// Copyright 2014 The Bazel Authors. All rights reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
package com.google.devtools.build.lib.graph;
import com.google.common.collect.ImmutableSet;
import com.google.common.collect.Maps;
import com.google.common.collect.Ordering;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Set;
import javax.annotation.Nullable;
/**
* <p> {@code Digraph} a generic directed graph or "digraph", suitable for
* modeling asymmetric binary relations. </p>
*
* <p> An instance <code>G = <V,E></code> consists of a set of nodes or
* vertices <code>V</code>, and a set of directed edges <code>E</code>, which
* is a subset of <code>V × V</code>. This permits self-edges but does
* not represent multiple edges between the same pair of nodes. </p>
*
* <p> Nodes may be labeled with values of any type (type parameter
* T). All nodes within a graph have distinct labels. The null
* pointer is not a valid label.</p>
*
* <p> The package supports various operations for modeling partial order
* relations, and supports input/output in AT&T's 'dot' format. See
* http://www.research.att.com/sw/tools/graphviz/. </p>
*
* <p> Some invariants: </p>
* <ul>
*
* <li> Each graph instances "owns" the nodes is creates. The behaviour of
* operations on nodes a graph does not own is undefined.
*
* <li> {@code Digraph} assumes immutability of node labels, much like {@link
* HashMap} assumes it for keys.
*
* <li> Mutating the underlying graph invalidates any sets and iterators backed
* by it.
*
* </ul>
*
* <p>Each node stores successor and predecessor adjacency sets using a
* representation that dynamically changes with size: small sets are stored as
* arrays, large sets using hash tables. This representation provides
* significant space and time performance improvements upon two prior versions:
* the earliest used only HashSets; a later version used linked lists, as
* described in Cormen, Leiserson & Rivest.
*/
public final class Digraph<T> implements Cloneable {
/**
* Maps labels to nodes, which are in strict 1:1 correspondence.
*/
private final HashMap<T, Node<T>> nodes = Maps.newHashMap();
/**
* A source of unique, deterministic hashCodes for {@link Node} instances.
*/
private int nextHashCode = 0;
/**
* Construct an empty Digraph.
*/
public Digraph() {}
/**
* Sanity-check: assert that a node is indeed a member of this graph and not
* another one. Perform this check whenever a function is supplied a node by
* the user.
*/
private final void checkNode(Node<T> node) {
if (getNode(node.getLabel()) != node) {
throw new IllegalArgumentException("node " + node
+ " is not a member of this graph");
}
}
/**
* Adds a directed edge between the nodes labelled 'from' and 'to', creating
* them if necessary.
*
* @return true iff the edge was not already present.
*/
public boolean addEdge(T from, T to) {
Node<T> fromNode = createNode(from);
Node<T> toNode = createNode(to);
return addEdge(fromNode, toNode);
}
/**
* Adds a directed edge between the specified nodes, which must exist and
* belong to this graph.
*
* @return true iff the edge was not already present.
*
* Note: multi-edges are ignored. Self-edges are permitted.
*/
public boolean addEdge(Node<T> fromNode, Node<T> toNode) {
checkNode(fromNode);
checkNode(toNode);
boolean isNewSuccessor = fromNode.addSuccessor(toNode);
boolean isNewPredecessor = toNode.addPredecessor(fromNode);
if (isNewPredecessor != isNewSuccessor) {
throw new IllegalStateException();
}
return isNewSuccessor;
}
/**
* Returns true iff the graph contains an edge between the
* specified nodes, which must exist and belong to this graph.
*/
public boolean containsEdge(Node<T> fromNode, Node<T> toNode) {
checkNode(fromNode);
checkNode(toNode);
// TODO(bazel-team): (2009) iterate only over the shorter of from.succs, to.preds.
return fromNode.getSuccessors().contains(toNode);
}
/**
* Removes the edge between the specified nodes. Idempotent: attempts to
* remove non-existent edges have no effect.
*
* @return true iff graph changed.
*/
public boolean removeEdge(Node<T> fromNode, Node<T> toNode) {
checkNode(fromNode);
checkNode(toNode);
boolean changed = fromNode.removeSuccessor(toNode);
if (changed) {
toNode.removePredecessor(fromNode);
}
return changed;
}
/**
* Remove all nodes and edges.
