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/*
* Copyright (C) 2014 The Guava Authors
*
* 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.common.graph;
import static com.google.common.base.Preconditions.checkArgument;
import static com.google.common.graph.GraphConstants.NODE_NOT_IN_GRAPH;
import com.google.common.annotations.Beta;
import com.google.common.base.Objects;
import com.google.common.collect.Iterables;
import com.google.common.collect.Maps;
import com.google.errorprone.annotations.CanIgnoreReturnValue;
import java.util.ArrayDeque;
import java.util.Collections;
import java.util.HashSet;
import java.util.LinkedHashSet;
import java.util.Map;
import java.util.Queue;
import java.util.Set;
import javax.annotation.Nullable;
/**
* Static utility methods for {@link Graph} and {@link Network} instances.
*
* @author James Sexton
* @author Joshua O'Madadhain
* @since 20.0
*/
@Beta
public final class Graphs {
private Graphs() {}
// Graph query methods
/**
* Returns true if {@code graph} has at least one cycle. A cycle is defined as a non-empty subset
* of edges in a graph arranged to form a path (a sequence of adjacent outgoing edges) starting
* and ending with the same node.
*
* This method will detect any non-empty cycle, including self-loops (a cycle of length 1).
*/
public static boolean hasCycle(Graph graph) {
int numEdges = graph.edges().size();
if (numEdges == 0) {
return false; // An edge-free graph is acyclic by definition.
}
if (!graph.isDirected() && numEdges >= graph.nodes().size()) {
return true; // Optimization for the undirected case: at least one cycle must exist.
}
Map visitedNodes =
Maps.newHashMapWithExpectedSize(graph.nodes().size());
for (Object node : graph.nodes()) {
if (subgraphHasCycle(graph, visitedNodes, node, null)) {
return true;
}
}
return false;
}
/**
* Returns true if {@code network} has at least one cycle. A cycle is defined as a non-empty
* subset of edges in a graph arranged to form a path (a sequence of adjacent outgoing edges)
* starting and ending with the same node.
*
* This method will detect any non-empty cycle, including self-loops (a cycle of length 1).
*/
public static boolean hasCycle(Network network) {
// In a directed graph, parallel edges cannot introduce a cycle in an acyclic graph.
// However, in an undirected graph, any parallel edge induces a cycle in the graph.
if (!network.isDirected()
&& network.allowsParallelEdges()
&& network.edges().size() > network.asGraph().edges().size()) {
return true;
}
return hasCycle(network.asGraph());
}
/**
* Performs a traversal of the nodes reachable from {@code node}. If we ever reach a node we've
* already visited (following only outgoing edges and without reusing edges), we know there's a
* cycle in the graph.
*/
private static boolean subgraphHasCycle(
Graph graph,
Map visitedNodes,
Object node,
@Nullable Object previousNode) {
NodeVisitState state = visitedNodes.get(node);
if (state == NodeVisitState.COMPLETE) {
return false;
}
if (state == NodeVisitState.PENDING) {
return true;
}
visitedNodes.put(node, NodeVisitState.PENDING);
for (Object nextNode : graph.successors(node)) {
if (canTraverseWithoutReusingEdge(graph, nextNode, previousNode)
&& subgraphHasCycle(graph, visitedNodes, nextNode, node)) {
return true;
}
}
visitedNodes.put(node, NodeVisitState.COMPLETE);
return false;
}
/**
* Determines whether an edge has already been used during traversal. In the directed case a cycle
* is always detected before reusing an edge, so no special logic is required. In the undirected
* case, we must take care not to "backtrack" over an edge (i.e. going from A to B and then going
* from B to A).
*/
private static boolean canTraverseWithoutReusingEdge(
Graph graph, Object nextNode, @Nullable Object previousNode) {
if (graph.isDirected() || !Objects.equal(previousNode, nextNode)) {
return true;
}
// This falls into the undirected A->B->A case. The Graph interface does not support parallel
// edges, so this traversal would require reusing the undirected AB edge.
return false;
}
/**
* Returns the transitive closure of {@code graph}. The transitive closure of a graph is another
* graph with an edge connecting node A to node B if node B is {@link #reachableNodes(Graph,
* Object) reachable} from node A.
