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AbstractDirectedGraph.php
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Wed, Apr 2, 09:54

AbstractDirectedGraph.php
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<?php
/**
* Models a directed graph in a generic way that works well with graphs stored
* in a database, and allows you to perform operations like cycle detection.
*
* To use this class, seed it with a set of edges (e.g., the new candidate
* edges the user is trying to create) using @{method:addNodes}, then
* call @{method:loadGraph} to construct the graph.
*
* $detector = new ExamplePhabricatorGraphCycleDetector();
* $detector->addNodes(
* array(
* $object->getPHID() => $object->getChildPHIDs(),
* ));
* $detector->loadGraph();
*
* Now you can query the graph, e.g. by detecting cycles:
*
* $cycle = $detector->detectCycles($object->getPHID());
*
* If ##$cycle## is empty, no graph cycle is reachable from the node. If it
* is nonempty, it contains a list of nodes which form a graph cycle.
*
* NOTE: Nodes must be represented with scalars.
*
* @task build Graph Construction
* @task cycle Cycle Detection
* @task explore Graph Exploration
*/
abstract class AbstractDirectedGraph {
private $knownNodes = array();
private $graphLoaded = false;
/* -( Graph Construction )------------------------------------------------- */
/**
* Load the edges for a list of nodes. You must override this method. You
* will be passed a list of nodes, and should return a dictionary mapping
* each node to the list of nodes that can be reached by following its the
* edges which originate at it: for example, the child nodes of an object
* which has a parent-child relationship to other objects.
*
* The intent of this method is to allow you to issue a single query per
* graph level for graphs which are stored as edge tables in the database.
* Generally, you will load all the objects which correspond to the list of
* nodes, and then return a map from each of their IDs to all their children.
*
* NOTE: You must return an entry for every node you are passed, even if it
* is invalid or can not be loaded. Either return an empty array (if this is
* acceptable for your application) or throw an exception if you can't satisfy
* this requirement.
*
* @param list A list of nodes.
* @return dict A map of nodes to the nodes reachable along their edges.
* There must be an entry for each node you were provided.
* @task build
*/
abstract protected function loadEdges(array $nodes);
/**
* Seed the graph with known nodes. Often, you will provide the candidate
* edges that a user is trying to create here, or the initial set of edges
* you know about.
*
* @param dict A map of nodes to the nodes reachable along their edges.
* @return this
* @task build
*/
final public function addNodes(array $nodes) {
if ($this->graphLoaded) {
throw new Exception(
'Call addNodes() before calling loadGraph(). You can not add more '.
'nodes once you have loaded the graph.');
}
$this->knownNodes += $nodes;
return $this;
}
final public function getNodes() {
return $this->knownNodes;
}
/**
* Utility function to get a list of topographically sorted nodes out of a
* graph.
*
* This could be useful for example to figure out what order you can safely
* apply dependencies.
*
* Note this will loop indefinitely if the graph has a cycle.
*/
final public function getTopographicallySortedNodes() {
$sorted = array();
$nodes = $this->getNodes();
$inverse_map = array();
foreach ($nodes as $node => $edges) {
if (!isset($inverse_map[$node])) {
$inverse_map[$node] = array();
}
foreach ($edges as $edge) {
if (!isset($inverse_map[$edge])) {
$inverse_map[$edge] = array();
}
$inverse_map[$edge][$node] = $node;
}
}
$end_nodes = array();
foreach ($inverse_map as $node => $edges) {
if (empty($edges)) {
$end_nodes[] = $node;
}
}
while (!empty($end_nodes)) {
$current_node = array_pop($end_nodes);
$sorted[] = $current_node;
$current_edges = $nodes[$current_node];
foreach ($current_edges as $index => $current_edge) {
// delete the edge from the normal map
unset($nodes[$current_node][$index]);
// and from the inverse map which is modestly trickier
$inverse_nodes = $inverse_map[$current_edge];
unset($inverse_nodes[$current_node]);
$inverse_map[$current_edge] = $inverse_nodes;
// no more edges means this is an "end node" now
if (empty($inverse_map[$current_edge])) {
$end_nodes[] = $current_edge;
}
}
}
return $sorted;
}
/**
* Utility function to get the best effort topographically sorted
* nodes out of a graph.