*/
public void clear() {
nodes.clear();
}
@Override
public String toString() {
return "Digraph[" + getNodeCount() + " nodes]";
}
@Override
public int hashCode() {
throw new UnsupportedOperationException(); // avoid nondeterminism
}
/**
* Returns true iff the two graphs are equivalent, i.e. have the same set
* of node labels, with the same connectivity relation.
*
* O(n^2) in the worst case, i.e. equivalence. The algorithm could be speed up by
* close to a factor 2 in the worst case by a more direct implementation instead
* of using isSubgraph twice.
*/
@Override
public boolean equals(Object thatObject) {
/* If this graph is a subgraph of thatObject, then we know that thatObject is of
* type Digraph<?> and thatObject can be cast to this type.
*/
return isSubgraph(thatObject) && ((Digraph<?>) thatObject).isSubgraph(this);
}
/**
* Returns true iff this graph is a subgraph of the argument. This means that this graph's nodes
* are a subset of those of the argument; moreover, for each node of this graph the set of
* successors is a subset of those of the corresponding node in the argument graph.
*
* This algorithm is O(n^2), but linear in the total sizes of the graphs.
*/
public boolean isSubgraph(Object thatObject) {
if (this == thatObject) {
return true;
}
if (!(thatObject instanceof Digraph)) {
return false;
}
@SuppressWarnings("unchecked")
Digraph<T> that = (Digraph<T>) thatObject;
if (this.getNodeCount() > that.getNodeCount()) {
return false;
}
for (Node<T> n1: nodes.values()) {
Node<T> n2 = that.getNodeMaybe(n1.getLabel());
if (n2 == null) {
return false; // 'that' is missing a node
}
// Now compare the successor relations.
// Careful:
// - We can't do simple equality on the succs-sets because the
// nodes belong to two different graphs!
// - There's no need to check both predecessor and successor
// relations, either one is sufficient.
Collection<Node<T>> n1succs = n1.getSuccessors();
Collection<Node<T>> n2succs = n2.getSuccessors();
if (n1succs.size() > n2succs.size()) {
return false;
}
// foreach successor of n1, ensure n2 has a similarly-labeled succ.
for (Node<T> succ1: n1succs) {
Node<T> succ2 = that.getNodeMaybe(succ1.getLabel());
if (succ2 == null) {
return false;
}
if (!n2succs.contains(succ2)) {
return false;
}
}
}
return true;
}
/**
* Returns a duplicate graph with the same set of node labels and the same
* connectivity relation. The labels themselves are not cloned.
*/
@Override
public Digraph<T> clone() {
final Digraph<T> that = new Digraph<T>();
visitNodesBeforeEdges(
new AbstractGraphVisitor<T>() {
@Override
public void visitEdge(Node<T> lhs, Node<T> rhs) {
that.addEdge(lhs.getLabel(), rhs.getLabel());
}
@Override
public void visitNode(Node<T> node) {
that.createNode(node.getLabel());
}
},
nodes.values(),
null);
return that;
}
/**
* Returns a deterministic immutable view of the nodes of this graph.
*/
public Collection<Node<T>> getNodes(final Comparator<? super T> comparator) {
Ordering<Node<T>> ordering = new Ordering<Node<T>>() {
@Override
public int compare(Node<T> o1, Node<T> o2) {
return comparator.compare(o1.getLabel(), o2.getLabel());
}
};
return ordering.immutableSortedCopy(nodes.values());
}
/**
* Returns an immutable view of the nodes of this graph.
*
* Note: we have to return Collection and not Set because values() returns
* one: the 'nodes' HashMap doesn't know that it is injective. :-(
*/
public Collection<Node<T>> getNodes() {
return Collections.unmodifiableCollection(nodes.values());
}
/**
* @return the set of root nodes: those with no predecessors.
*
* NOTE: in a cyclic graph, there may be nodes that are not reachable from
* any "root".
*/
public Set<Node<T>> getRoots() {
Set<Node<T>> roots = new HashSet<>();
for (Node<T> node: nodes.values()) {
if (!node.hasPredecessors()) {
roots.add(node);
}
}
return roots;
}
/**
* @return the set of leaf nodes: those with no successors.
