ndgrid(A);
C = cat(s+1, C{:});
C = fliplr(reshape(C, t^s, s));
min=0;
for row=1:size(C,1)
for col=1:size(C,2)
if(C(row,col)>min)
min=C(row,col);
elseif(C(row,col)<min)
C(row,:)=0;
continue;
end
end
min=0;
end
C = C(any(C,2),:); %remove all zero rows
The desired output is now:
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 2
1 1 1 1 1 1 1 1 2 2
1 1 1 1 1 1 1 2 2 2
1 1 1 1 1 1 2 2 2 2
1 1 1 1 1 2 2 2 2 2
1 1 1 1 2 2 2 2 2 2
1 1 1 2 2 2 2 2 2 2
1 1 2 2 2 2 2 2 2 2
1 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2
Any ideas on how to optimize my code so I do not need to use nested loops?

Answer 1

The super-simple but not-quite-so-obvious solution via a couple of row-wise operations:
d = diff(C, [], 2);
m = min(d, [], 2);
C = C(m>=0, :);
Of course, in this particular example it would be far easier to just generate the resulting matrix directly:
C = flipud(triu(ones(s+1,s).*(max(A)-min(A))) + min(A));
but I assume you're also interested in less trivial values of A ;)