# NAME

Path::Graph - Generate paths from hash graph.

# SYNOPSIS

## Code 1

#!usr/bin/perl

my %graph = ( A => {B=>1,C=>4}, B => {A=>1,C=>2}, C => {A=>4,B=>2}

);

use Paths::Graph;

my $g = Paths::Graph->new(-origin=>"A",-destiny=>"C",-graph=>\%graph);

my @paths = $g->shortest_path();

for my $path (@paths) {

` print "Shortest Path:" . join ("->" , @$path) . " Cost:". $g->get_path_cost(@$path) ."\n";`

}

# RECOMMENDED

Understanding the Graph's filosofy and how to trace it.

Reach for graph's books , also Dijkstra's algorithm.

# ABSTRACT

This example cover all possibilities to find the graph's paths from Node A to Node C and the cost for itself.

## Graph

```
(A)---4---(C)
/ \ / \
2 1 2 6
/ \ / \
(G)---8---(B)---9---(F)
\ / \ /
3 1 5 2
\ / \ /
(D)---7---(E)
```

## Matriz costs nodes

```
-----------------
|.|A|B|C|D|E|F|G|
|-+-+-+-+-+-+-+-|
|A|0|1|4|0|0|0|2|
|-+-+-+-+-+-+-+-|
|B|1|0|2|1|5|9|8|
|-+-+-+-+-+-+-+-|
|C|4|2|0|0|0|6|0|
|-+-+-+-+-+-+-+-+
|D|0|1|0|0|7|0|3|
|-+-+-+-+-+-+-+-|
|E|0|5|0|7|0|2|0|
|-+-+-+-+-+-+-+-|
|F|0|9|6|0|2|0|0|
|-+-+-+-+-+-+-+-|
|G|2|8|0|3|0|0|0|
-----------------
```

# From A to C paths and costs

```
A->B->G->D->E->F->C = 27
A->G->B->E->F->C = 23
A->G->B->C = 12
A->B->D->E->F->C = 17
A->G->D->E->B->C = 19
A->C = 4
A->G->D->E->B->F->C = 28
A->G->D->B->C = 8
A->B->C = 3
A->G->D->B->F->C = 21
A->B->F->C = 16
A->G->D->B->E->F->C = 19
A->G->D->E->F->C = 18
A->B->D->E->F->C = 17
A->G->B->D->E->F->C = 26
A->G->B->F->C = 25
A->G->D->E->F->B->C = 19
```

# DESCRIPTION

This package provides an object class which can be used to get diferents graph paths , with only pure perl code and I don't use other packet or module cpan.

This class calculates the shortest path between two nodes in a graph and return in other method , vals in the execution time (free_path_event).

Technically , the graph is composed of vertices (nodes) and edges (with optional weights) linked between them.

The shortest path is found using the Dijkstra's algorithm. This algorithm is the fastest and requires all weights to be positive.

The object builds a help about this concept of the graph's , exist a method named debug().

Three Case how to call Object and get a good performance as following:

## CASE 1 $obj->shortest_path

```
#!/usr/bin/perl
my %graph = (
A => {B=>1,C=>4,G=>2},
B => {A=>1,C=>2,D=>1,E=>5,F=>9,G=>8},
C => {A=>4,B=>2,F=>6},
D => {B=>1,E=>7,G=>3},
E => {B=>5,D=>7,F=>2},
F => {B=>9,C=>6,E=>2},
G => {A=>2,B=>8,D=>3}
);
use Paths::Graph;
my $obj = Paths::Graph->new(-origin=>"A",-destiny=>"F",-graph=>\%graph);
my @paths = $obj->shortest_path();
for my $path (@paths) {
print "Shortest Path:" . join ("->" , @$path) .
" Cost:". $obj->get_path_cost(@$path) . "\n";
}
```

## CASE 2 $obj->free_path_event

```
#!/usr/bin/perl
my %graph = (
A => {B=>1,C=>4,G=>2},
B => {A=>1,C=>2,D=>1,E=>5,F=>9,G=>8},
C => {A=>4,B=>2,F=>6},
D => {B=>1,E=>7,G=>3},
E => {B=>5,D=>7,F=>2},
F => {B=>9,C=>6,E=>2},
G => {A=>2,B=>8,D=>3},
);
use Paths::Graph;
my $obj = Paths::Graph->new(-origin=>"A",-destiny=>"F",-graph=>\%graph,-sub=>\&get_paths);
$obj->free_path_event();
sub get_paths {
my ($self , @nodes) = @_;
print join("->",@nodes) . "\n";
}
```