*/
public Set<Node<T>> getLeaves() {
Set<Node<T>> leaves = new HashSet<>();
for (Node<T> node: nodes.values()) {
if (!node.hasSuccessors()) {
leaves.add(node);
}
}
return leaves;
}
/**
* @return an immutable view of the set of labels of this graph's nodes.
*/
public Set<T> getLabels() {
return Collections.unmodifiableSet(nodes.keySet());
}
/**
* Finds and returns the node with the specified label. If there is no such
* node, an exception is thrown. The null pointer is not a valid label.
*
* @return the node whose label is "label".
* @throws IllegalArgumentException if no node was found with the specified
* label.
*/
public Node<T> getNode(T label) {
if (label == null) {
throw new NullPointerException();
}
Node<T> node = nodes.get(label);
if (node == null) {
throw new IllegalArgumentException("No such node label: " + label);
}
return node;
}
/**
* Find the node with the specified label. Returns null if it doesn't exist.
* The null pointer is not a valid label.
*
* @return the node whose label is "label", or null if it was not found.
*/
public Node<T> getNodeMaybe(T label) {
if (label == null) {
throw new NullPointerException();
}
return nodes.get(label);
}
/**
* @return the number of nodes in the graph.
*/
public int getNodeCount() {
return nodes.size();
}
/**
* @return the number of edges in the graph.
*
* Note: expensive! Useful when asserting against mutations though.
*/
public int getEdgeCount() {
int edges = 0;
for (Node<T> node: nodes.values()) {
edges += node.getSuccessors().size();
}
return edges;
}
/**
* Find or create a node with the specified label. This is the <i>only</i>
* factory of Nodes. The null pointer is not a valid label.
*/
public Node<T> createNode(T label) {
if (label == null) {
throw new NullPointerException();
}
Node<T> n = nodes.get(label);
if (n == null) {
nodes.put(label, n = new Node<T>(label, nextHashCode++));
}
return n;
}
/******************************************************************
* *
* Graph Algorithms *
* *
******************************************************************/
/**
* These only manipulate the graph through methods defined above.
*/
/**
* Returns true iff the graph is cyclic. Time: O(n).
*/
public boolean isCyclic() {
// To detect cycles, we use a colored depth-first search. All nodes are
// initially marked white. When a node is encountered, it is marked grey,
// and when its descendants are completely visited, it is marked black.
// If a grey node is ever encountered, then there is a cycle.
final Object WHITE = null; // i.e. not present in nodeToColor, the default.
final Object GREY = new Object();
final Object BLACK = new Object();
final Map<Node<T>, Object> nodeToColor = new HashMap<>(); // empty => all white
class CycleDetector { /* defining a class gives us lexical scope */
boolean visit(Node<T> node) {
nodeToColor.put(node, GREY);
for (Node<T> succ: node.getSuccessors()) {
if (nodeToColor.get(succ) == GREY) {
return true;
} else if (nodeToColor.get(succ) == WHITE) {
if (visit(succ)) {
return true;
}
}
}
nodeToColor.put(node, BLACK);
return false;
}
}
CycleDetector detector = new CycleDetector();
for (Node<T> node: nodes.values()) {
if (nodeToColor.get(node) == WHITE) {
if (detector.visit(node)) {
return true;
}
}
}
return false;
}
/**
* Returns the strong component graph of "this". That is, returns a new
* acyclic graph in which all strongly-connected components in the original
* graph have been "fused" into a single node.
*
* @return a new graph, whose node labels are sets of nodes of the
* original graph. (Do not get confused as to which graph each
* set of Nodes belongs!)
*/
public Digraph<Set<Node<T>>> getStrongComponentGraph() {
Collection<Set<Node<T>>> sccs = getStronglyConnectedComponents();
Digraph<Set<Node<T>>> scGraph = createImageUnderPartition(sccs);
scGraph.removeSelfEdges(); // scGraph should be acyclic: no self-edges
return scGraph;
}
/**
* Returns a partition of the nodes of this graph into sets, each set being
* one strongly-connected component of the graph.