*/
final public function getBestEffortTopographicallySortedNodes() {
$nodes = $this->getNodes();
$edges = $this->loadEdges($nodes);
$results = array();
$completed = array();
$depth = 0;
while (true) {
$next = array();
foreach ($nodes as $node) {
if (isset($completed[$node])) {
continue;
}
$capable = true;
foreach ($edges[$node] as $edge) {
if (!isset($completed[$edge])) {
$capable = false;
break;
}
}
if ($capable) {
$next[] = $node;
}
}
if (count($next) === 0) {
// No more nodes to traverse; we are deadlocked if the number
// of completed nodes is less than the total number of nodes.
break;
}
foreach ($next as $node) {
$results[] = array(
'node' => $node,
'depth' => $depth,
'cycle' => false,
);
$completed[$node] = true;
}
$depth++;
}
foreach ($nodes as $node) {
if (!isset($completed[$node])) {
$results[] = array(
'node' => $node,
'depth' => $depth,
'cycle' => true,
);
}
}
return $results;
}
/**
* Load the graph, building it out so operations can be performed on it. This
* constructs the graph level-by-level, calling @{method:loadEdges} to
* expand the graph at each stage until it is complete.
*
* @return this
* @task build
*/
final public function loadGraph() {
$new_nodes = $this->knownNodes;
while (true) {
$load = array();
foreach ($new_nodes as $node => $edges) {
foreach ($edges as $edge) {
if (!isset($this->knownNodes[$edge])) {
$load[$edge] = true;
}
}
}
if (empty($load)) {
break;
}
$load = array_keys($load);
$new_nodes = $this->loadEdges($load);
foreach ($load as $node) {
if (!isset($new_nodes[$node]) || !is_array($new_nodes[$node])) {
throw new Exception(
'loadEdges() must return an edge list array for each provided '.
'node, or the cycle detection algorithm may not terminate.');
}
}
$this->addNodes($new_nodes);
}
$this->graphLoaded = true;
return $this;
}
/* -( Cycle Detection )---------------------------------------------------- */
/**
* Detect if there are any cycles reachable from a given node.
*
* If cycles are reachable, it returns a list of nodes which create a cycle.
* Note that this list may include nodes which aren't actually part of the
* cycle, but lie on the graph between the specified node and the cycle.
* For example, it might return something like this (when passed "A"):
*
* A, B, C, D, E, C
*
* This means you can walk from A to B to C to D to E and then back to C,
* which forms a cycle. A and B are included even though they are not part
* of the cycle. When presenting information about graph cycles to users,
* including these nodes is generally useful. This also shouldn't ever happen
* if you've vetted prior edges before writing them, because it means there
* is a preexisting cycle in the graph.
*
* NOTE: This only detects cycles reachable from a node. It does not detect
* cycles in the entire graph.
*
* @param scalar The node to walk from, looking for graph cycles.
* @return list|null Returns null if no cycles are reachable from the node,
* or a list of nodes that form a cycle.
* @task cycle
*/
final public function detectCycles($node) {
if (!$this->graphLoaded) {
throw new Exception(
'Call loadGraph() to build the graph out before calling '.
'detectCycles().');
}
if (!isset($this->knownNodes[$node])) {
throw new Exception(
"The node '{$node}' is not known. Call addNodes() to seed the graph ".
"with nodes.");
}
$visited = array();
return $this->performCycleDetection($node, $visited);
}
/**
* Internal cycle detection implementation. Recursively walks the graph,
* keeping track of where it's been, and returns the first cycle it finds.
*
* @param scalar The node to walk from.
* @param list Previously visited nodes.
* @return null|list Null if no cycles are found, or a list of nodes
* which cycle.
* @task cycle
*/
final private function performCycleDetection($node, array $visited) {
$visited[$node] = true;
foreach ($this->knownNodes[$node] as $edge) {
if (isset($visited[$edge])) {
$result = array_keys($visited);
$result[] = $edge;
return $result;
}
$result = $this->performCycleDetection($edge, $visited);
if ($result) {
return $result;
}
}
return null;
}
}

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