class Graph

class Graph {
    
    /**
     * Holds the directed acyclic graph.
     */
    protected $graph;
    
    /**
     * Instantiates the depth first search object.
     *
     * @param $graph
     *   A three dimensional associated array, with the first keys being the names
     *   of the vertices, these can be strings or numbers. The second key is
     *   'edges' and the third one are again vertices, each such key representing
     *   an edge. Values of array elements are copied over.
     *
     *   Example:
     *   @code
     *     $graph[1]['edges'][2] = 1;
     *     $graph[2]['edges'][3] = 1;
     *     $graph[2]['edges'][4] = 1;
     *     $graph[3]['edges'][4] = 1;
     *   @endcode
     *
     *   On return you will also have:
     *   @code
     *     $graph[1]['paths'][2] = 1;
     *     $graph[1]['paths'][3] = 1;
     *     $graph[2]['reverse_paths'][1] = 1;
     *     $graph[3]['reverse_paths'][1] = 1;
     *   @endcode
     */
    public function __construct($graph) {
        $this->graph = $graph;
    }
    
    /**
     * Performs a depth-first search and sort on the directed acyclic graph.
     *
     * @return array
     *   The given $graph with more secondary keys filled in:
     *   - 'paths': Contains a list of vertices than can be reached on a path from
     *     this vertex.
     *   - 'reverse_paths': Contains a list of vertices that has a path from them
     *     to this vertex.
     *   - 'weight': If there is a path from a vertex to another then the weight of
     *     the latter is higher.
     *   - 'component': Vertices in the same component have the same component
     *     identifier.
     */
    public function searchAndSort() {
        $state = [
            // The order of last visit of the depth first search. This is the reverse
            // of the topological order if the graph is acyclic.
'last_visit_order' => [],
            // The components of the graph.
'components' => [],
        ];
        // Perform the actual search.
        foreach ($this->graph as $start => $data) {
            $this->depthFirstSearch($state, $start);
        }
        // We do such a numbering that every component starts with 0. This is useful
        // for module installs as we can install every 0 weighted module in one
        // request, and then every 1 weighted etc.
        $component_weights = [];
        foreach ($state['last_visit_order'] as $vertex) {
            $component = $this->graph[$vertex]['component'];
            if (!isset($component_weights[$component])) {
                $component_weights[$component] = 0;
            }
            $this->graph[$vertex]['weight'] = $component_weights[$component]--;
        }
        return $this->graph;
    }
    
    /**
     * Performs a depth-first search on a graph.
     *
     * @param $state
     *   An associative array. The key 'last_visit_order' stores a list of the
     *   vertices visited. The key components stores list of vertices belonging
     *   to the same the component.
     * @param $start
     *   An arbitrary vertex where we started traversing the graph.
     * @param $component
     *   The component of the last vertex.
     *
     * @see \Drupal\Component\Graph\Graph::searchAndSort()
     */
    protected function depthFirstSearch(&$state, $start, &$component = NULL) {
        // Assign new component for each new vertex, i.e. when not called recursively.
        if (!isset($component)) {
            $component = $start;
        }
        // Nothing to do, if we already visited this vertex.
        if (isset($this->graph[$start]['paths'])) {
            return;
        }
        // Mark $start as visited.
        $this->graph[$start]['paths'] = [];
        // Assign $start to the current component.
        $this->graph[$start]['component'] = $component;
        $state['components'][$component][] = $start;
        // Visit edges of $start.
        if (isset($this->graph[$start]['edges'])) {
            foreach ($this->graph[$start]['edges'] as $end => $v) {
                // Mark that $start can reach $end.
                $this->graph[$start]['paths'][$end] = $v;
                if (isset($this->graph[$end]['component']) && $component != $this->graph[$end]['component']) {
                    // This vertex already has a component, use that from now on and
                    // reassign all the previously explored vertices.
                    $new_component = $this->graph[$end]['component'];
                    foreach ($state['components'][$component] as $vertex) {
                        $this->graph[$vertex]['component'] = $new_component;
                        $state['components'][$new_component][] = $vertex;
                    }
                    unset($state['components'][$component]);
                    $component = $new_component;
                }
                // Only visit existing vertices.
                if (isset($this->graph[$end])) {
                    // Visit the connected vertex.
                    $this->depthFirstSearch($state, $end, $component);
                    // All vertices reachable by $end are also reachable by $start.
                    $this->graph[$start]['paths'] += $this->graph[$end]['paths'];
                }
            }
        }
        // Now that any other subgraph has been explored, add $start to all reverse
        // paths.
        foreach ($this->graph[$start]['paths'] as $end => $v) {
            if (isset($this->graph[$end])) {
                $this->graph[$end]['reverse_paths'][$start] = $v;
            }
        }
        // Record the order of the last visit. This is the reverse of the
        // topological order if the graph is acyclic.
        $state['last_visit_order'][] = $start;
    }

}