*/
public Collection<Set<Node<T>>> getStronglyConnectedComponents() {
final List<Set<Node<T>>> sccs = new ArrayList<>();
NodeSetReceiver<T> r = new NodeSetReceiver<T>() {
@Override
public void accept(Set<Node<T>> scc) {
sccs.add(scc);
}
};
SccVisitor<T> v = new SccVisitor<T>();
for (Node<T> node : nodes.values()) {
v.visit(r, node);
}
return sccs;
}
/**
* <p> Given a partition of the graph into sets of nodes, returns the image
* of this graph under the function which maps each node to the
* partition-set in which it appears. The labels of the new graph are the
* (immutable) sets of the partition, and the edges of the new graph are the
* edges of the original graph, mapped via the same function. </p>
*
* <p> Note: the resulting graph may contain self-edges. If these are not
* wanted, call <code>removeSelfEdges()</code>> on the result. </p>
*
* <p> Interesting special case: if the partition is the set of
* strongly-connected components, the result of this function is the
* strong-component graph. </p>
*/
public Digraph<Set<Node<T>>>
createImageUnderPartition(Collection<Set<Node<T>>> partition) {
// Build mapping function: each node label is mapped to its equiv class:
Map<T, Set<Node<T>>> labelToImage = new HashMap<>();
for (Set<Node<T>> set: partition) {
// It's important to use immutable sets of node labels when sets are keys
// in a map; see ImmutableSet class for explanation.
Set<Node<T>> imageSet = ImmutableSet.copyOf(set);
for (Node<T> node: imageSet) {
labelToImage.put(node.getLabel(), imageSet);
}
}
if (labelToImage.size() != getNodeCount()) {
throw new IllegalArgumentException(
"createImageUnderPartition(): argument is not a partition");
}
return createImageUnderMapping(labelToImage);
}
/**
* Returns the image of this graph in a given function, expressed as a
* mapping from labels to some other domain.
*/
public <IMAGE> Digraph<IMAGE>
createImageUnderMapping(Map<T, IMAGE> map) {
Digraph<IMAGE> imageGraph = new Digraph<>();
for (Node<T> fromNode: nodes.values()) {
T fromLabel = fromNode.getLabel();
IMAGE fromImage = map.get(fromLabel);
if (fromImage == null) {
throw new IllegalArgumentException(
"Incomplete function: undefined for " + fromLabel);
}
imageGraph.createNode(fromImage);
for (Node<T> toNode: fromNode.getSuccessors()) {
T toLabel = toNode.getLabel();
IMAGE toImage = map.get(toLabel);
if (toImage == null) {
throw new IllegalArgumentException(
"Incomplete function: undefined for " + toLabel);
}
imageGraph.addEdge(fromImage, toImage);
}
}
return imageGraph;
}
/**
* Removes any self-edges (x,x) in this graph.
*/
public void removeSelfEdges() {
for (Node<T> node: nodes.values()) {
removeEdge(node, node);
}
}
/**
* Finds the shortest directed path from "fromNode" to "toNode". The path is
* returned as an ordered list of nodes, including both endpoints. Returns
* null if there is no path. Uses breadth-first search. Running time is
* O(n).
*/
public List<Node<T>> getShortestPath(Node<T> fromNode,
Node<T> toNode) {
checkNode(fromNode);
checkNode(toNode);
if (fromNode == toNode) {
return Collections.singletonList(fromNode);
}
Map<Node<T>, Node<T>> pathPredecessor = new HashMap<>();
Set<Node<T>> marked = new HashSet<>();
LinkedList<Node<T>> queue = new LinkedList<>();
queue.addLast(fromNode);
marked.add(fromNode);
while (!queue.isEmpty()) {
Node<T> u = queue.removeFirst();
for (Node<T> v: u.getSuccessors()) {
if (marked.add(v)) {
pathPredecessor.put(v, u);
if (v == toNode) {
return getPathToTreeNode(pathPredecessor, v); // found a path
}
queue.addLast(v);
}
}
}
return null; // no path
}
/**
* Given a tree (expressed as a map from each node to its parent), and a
* starting node, returns the path from the root of the tree to 'node' as a
* list.
