First commit

includes/graph.inc

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+<?php
+
+/**
+ * @file
+ * Directed acyclic graph manipulation.
+ */
+
+
+/**
+ * Performs a depth-first search and sort on a directed acyclic graph.
+ *
+ * @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
+ *
+ * @return
+ *   The passed-in $graph with more secondary keys filled in:
+ *   - 'paths': Contains a list of vertices than can be reached on a path from
+ *     this vertex.
+ *   - 'reverse_paths': Contains a list of vertices that has a path from them
+ *     to this vertex.
+ *   - 'weight': If there is a path from a vertex to another then the weight of
+ *     the latter is higher.
+ *   - 'component': Vertices in the same component have the same component
+ *     identifier.
+ *
+ * @see _drupal_depth_first_search()
+ */
+function drupal_depth_first_search(&$graph) {
+  $state = array(
+    // The order of last visit of the depth first search. This is the reverse
+    // of the topological order if the graph is acyclic.
+    'last_visit_order' => array(),
+    // The components of the graph.
+    'components' => array(),
+  );
+  // Perform the actual search.
+  foreach ($graph as $start => $data) {
+    _drupal_depth_first_search($graph, $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.
+  $component_weights = array();
+
+  foreach ($state['last_visit_order'] as $vertex) {
+    $component = $graph[$vertex]['component'];
+    if (!isset($component_weights[$component])) {
+      $component_weights[$component] = 0;
+    }
+    $graph[$vertex]['weight'] = $component_weights[$component]--;
+  }
+}
+
+/**
+ * Performs a depth-first search on a graph.
+ *
+ * @param $graph
+ *   A three dimensional associated graph array.
+ * @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 $component
+ *   The component of the last vertex.
+ *
+ * @see drupal_depth_first_search()
+ */
+function _drupal_depth_first_search(&$graph, &$state, $start, &$component = NULL) {
+  // Assign new component for each new vertex, i.e. when not called recursively.
+  if (!isset($component)) {
+    $component = $start;
+  }
+  // Nothing to do, if we already visited this vertex.
+  if (isset($graph[$start]['paths'])) {
+    return;
+  }
+  // Mark $start as visited.
+  $graph[$start]['paths'] = array();
+
+  // Assign $start to the current component.
+  $graph[$start]['component'] = $component;
+  $state['components'][$component][] = $start;
+
+  // Visit edges of $start.
+  if (isset($graph[$start]['edges'])) {
+    foreach ($graph[$start]['edges'] as $end => $v) {
+      // Mark that $start can reach $end.
+      $graph[$start]['paths'][$end] = $v;
+
+      if (isset($graph[$end]['component']) && $component != $graph[$end]['component']) {
+        // This vertex already has a component, use that from now on and
+        // reassign all the previously explored vertices.
+        $new_component = $graph[$end]['component'];
+        foreach ($state['components'][$component] as $vertex) {
+          $graph[$vertex]['component'] = $new_component;
+          $state['components'][$new_component][] = $vertex;
+        }
+        unset($state['components'][$component]);
+        $component = $new_component;
+      }
+      // Only visit existing vertices.
+      if (isset($graph[$end])) {
+        // Visit the connected vertex.
+        _drupal_depth_first_search($graph, $state, $end, $component);
+
+        // All vertices reachable by $end are also reachable by $start.
+        $graph[$start]['paths'] += $graph[$end]['paths'];
+      }
+    }
+  }
+
+  // Now that any other subgraph has been explored, add $start to all reverse
+  // paths.
+  foreach ($graph[$start]['paths'] as $end => $v) {
+    if (isset($graph[$end])) {
+      $graph[$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;
+}