Minimum weight cycle in an undirected weighted graph in php
Php program for Minimum weight cycle in an undirected weighted graph. Here problem description and explanation.
<?php
/*
Php program for
Minimum weight cycle in an undirected graph
*/
class AjlistNode
{
// Vertices node key
public $id;
public $weight;
public $next;
public function __construct($id, $weight)
{
// Set value of node key
$this->id = $id;
$this->weight = $weight;
$this->next = NULL;
}
}
class Vertices
{
public $data;
public $next;
public $last;
public function __construct($data)
{
$this->data = $data;
$this->next = NULL;
$this->last = NULL;
}
}
class Graph
{
// Number of Vertices
public $size;
public $result;
public $node;
public function __construct($size)
{
// Set value
$this->size = $size;
$this->result = 0;
$this->node = array_fill(0, $size, NULL);
$this->setData();
}
// Set initial node value
public function setData()
{
if ($this->size <= 0)
{
echo "\nEmpty Graph", "\n";
}
else
{
for ($index = 0; $index < $this->size; $index++)
{
// Set initial node value
$this->node[$index] = new Vertices($index);
}
}
}
public function connection($start, $last, $weight)
{
// Safe connection
$edge = new AjlistNode($last, $weight);
if ($this->node[$start]->next == NULL)
{
$this->node[$start]->next = $edge;
}
else
{
// Add edge at the end
$this->node[$start]->last->next = $edge;
}
// Get last edge
$this->node[$start]->last = $edge;
}
// Handling the request of adding new edge
public function addEdge($start, $last, $weight)
{
if ($start >= 0 && $start < $this->size &&
$last >= 0 && $last < $this->size)
{
// Connect edge with weight
$this->connection($start, $last, $weight);
$this->connection($last, $start, $weight);
}
else
{
// When invalid nodes
printf("\nNode missing (%d,%d)", $start, $last);
}
}
public function printGraph()
{
if ($this->size > 0)
{
// Print graph ajlist
for ($index = 0; $index < $this->size; ++$index)
{
echo "\nAdjacency list of vertex ",$index,
" :";
$edge = $this->node[$index]->next;
while ($edge != NULL)
{
// Display graph node value and weight
echo " ",$this->node[$edge->id]->data,
"[",$edge->weight,
"]";
// Visit to next edge
$edge = $edge->next;
}
}
}
}
public function minimumCycle($start, $last, &$visit, $sum, $length)
{
if ($start >= $this->size ||
$last >= $this->size ||
$start < 0 || $last < 0 ||
$this->size <= 0)
{
return;
}
if ($visit[$start] == true)
{
// Here length are indicate loop length
if ($length > 2 && $start == $last &&
$sum < $this->result)
{
// Here length is indicate number of nodes
// Because graph is undirected so we consider all cycle
// Which contains more than 2 node
// ---------------------
// When find a new min weight cycle
$this->result = $sum;
}
return;
}
// Here modified the value of visited node
$visit[$start] = true;
// This is used to iterate nodes edges
$edge = $this->node[$start]->next;
while ($edge != NULL)
{
// Find solution using recursion
$this->minimumCycle($edge->id, $last,
$visit,
$sum + ($edge->weight),
$length + 1);
// Visit to next edge
$edge = $edge->next;
}
// Reset the value of visited node status
$visit[$start] = false;
}
public function minWeightCycle()
{
if ($this->size <= 0)
{
// Empty graph
return;
}
// Auxiliary space which is used to store
// information about visited node
// Set initial visited node status
$visit = array_fill(0, $this->size, false);
$this->result = PHP_INT_MAX;
for ($i = 0; $i < $this->size; ++$i)
{
// Check cycle of node i to i
// Here initial cycle weight is zero
$this->minimumCycle($i, $i, $visit, 0, 0);
}
// Display result
echo "\nMin weight cycle : ",$this->result, "\n";
}
public static
function main($args)
{
// 6 implies the number of nodes in graph
$g = new Graph(6);
// Connect node with an edge
// First and second parameter indicate node
// Last parameter is indicate weight
$g->addEdge(0, 1, 3);
$g->addEdge(0, 3, -3);
$g->addEdge(0, 4, 7);
$g->addEdge(0, 5, 1);
$g->addEdge(1, 2, 11);
$g->addEdge(1, 4, 8);
$g->addEdge(2, 3, 1);
$g->addEdge(2, 5, 4);
$g->addEdge(3, 4, 2);
$g->addEdge(4, 5, 8);
$g->addEdge(5, 1, 0);
// Print graph element
$g->printGraph();
// Test
$g->minWeightCycle();
}
}
Graph::main(array());
Output
Adjacency list of vertex 0 : 1[3] 3[-3] 4[7] 5[1]
Adjacency list of vertex 1 : 0[3] 2[11] 4[8] 5[0]
Adjacency list of vertex 2 : 1[11] 3[1] 5[4]
Adjacency list of vertex 3 : 0[-3] 2[1] 4[2]
Adjacency list of vertex 4 : 0[7] 1[8] 3[2] 5[8]
Adjacency list of vertex 5 : 0[1] 2[4] 4[8] 1[0]
Min weight cycle : 3
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