An array of hashes, each hash containing one path, its ID, and its order ( foreward (F) or reverse (R) )

each path is initialized in the F position 

my @paths = [ { id => 1, path => [A,B], order => 'F' }, { id => 2, pat
+h => [C,D,E], order => 'F' }, { id => 3, path => [E,B], order => 'F' 
+} ];

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each node or vertex of each path also has an orientation ( + or - ) 

my %plus_minus;
$plus_minus{1}{A} = '+';
$plus_minus{1}{B} = '+';
$plus_minus{2}{C} = '+';
$plus_minus{2}{D} = '-';
$plus_minus{2}{E} = '-';
$plus_minus{3}{E} = '-';
$plus_minus{3}{B} = '-';

[download]

You can reverse the order of a path ( e.g., A, B to B, A )

When you reverse order from F => R or R => F you also switch the orientation of each node in the path from + to - or - to +

The paths with orientations look like this:

1 .A+ : B+

2. C+ : D- : E-

3. E- : B-

this is the problem input for output, i'd like to know whether or not it is possible by reverseing path orders to create a consensus path and also what is the way to do this such that you are guaranteed to find the consensus path

for example, if we reversed path 1 we'd get:

1. B- : A-

2. C+ : D- : E-

3. E- : B-

and the resulting consensus path would be:

C+ : D- : E- : B- : A-

but it's not clear to reverse path 1 first; for example; what if started by reversing path 3? So you can't proceed randomly. Does anyone recognize this problem? Does it have a solution? Thanks.

In reply to Formalizing an array type problem, looking for solution by melmoth

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