Monks, I am having trouble coding the Forward Dynamic programming algorithm. I have recently updated this post to account for new information. User kcott helped me simplify the code that I had written already to make it easier to read and use. The content of this post now reflects his advice and changes. My problem is still unsolved however, and I continue to ask for help

The forward dynamic programming algorithm finds the shortest path in a connected unidirectional graph. I am playing with an NP-complete problem that can be searched with the A* algorithm, however to improve the efficiency of A*, I need to optimize the estimation function. The Forward Dynamic programming algorithm will solve the problem if I can implement it correctly.

The chunk of code below sets up an identical data structure to the program I am working on. Please help me by showing how I would implement the forward dynamic programming algorithm to find the shortest path through the data. **Disclaimer** This is not homework. You are not helping me cheat. I am a biology Ph.D. candidate who enjoys playing with perl and DNA sequence data. I have just enough coding experience to hang myself with a short rope.

my $x = [some number];
my $y = [some number];
my $distance_mat;
####################
for(my $i=1; $i<=$x; ++$i){
        for(my $j=0; $j<$y; ++$j){
                for(my $k=0; $k<$y; ++$j){                       
                        $distance_mat -> [$i][$j][$k] = rand 1;
                }   
        }   
}
##############Start and end nodes have zero cost
for(my $i=0; $i<scalar(@{$distance_mat[1]}); ++$i){
        $distance_mat -> [0][0][$i] = 0;
}
for(my $i=0; $i<scalar(@{$distance_mat[-1]}); ++$i){
        $distance_mat -> [-1][0][$i] = 0;
}
#######################################

#call the recursive min_dist subroutine

my $last = scalar ( @{$distance_mat} );
my @minimum_path = &min_dist (\$distance_mat,$last);
## I want @minumum_path array to store the best path for each $i level
+ as a pointer or index.

sub min_dist { 
       #I dont know how to program this recursive subroutine

       #My incorrect attempt looks like this

        my $k = $_[1];
        my @array = @{ $_[0]->[$k] };
        foreach( @array ){
              $_ += min_dist( $_[0],$_[1]-1 );
        }

        my $return=min( min_dist($_[0],$_[1]-1)+ ###I cannot figure ou
+t how to write this statement

        return $return;

        }   

sub min { #pass array of values
        my @array = sort { $a <=> $b } @_; 
        return $array[0];
}

[download]

The @distance_matrix can be interpreted as a classic trellis diagram of nodes and paths. The $i dimension is the number of horizontal slices of a trellis graph. The $j dimension is the number of nodes for each $i slice. The $k dimension is the distance cost to the next slice nodes. In this example, all nodes of each trellis slice are connected to all nodes in adjacent slices.

I have tried and failed to write a working piece of code for several days now and I need a push in the right direction. I know the min_dist subroutine is not even close to being correct. I am not sure how to write it correctly. The following website describes the algorithm I want to implement. http://www.cob.sjsu.edu/facstaff/davis_r/courses/QBAreader/dynprog.html

In reply to Viterbi application by azheid

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