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<?php |
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namespace Fisharebest\Algorithm; |
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/** |
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* @author Greg Roach <[email protected]> |
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* @copyright (c) 2021 Greg Roach <[email protected]> |
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* @license GPL-3.0+ |
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* |
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* This program is free software: you can redistribute it and/or modify |
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* it under the terms of the GNU General Public License as published by |
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* the Free Software Foundation, either version 3 of the License, or |
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* (at your option) any later version. |
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* This program is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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* GNU General Public License for more details. |
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* You should have received a copy of the GNU General Public License |
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* along with this program. If not, see <https://www.gnu.org/licenses>. |
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*/ |
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/** |
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* Class Dijkstra - Use Dijkstra's algorithm to calculate the shortest path |
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* through a weighted, directed graph. |
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*/ |
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class Dijkstra |
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{ |
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/** @var integer[][] The graph, where $graph[node1][node2]=cost */ |
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protected $graph; |
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/** @var int[] Distances from the source node to each other node */ |
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protected $distance; |
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/** @var string[][] The previous node(s) in the path to the current node */ |
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protected $previous; |
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/** @var int[] Nodes which have yet to be processed */ |
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protected $queue; |
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/** |
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* @param integer[][] $graph |
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*/ |
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public function __construct($graph) |
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{ |
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$this->graph = $graph; |
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} |
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/** |
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* Process the next (i.e. closest) entry in the queue. |
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* |
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* @param string[] $exclude A list of nodes to exclude - for calculating next-shortest paths. |
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* |
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* @return void |
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*/ |
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protected function processNextNodeInQueue(array $exclude) |
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{ |
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// Process the closest vertex |
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$closest = array_search(min($this->queue), $this->queue); |
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if (!empty($this->graph[$closest]) && !in_array($closest, $exclude)) { |
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foreach ($this->graph[$closest] as $neighbor => $cost) { |
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if (isset($this->distance[$neighbor])) { |
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if ($this->distance[$closest] + $cost < $this->distance[$neighbor]) { |
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// A shorter path was found |
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$this->distance[$neighbor] = $this->distance[$closest] + $cost; |
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$this->previous[$neighbor] = array($closest); |
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$this->queue[$neighbor] = $this->distance[$neighbor]; |
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} elseif ($this->distance[$closest] + $cost === $this->distance[$neighbor]) { |
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// An equally short path was found |
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$this->previous[$neighbor][] = $closest; |
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$this->queue[$neighbor] = $this->distance[$neighbor]; |
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} |
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} |
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} |
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} |
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unset($this->queue[$closest]); |
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} |
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/** |
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* Extract all the paths from $source to $target as arrays of nodes. |
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* |
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* @param string $target The starting node (working backwards) |
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* |
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* @return string[][] One or more shortest paths, each represented by a list of nodes |
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*/ |
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protected function extractPaths($target) |
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{ |
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$paths = array(array($target)); |
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for ($key = 0; isset($paths[$key]); ++$key) { |
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$path = $paths[$key]; |
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if (!empty($this->previous[$path[0]])) { |
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foreach ($this->previous[$path[0]] as $previous) { |
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$copy = $path; |
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array_unshift($copy, $previous); |
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$paths[] = $copy; |
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} |
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unset($paths[$key]); |
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} |
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} |
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return array_values($paths); |
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} |
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/** |
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* Calculate the shortest path through a a graph, from $source to $target. |
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* |
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* @param string $source The starting node |
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* @param string $target The ending node |
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* @param string[] $exclude A list of nodes to exclude - for calculating next-shortest paths. |
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* |
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* @return string[][] Zero or more shortest paths, each represented by a list of nodes |
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*/ |
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public function shortestPaths($source, $target, array $exclude = array()) |
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{ |
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// The shortest distance to all nodes starts with infinity... |
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$this->distance = array_fill_keys(array_keys($this->graph), INF); |
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// ...except the start node |
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$this->distance[$source] = 0; |
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// The previously visited nodes |
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$this->previous = array_fill_keys(array_keys($this->graph), array()); |
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// Process all nodes in order |
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$this->queue = array($source => 0); |
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while (!empty($this->queue)) { |
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$this->processNextNodeInQueue($exclude); |
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} |
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if ($source === $target) { |
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// A null path |
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return array(array($source)); |
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} elseif (empty($this->previous[$target])) { |
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// No path between $source and $target |
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return array(); |
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} else { |
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// One or more paths were found between $source and $target |
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return $this->extractPaths($target); |
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} |
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} |
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} |
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fisharebest /
algorithm