## CASE 3 $obj->debug()

```
#!/usr/bin/perl
my %graph = (
A => {B=>1,C=>4,G=>2},
B => {A=>1,C=>2,D=>1,E=>5,F=>9,G=>8},
C => {A=>4,B=>2,F=>6},
D => {B=>1,E=>7,G=>3},
E => {B=>5,D=>7,F=>2},
F => {B=>9,C=>6,E=>2},
G => {A=>2,B=>8,D=>3},
);
use Paths::Graph;
my $obj = Paths::Graph->new(-origin=>"A",-destiny=>"F",-graph=>\%graph);
$obj->debug();
```

# PARAMETERS

## $obj->{graph}

This object is the main element to resolve the trace graph problem.

The following cases are options of how this hash operate.

Note:It's not important the nodes's names , it's only important the nodes's values. example.

```
my %g = (
Linux => {Perl=>10,Regex=>20}
CPAN => {Modules=>1,Opensource=>100}
);
```

### CASE 1 Directed Graph

The directed graph are covered too.

```
my %g = (
A => {B=>10,C=>20,D=>1},
C => {B=>25,G=>1}
);
```

Fixed D and G do not exist , but it's fine.

### CASE 2 Jumper Graph

```
my %g = (
A => {B=>1,C=>1,D=>1},
C => {B=>1,G=>1}
);
```

Fixed D and G do not exist , but it's fine.

or

```
my %g = (
A => {B=>1,C=>1},
B => {B=>1,C=>1},
C => {A=>1,B=>1}
);
```

### CASE 3 Cost Graph

```
my %graph = (
A => {B=>1,C=>4},
B => {A=>1,C=>2},
C => {A=>4,B=>2},
);
```

The cost from A->C=4 and C->A=4

```
my %graph = (
A => {B=>1,C=>1},
B => {A=>1,C=>2},
C => {A=>4,B=>2},
);
```

The cost from A->C=1 and C->A=4

If the cost is distinct , it's not a problem.

## $obj->{origin} and $obj->{destiny}

It's not important the order on the hash graph.

```
$obj->{origin} = "A";
$obj->{destiny} = "B";
```

or

```
$obj->{origin} = "A";
$obj->{destiny} = "A";
```

Is not a problem if the origin and destiny nodes are equals. In this case the graph is traced from A to A.

## $obj->{sub}

This method returns the parameters from the object:

$self = some object control. @nodes = vals of arrays.

Note:The values's names do not have to be necesary equals , example;

```
$obj->{sub} = \&my_method;
sub my_method {
my ($obj,@nodes) = @_ ; # good
}
```

The method described above assigned its values to the object (my_method).

## $obj->shortest_path()

This object's method find the shortest path and cost for the graph using the hash.

## $obj->free_paths_event()

This method return a paths array during the execution time , it's generated a method to receive an array and the object with its methods and values.

## $obj->get_path_cost();

This method returns the paths cost (nodes array).

Trace graph hash recurcive.

## $obj->debug()

Educational procedure traces and shows the algorithm during execution time ($obj->debug). This method shows how the algorithm is being deploy background.

# DEBUGGING

Implementation of educational procedure of the object to call the debug() method;

# GLOBAL PROCESSING

Using the recursive technique in the object methods.

# EXPORT

These methods are exported as follow: shortest_path() free_path_event() debug()

# SEE ALSO

None by default. But can be exported if it's required.

Please report bugs using: <cristian@codigolibre.cl>.

Powerfull features in the future.

# HISTORY

Update in 2008 problem found by Keunwan Park problem produced in search where node value is equal to '0'

Thank , Keunwan Park will be contribute to perl comunity

Solucionate by me ;) , update available in version 0.03

# AUTHOR

Cristian Vasquez Diaz , cristian@codigolibre.cl.

# COPYRIGHT AND LICENSE

Copyright 2004 by Cristian Vasquez Diaz

This library is free software you can redistribute it and/or modify it under the same terms as Perl itself.