*/
public static <X> List<X> getPathToTreeNode(Map<X, X> tree, X node) {
List<X> path = new ArrayList<X>();
while (node != null) {
path.add(node);
node = tree.get(node); // get parent
}
Collections.reverse(path);
return path;
}
/**
* Returns the nodes of an acyclic graph in topological order
* [a.k.a "reverse post-order" of depth-first search.]
*
* A topological order is one such that, if (u, v) is a path in
* acyclic graph G, then u is before v in the topological order.
* In other words "tails before heads" or "roots before leaves".
*
* @return The nodes of the graph, in a topological order
*/
public List<Node<T>> getTopologicalOrder() {
List<Node<T>> order = getPostorder();
Collections.reverse(order);
return order;
}
/**
* Returns the nodes of an acyclic graph in topological order
* [a.k.a "reverse post-order" of depth-first search.]
*
* A topological order is one such that, if (u, v) is a path in
* acyclic graph G, then u is before v in the topological order.
* In other words "tails before heads" or "roots before leaves".
*
* If an ordering is given, returns a specific topological order from the set
* of all topological orders; if no ordering given, returns an arbitrary
* (nondeterministic) one, but is a bit faster because no sorting needs to be
* done for each node.
*
* @param edgeOrder the ordering in which edges originating from the same node
* are visited.
* @return The nodes of the graph, in a topological order
*/
public List<Node<T>> getTopologicalOrder(Comparator<? super T> edgeOrder) {
CollectingVisitor<T> visitor = new CollectingVisitor<T>();
DFS<T> visitation = new DFS<T>(DFS.Order.POSTORDER, edgeOrder, false);
visitor.beginVisit();
for (Node<T> node : getNodes(edgeOrder)) {
visitation.visit(node, visitor);
}
visitor.endVisit();
List<Node<T>> order = visitor.getVisitedNodes();
Collections.reverse(order);
return order;
}
/**
* Returns the nodes of an acyclic graph in post-order.
*/
public List<Node<T>> getPostorder() {
CollectingVisitor<T> collectingVisitor = new CollectingVisitor<T>();
visitPostorder(collectingVisitor);
return collectingVisitor.getVisitedNodes();
}
/**
* Returns the (immutable) set of nodes reachable from node 'n' (reflexive
* transitive closure).
*/
public Set<Node<T>> getFwdReachable(Node<T> n) {
return getFwdReachable(Collections.singleton(n));
}
/**
* Returns the (immutable) set of nodes reachable from any node in {@code
* startNodes} (reflexive transitive closure).
*/
public Set<Node<T>> getFwdReachable(Collection<Node<T>> startNodes) {
// This method is intentionally not static, to permit future expansion.
DFS<T> dfs = new DFS<T>(DFS.Order.PREORDER, false);
for (Node<T> n : startNodes) {
dfs.visit(n, new AbstractGraphVisitor<T>());
}
return dfs.getMarked();
}
/**
* Returns the (immutable) set of nodes that reach node 'n' (reflexive
* transitive closure).
*/
public Set<Node<T>> getBackReachable(Node<T> n) {
return getBackReachable(Collections.singleton(n));
}
/**
* Returns the (immutable) set of nodes that reach some node in {@code
* startNodes} (reflexive transitive closure).
*/
public Set<Node<T>> getBackReachable(Collection<Node<T>> startNodes) {
// This method is intentionally not static, to permit future expansion.
DFS<T> dfs = new DFS<T>(DFS.Order.PREORDER, true);
for (Node<T> n : startNodes) {
dfs.visit(n, new AbstractGraphVisitor<T>());
}
return dfs.getMarked();
}
/**
* Removes the node in the graph specified by the given label. Optionally,
* preserves the graph order (by connecting up the broken edges) or drop them
* all. If the specified label is not the label of any node in the graph,
* does nothing.
*
* @param label the label of the node to remove.
* @param preserveOrder if true, adds edges between the neighbours
* of the removed node so as to maintain the graph ordering
* relation between all pairs of such nodes. If false, simply
* discards all edges from the deleted node to its neighbours.
* @return true iff 'label' identifies a node (i.e. the graph was changed).
*/
public boolean removeNode(T label, boolean preserveOrder) {
Node<T> node = getNodeMaybe(label);
if (node != null) {
removeNode(node, preserveOrder);
return true;
} else {
return false;
}
}
/**
* Removes the specified node in the graph.
