<?php
namespace Fisharebest\Algorithm;

/**
 * @package   fisharebest/algorithm
 * @author    Greg Roach <greg@subaqua.co.uk>
 * @copyright (c) 2015 Greg Roach <greg@subaqua.co.uk>
 * @license   GPL-3.0+
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License for more details.
 * You should have received a copy of the GNU General Public License
 * along with this program. If not, see <http://www.gnu.org/licenses/>.
 */

/**
 * Class Dijkstra - Use Dijkstra's algorithm to calculate the shortest path
 * through a weighted, directed graph.
 */
class Dijkstra {
	/** @var integer[][] The graph, where $graph[node1][node2]=cost */
	protected $graph;
	
	/** @var integer[] Distances from the source node to each other node */
	protected $distance;

	/** @var string[][] The previous node(s) in the path to the current node */
	protected $previous;

	/** @var integer[] Nodes which have yet to be processed */
	protected $queue;

	/**
	 * @param integer[][] $graph
	 */
	public function __construct($graph) {
		$this->graph = $graph;
	}

	/**
	 * Process the next (i.e. closest) entry in the queue
	 *
	 * @param string[] $exclude A list of nodes to exclude - for calculating next-shortest paths.
	 *
	 * @return void
	 */
	protected function processNextNodeInQueue(array $exclude) {
		// Process the closest vertex
		$closest = array_search(min($this->queue), $this->queue);
		if (!empty($this->graph[$closest]) && !in_array($closest, $exclude)) {
			foreach ($this->graph[$closest] as $neighbor => $cost) {
				if (isset($this->distance[$neighbor])) {
					if ($this->distance[$closest] + $cost < $this->distance[$neighbor]) {
						// A shorter path was found
						$this->distance[$neighbor] = $this->distance[$closest] + $cost;
						$this->previous[$neighbor] = array($closest);
						$this->queue[$neighbor]    = $this->distance[$neighbor];
					} elseif ($this->distance[$closest] + $cost === $this->distance[$neighbor]) {
						// An equally short path was found
						$this->previous[$neighbor][] = $closest;
						$this->queue[$neighbor]      = $this->distance[$neighbor];
					}
				}
			}
		}
		unset($this->queue[$closest]);
	}

	/**
	 * Extract all the paths from $source to $target as arrays of nodes.
	 *
	 * @param string $target The starting node (working backwards)
	 *
	 * @return string[][] One or more shortest paths, each represented by a list of nodes
	 */
	protected function extractPaths($target) {
		$paths = array(array($target));
		while (list($key, $path) = each($paths)) {
			if ($this->previous[$path[0]]) {
				foreach ($this->previous[$path[0]] as $previous) {
					$copy = $path;
					array_unshift($copy, $previous);
					$paths[] = $copy;
				}
				unset($paths[$key]);
			}
		}

		return array_values($paths);
	}

	/**
	 * Calculate the shortest path through a a graph, from $source to $target.
	 *
	 * @param string   $source  The starting node
	 * @param string   $target  The ending node
	 * @param string[] $exclude A list of nodes to exclude - for calculating next-shortest paths.
	 *
	 * @return string[][] Zero or more shortest paths, each represented by a list of nodes
	 */
	public function shortestPaths($source, $target, array $exclude = array()) {
		// The shortest distance to all nodes starts with infinity...
		$this->distance = array_fill_keys(array_keys($this->graph), INF);
		// ...except the start node
		$this->distance[$source] = 0;

		// The previously visited nodes
		$this->previous = array_fill_keys(array_keys($this->graph), array());

		// Process all nodes in order
		$this->queue = array($source => 0);
		while ($this->queue) {
			$this->processNextNodeInQueue($exclude);
		}

		if ($source === $target) {
			// A null path
			return array(array($source));
		} elseif (empty($this->previous[$target])) {
			// No path between $source and $target
			return array();
		} else {
			// One or more paths were found between $source and $target
			return $this->extractPaths($target);
		}
	}
}