*
* This is a "snapshot" based on the current topology of {@code graph}, rather than a live view
* of the transitive closure of {@code graph}. In other words, the returned {@link Graph} will not
* be updated after modifications to {@code graph}.
*/
// TODO(b/31438252): Consider potential optimizations for this algorithm.
public static Graph transitiveClosure(Graph graph) {
MutableGraph transitiveClosure = GraphBuilder.from(graph).allowsSelfLoops(true).build();
// Every node is, at a minimum, reachable from itself. Since the resulting transitive closure
// will have no isolated nodes, we can skip adding nodes explicitly and let putEdge() do it.
if (graph.isDirected()) {
// Note: works for both directed and undirected graphs, but we only use in the directed case.
for (N node : graph.nodes()) {
for (N reachableNode : reachableNodes(graph, node)) {
transitiveClosure.putEdge(node, reachableNode);
}
}
} else {
// An optimization for the undirected case: for every node B reachable from node A,
// node A and node B have the same reachability set.
Set visitedNodes = new HashSet();
for (N node : graph.nodes()) {
if (!visitedNodes.contains(node)) {
Set reachableNodes = reachableNodes(graph, node);
visitedNodes.addAll(reachableNodes);
int pairwiseMatch = 1; // start at 1 to include self-loops
for (N nodeU : reachableNodes) {
for (N nodeV : Iterables.limit(reachableNodes, pairwiseMatch++)) {
transitiveClosure.putEdge(nodeU, nodeV);
}
}
}
}
}
return transitiveClosure;
}
/**
* Returns the set of nodes that are reachable from {@code node}. Node B is defined as reachable
* from node A if there exists a path (a sequence of adjacent outgoing edges) starting at node A
* and ending at node B. Note that a node is always reachable from itself via a zero-length path.
*
* This is a "snapshot" based on the current topology of {@code graph}, rather than a live view
* of the set of nodes reachable from {@code node}. In other words, the returned {@link Set} will
* not be updated after modifications to {@code graph}.
*
* @throws IllegalArgumentException if {@code node} is not present in {@code graph}
*/
@SuppressWarnings("unchecked") // Safe because we only cast if node is an element of the graph.
public static Set reachableNodes(Graph graph, Object node) {
checkArgument(graph.nodes().contains(node), NODE_NOT_IN_GRAPH, node);
Set visitedNodes = new LinkedHashSet();
Queue queuedNodes = new ArrayDeque();
visitedNodes.add((N) node);
queuedNodes.add((N) node);
// Perform a breadth-first traversal rooted at the input node.
while (!queuedNodes.isEmpty()) {
N currentNode = queuedNodes.remove();
for (N successor : graph.successors(currentNode)) {
if (visitedNodes.add(successor)) {
queuedNodes.add(successor);
}
}
}
return Collections.unmodifiableSet(visitedNodes);
}
/**
* Returns {@code true} if {@code graphA} and {@code graphB} have the same elements and the same
* relationships between elements, as exposed via the {@link Graph} interface.
*
* Thus, two graphs A and B are equivalent if both are null or all of the following are
* true:
*
*
* - A and B have equal {@link Graph#isDirected() directedness}.
*
- A and B have equal {@link Graph#nodes() node sets}.
*
- A and B have equal {@link Graph#edges() edge sets}.
*
*
* Graph properties besides {@link Graph#isDirected() directedness} do not affect
* equivalence. For example, two graphs may be considered equivalent even if one allows self-loops
* and the other doesn't. Additionally, the order in which nodes or edges are added to the graph,
* and the order in which they are iterated over, are irrelevant.
*/
public static boolean equivalent(@Nullable Graph graphA, @Nullable Graph graphB) {
if (graphA == graphB) {
return true;
}
if (graphA == null || graphB == null) {
return false;
}
return graphA.isDirected() == graphB.isDirected()
&& graphA.nodes().equals(graphB.nodes())
&& graphA.edges().equals(graphB.edges());
}
/**
* Returns {@code true} if {@code graphA} and {@code graphB} have the same elements (including
* edge values) and the same relationships between elements, as exposed via the {@link ValueGraph}
* interface.