*
* @param n the node to remove (must be in the graph).
* @param preserveOrder see removeNode(T, boolean).
*/
public void removeNode(Node<T> n, boolean preserveOrder) {
checkNode(n);
for (Node<T> b: n.getSuccessors()) { // edges from n
// exists: n -> b
if (preserveOrder) {
for (Node<T> a: n.getPredecessors()) { // edges to n
// exists: a -> n
// beware self edges: they prevent n's deletion!
if (a != n && b != n) {
addEdge(a, b); // concurrent mod?
}
}
}
b.removePredecessor(n); // remove edge n->b in b
}
for (Node<T> a: n.getPredecessors()) { // edges to n
a.removeSuccessor(n); // remove edge a->n in a
}
n.removeAllEdges(); // remove edges b->n and a->n in n
Object del = nodes.remove(n.getLabel());
if (del != n) {
throw new IllegalStateException(del + " " + n);
}
}
/**
* Extracts the subgraph G' of this graph G, containing exactly the nodes
* specified by the labels in V', and preserving the original
* <i>transitive</i> graph relation among those nodes. </p>
*
* @param subset a subset of the labels of this graph; the resulting graph
* will have only the nodes with these labels.
*/
public Digraph<T> extractSubgraph(final Set<T> subset) {
Digraph<T> subgraph = this.clone();
subgraph.subgraph(subset);
return subgraph;
}
/**
* Removes all nodes from this graph except those whose label is an element of {@code keepLabels}.
* Edges are added so as to preserve the <i>transitive</i> closure relation.
*
* @param keepLabels a subset of the labels of this graph; the resulting graph
* will have only the nodes with these labels.
*/
public void subgraph(final Set<T> keepLabels) {
// This algorithm does the following:
// Let keep = nodes that have labels in keepLabels.
// Let toRemove = nodes \ keep. reachables = successors and predecessors of keep in nodes.
// reachables is the subset of nodes of remove that are an immediate neighbor of some node in
// keep.
//
// Removes all nodes of reachables from keepLabels.
// Until reachables is empty:
// Takes n from reachables
// for all s in succ(n)
// for all p in pred(n)
// add the edge (p, s)
// add s to reachables
// for all p in pred(n)
// add p to reachables
// Remove n and its edges
//
// A few adjustments are needed to do the whole computation.
final Set<Node<T>> toRemove = new HashSet<>();
final Set<Node<T>> keepNeighbors = new HashSet<>();
// Look for all nodes if they are to be kept or removed
for (Node<T> node : nodes.values()) {
if (keepLabels.contains(node.getLabel())) {
// Node is to be kept
keepNeighbors.addAll(node.getPredecessors());
keepNeighbors.addAll(node.getSuccessors());
} else {
// node is to be removed.
toRemove.add(node);
}
}
if (toRemove.isEmpty()) {
// This premature return is needed to avoid 0-size priority queue creation.
return;
}
// We use a priority queue to look for low-order nodes first so we don't propagate the high
// number of paths of high-order nodes making the time consumption explode.
// For perfect results we should reorder the set each time we add a new edge but this would
// be too expensive, so this is a good enough approximation.
final PriorityQueue<Node<T>> reachables = new PriorityQueue<>(toRemove.size(),
new Comparator<Node<T>>() {
@Override
public int compare(Node<T> o1, Node<T> o2) {
return Long.compare((long) o1.numPredecessors() * (long) o1.numSuccessors(),
(long) o2.numPredecessors() * (long) o2.numSuccessors());
}
});
// Construct the reachables queue with the list of successors and predecessors of keep in
// toRemove.
keepNeighbors.retainAll(toRemove);
reachables.addAll(keepNeighbors);
toRemove.removeAll(reachables);
// Remove nodes, least connected first, preserving reachability.
