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find the unique path in a matrix

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Ali
Ali 2017-5-30
评论： KSSV 2017-6-1
Hello! I have a matrix (shown below). The matrix is the possible indices of a vector. The width of the matrix is 18 here. The width varies for different examples. We have to choose one index from each column so that the final answer, which is a vector of length 18, should be unique. That means the final vector, if sorted, is exactly 1,2,3...,18. A sample solution is shown in the attached picture.
I do not have "graph" on my Matlab R2015a. Maybe the optimization function "fgoalattain" helps. Thank you for your help!
13 6 1 1 1 2 5 2 7 9 3 8 9 9 1 8 6 6
1 2 2 2 3 12 6 8 9 10 11 11 10 15 4 12 14 14
12 12 3 4 4 16 4 12 10 15 7 12 15 17 10 16 1 2
16 16 11 11 8 7 8 16 15 17 9 16 5 18 15 13 2 16
5 5 3 14 12 9 14 5 6 6 17 12 6 15 6 11 16 1
6 9 4 3 16 15 1 13 13 13 5 5 13 17 9 12 2 4
10 15 15 4 9 17 2 8 14 6 18 13 NaN 6 10 16 3 NaN
15 17 17 11 10 14 3 12 6 14 NaN 2 NaN 13 15 15 11 NaN
18 6 18 9 15 7 4 7 1 2 NaN 8 NaN 14 18 17 NaN NaN
6 13 10 15 13 9 NaN 10 3 3 NaN 12 NaN 2 6 9 NaN NaN
13 NaN 17 18 NaN 10 NaN 15 4 4 NaN 16 NaN 3 14 15 NaN NaN
14 NaN 2 7 NaN 5 NaN 9 12 8 NaN 15 NaN 4 NaN 2 NaN NaN
NaN NaN 3 15 NaN 6 NaN 10 16 11 NaN NaN NaN 12 NaN 8 NaN NaN
NaN NaN 11 17 NaN NaN NaN 8 5 12 NaN NaN NaN 9 NaN 16 NaN NaN
NaN NaN NaN 18 NaN NaN NaN 16 6 16 NaN NaN NaN 15 NaN NaN NaN NaN
NaN NaN NaN 1 NaN NaN NaN NaN 13 5 NaN NaN NaN NaN NaN NaN NaN NaN
NaN NaN NaN 4 NaN NaN NaN NaN NaN 13 NaN NaN NaN NaN NaN NaN NaN NaN
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Ali
Ali 2017-5-30
Thanks! I could not do anything due to out of memory problem.
Rik
Rik 2017-5-30
Then this is not really a question. Try following the steps outline here. Try to figure out what exactly it is you want as a result, then try to find a way to get there. If you can't explain your question to us, we have no way of helping you.

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KSSV
KSSV 2017-5-31
How about this code? Let A be your matrix, which you have given. This code is like a trial/ random, for few runs it will throw error, for the paths which we expect, it will run and show no error, this is the path which you expect.
[nx,ny] = size(A) ;
path = zeros(1,ny) ;
%%consider first column
col = A(:,1) ;
col = col(~isnan(col)) ; % remove NaN's
path(1) = randsample(col,1) ;
for i = 2:ny
col = A(:,i) ;
col = col(~isnan(col)) ; % remove NaN's
% Remove already selected number in path from this col
col = setdiff(col,path(1:i)) ;
%%pick one number in random from the column
if length(col) ~=1
path(i) = randsample(col,1) ;
else
path(i) = col ;
end
end
I have run the above code for seven times, for the first six times, it throwed error and the successful result was:
path = [ 10 16 1 14 15 7 6 8 12 13 17 11 5 4
18 9 3 2];
The above path satisfies your conditions.
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Ali
Ali 2017-5-31
This was brilliant KSSV! I hope this works. Thanks a lot.
KSSV
KSSV 2017-6-1
Thanking is accepting the answer...

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