while (!reachables.isEmpty()) {
Node<T> node = reachables.poll();
for (Node<T> s : node.getSuccessors()) {
if (s == node) { continue; } // ignore self-edge
for (Node<T> p : node.getPredecessors()) {
if (p == node) { continue; } // ignore self-edge
addEdge(p, s);
}
// removes n -> s
s.removePredecessor(node);
if (toRemove.remove(s)) {
reachables.add(s);
}
}
for (Node<T> p : node.getPredecessors()) {
if (p == node) { continue; } // ignore self-edge
p.removeSuccessor(node);
if (toRemove.remove(p)) {
reachables.add(p);
}
}
// After the node deletion, the graph is again well-formed and the original topological order
// is preserved.
nodes.remove(node.getLabel());
}
// Final cleanup for non-reachable nodes.
for (Node<T> node : toRemove) {
removeNode(node, false);
}
}
private interface NodeSetReceiver<T> {
void accept(Set<Node<T>> nodes);
}
/**
* Find strongly connected components using path-based strong component
* algorithm. This has the advantage over the default method of returning
* the components in postorder.
*
* We visit nodes depth-first, keeping track of the order that
* we visit them in (preorder). Our goal is to find the smallest node (in
* this preorder of visitation) reachable from a given node. We keep track of the
* smallest node pointed to so far at the top of a stack. If we ever find an
* already-visited node, then if it is not already part of a component, we
* pop nodes from that stack until we reach this already-visited node's number
* or an even smaller one.
*
* Once the depth-first visitation of a node is complete, if this node's
* number is at the top of the stack, then it is the "first" element visited
* in its strongly connected component. Hence we pop all elements that were
* pushed onto the visitation stack and put them in a strongly connected
* component with this one, then send a passed-in {@link Digraph.NodeSetReceiver} this component.
*/
private class SccVisitor<T> {
// Nodes already assigned to a strongly connected component.
private final Set<Node<T>> assigned = new HashSet<>();
// The order each node was visited in.
private final Map<Node<T>, Integer> preorder = new HashMap<>();
// Stack of all nodes visited whose SCC has not yet been determined. When an SCC is found,
// that SCC is an initial segment of this stack, and is popped off. Every time a new node is
// visited, it is put on this stack.
private final List<Node<T>> stack = new ArrayList<>();
// Stack of visited indices for the first-visited nodes in each of their known-so-far
// strongly connected components. A node pushes its index on when it is visited. If any of
// its successors have already been visited and are not in an already-found strongly connected
// component, then, since the successor was already visited, it and this node must be part of a
// cycle. So every node visited since the successor is actually in the same strongly connected
// component. In this case, preorderStack is popped until the top is at most the successor's
// index.
//
// After all descendants of a node have been visited, if the top element of preorderStack is
// still the current node's index, then it was the first element visited of the current strongly
// connected component. So all nodes on {@code stack} down to the current node are in its
// strongly connected component. And the node's index is popped from preorderStack.
private final List<Integer> preorderStack = new ArrayList<>();
// Index of node being visited.
private int counter = 0;
private void visit(NodeSetReceiver<T> visitor, Node<T> node) {
if (preorder.containsKey(node)) {
// This can only happen if this was a non-recursive call, and a previous
// visit call had already visited node.
return;
}
preorder.put(node, counter);
stack.add(node);
preorderStack.add(counter++);
int preorderLength = preorderStack.size();
for (Node<T> succ : node.getSuccessors()) {
Integer succPreorder = preorder.get(succ);
if (succPreorder == null) {
visit(visitor, succ);
} else {
// Does succ not already belong to an SCC? If it doesn't, then it
// must be in the same SCC as node. The "starting node" of this SCC
// must have been visited before succ (or is succ itself).
if (!assigned.contains(succ)) {
while (preorderStack.get(preorderStack.size() - 1) > succPreorder) {
preorderStack.remove(preorderStack.size() - 1);
}
}
}
}
if (preorderLength == preorderStack.size()) {
// If the length of the preorderStack is unchanged, we did not find any earlier-visited
// nodes that were part of a cycle with this node. So this node is the first-visited
// element in its strongly connected component, and we collect the component.
preorderStack.remove(preorderStack.size() - 1);
Set<Node<T>> scc = new HashSet<>();
Node<T> compNode;
do {
compNode = stack.remove(stack.size() - 1);
assigned.add(compNode);
scc.add(compNode);
} while (!node.equals(compNode));
visitor.accept(scc);
}
}
}
/********************************************************************
* *
* Orders, traversals and visitors *
* *
********************************************************************/
/**
* A visitation over all the nodes in the graph that invokes
* <code>visitor.visitNode()</code> for each node in a depth-first
* post-order: each node is visited <i>after</i> each of its successors; the
* order in which edges are traversed is the order in which they were added
* to the graph. <code>visitor.visitEdge()</code> is not called.
*
* @param startNodes the set of nodes from which to begin the visitation.
*/
public void visitPostorder(GraphVisitor<T> visitor,
Iterable<Node<T>> startNodes) {
visitDepthFirst(visitor, DFS.Order.POSTORDER, false, startNodes);
}
/**
* Equivalent to {@code visitPostorder(visitor, getNodes())}.
*/
public void visitPostorder(GraphVisitor<T> visitor) {
visitPostorder(visitor, nodes.values());
}
/**
* A visitation over all the nodes in the graph that invokes
* <code>visitor.visitNode()</code> for each node in a depth-first
* pre-order: each node is visited <i>before</i> each of its successors; the
* order in which edges are traversed is the order in which they were added
* to the graph. <code>visitor.visitEdge()</code> is not called.
*
* @param startNodes the set of nodes from which to begin the visitation.
*/
public void visitPreorder(GraphVisitor<T> visitor,
Iterable<Node<T>> startNodes) {
visitDepthFirst(visitor, DFS.Order.PREORDER, false, startNodes);
}
/**
* Equivalent to {@code visitPreorder(visitor, getNodes())}.
*/
public void visitPreorder(GraphVisitor<T> visitor) {
visitPreorder(visitor, nodes.values());
}
/**
* A visitation over all the nodes in the graph in depth-first order. See
* DFS constructor for meaning of 'order' and 'transpose' parameters.
*
* @param startNodes the set of nodes from which to begin the visitation.
*/
public void visitDepthFirst(GraphVisitor<T> visitor,
DFS.Order order,
boolean transpose,
Iterable<Node<T>> startNodes) {
DFS<T> visitation = new DFS<T>(order, transpose);
visitor.beginVisit();
for (Node<T> node: startNodes) {
visitation.visit(node, visitor);
}
visitor.endVisit();
}
private static <T> Comparator<Node<T>> makeNodeComparator(
final Comparator<? super T> comparator) {
return new Comparator<Node<T>>() {
@Override
public int compare(Node<T> o1, Node<T> o2) {
return comparator.compare(o1.getLabel(), o2.getLabel());
}
};
}
/**
* Given {@code unordered}, a collection of nodes and a (possibly null) {@code comparator} for
* their labels, returns a sorted collection if {@code comparator} is non-null, otherwise returns
* {@code unordered}.
*/
private static <T> Collection<Node<T>> maybeOrderCollection(
Collection<Node<T>> unordered, @Nullable final Comparator<? super T> comparator) {
if (comparator == null) {
return unordered;
}
List<Node<T>> result = new ArrayList<>(unordered);
// Do not inline this variable: a workaround for Java 7 type inference.
Comparator<Node<T>> nodeComparator = makeNodeComparator(comparator);
Collections.sort(result, nodeComparator);
return result;
}
private void visitNodesBeforeEdges(
GraphVisitor<T> visitor,
Iterable<Node<T>> startNodes,
@Nullable Comparator<? super T> comparator) {
visitor.beginVisit();
for (Node<T> fromNode: startNodes) {
visitor.visitNode(fromNode);
for (Node<T> toNode : maybeOrderCollection(fromNode.getSuccessors(), comparator)) {
visitor.visitEdge(fromNode, toNode);
}
}
visitor.endVisit();
}
/**
* A visitation over the graph that visits all nodes and edges in topological order
* such that each node is visited before any edge coming out of that node; ties among nodes are
* broken using the provided {@code comparator} if not null; edges are visited in order specified
* by the comparator, <b>not</b> topological order of the target nodes.
*/
public void visitNodesBeforeEdges(
GraphVisitor<T> visitor, @Nullable Comparator<? super T> comparator) {
visitNodesBeforeEdges(
visitor,
comparator == null ? getTopologicalOrder() : getTopologicalOrder(comparator),
comparator);
}
}