*
*
Thus, two value graphs A and B are equivalent if both are null or all of the
* following are true:
*
*
* - A and B have equal {@link Graph#isDirected() directedness}.
*
- A and B have equal {@link Graph#nodes() node sets}.
*
- A and B have equal {@link Graph#edges() edge sets}.
*
- Each edge in A has a {@link ValueGraph#edgeValue(Object, Object) value} equal to the {@link
* ValueGraph#edgeValue(Object, Object) value} of the corresponding edge in B.
*
*
* Graph properties besides {@link Graph#isDirected() directedness} do not affect
* equivalence. For example, two graphs may be considered equivalent even if one allows self-loops
* and the other doesn't. Additionally, the order in which nodes or edges are added to the graph,
* and the order in which they are iterated over, are irrelevant.
*/
public static boolean equivalent(
@Nullable ValueGraph graphA, @Nullable ValueGraph graphB) {
if (graphA == graphB) {
return true;
}
if (graphA == null || graphB == null) {
return false;
}
if (graphA.isDirected() != graphB.isDirected()
|| !graphA.nodes().equals(graphB.nodes())
|| !graphA.edges().equals(graphB.edges())) {
return false;
}
for (EndpointPair edge : graphA.edges()) {
if (!graphA
.edgeValue(edge.nodeU(), edge.nodeV())
.equals(graphB.edgeValue(edge.nodeU(), edge.nodeV()))) {
return false;
}
}
return true;
}
/**
* Returns {@code true} if {@code networkA} and {@code networkB} have the same elements and the
* same relationships between elements, as exposed via the {@link Network} interface.
*
*
Thus, two networks A and B are equivalent if both are null or all of the following
* are true:
*
*
* - A and B have equal {@link Network#isDirected() directedness}.
*
- A and B have equal {@link Network#nodes() node sets}.
*
- A and B have equal {@link Network#edges() edge sets}.
*
- Each edge in A connects the same nodes in the same direction (if any) as the corresponding
* edge in B.
*
*
* Network properties besides {@link Network#isDirected() directedness} do not affect
* equivalence. For example, two networks may be considered equal even if one allows parallel
* edges and the other doesn't. Additionally, the order in which nodes or edges are added to the
* network, and the order in which they are iterated over, are irrelevant.
*/
public static boolean equivalent(
@Nullable Network networkA, @Nullable Network networkB) {
if (networkA == networkB) {
return true;
}
if (networkA == null || networkB == null) {
return false;
}
if (networkA.isDirected() != networkB.isDirected()
|| !networkA.nodes().equals(networkB.nodes())
|| !networkA.edges().equals(networkB.edges())) {
return false;
}
for (Object edge : networkA.edges()) {
if (!networkA.incidentNodes(edge).equals(networkB.incidentNodes(edge))) {
return false;
}
}
return true;
}
// Graph mutation methods
// Graph view methods
/**
* Returns a view of {@code graph} with the direction (if any) of every edge reversed. All other
* properties remain intact, and further updates to {@code graph} will be reflected in the view.
*/
public static Graph transpose(Graph graph) {
if (!graph.isDirected()) {
return graph; // the transpose of an undirected graph is an identical graph
}
if (graph instanceof TransposedGraph) {
return ((TransposedGraph) graph).graph;
}
return new TransposedGraph(graph);
}
private static class TransposedGraph extends AbstractGraph {
private final Graph graph;
TransposedGraph(Graph graph) {
this.graph = graph;
}
@Override
public Set nodes() {
return graph.nodes();
}
/**
* Defer to {@link AbstractGraph#edges()} (based on {@link #successors(Object)}) for full
* edges() implementation.
*/
@Override
protected long edgeCount() {
return graph.edges().size();
}
@Override
public boolean isDirected() {
return graph.isDirected();
}
@Override
public boolean allowsSelfLoops() {
return graph.allowsSelfLoops();
}
@Override
public ElementOrder nodeOrder() {
return graph.nodeOrder();
}
@Override
public Set adjacentNodes(Object node) {
return graph.adjacentNodes(node);
}
@Override
public Set predecessors(Object node) {
return graph.successors(node); // transpose
}
@Override
public Set successors(Object node) {
return graph.predecessors(node); // transpose
}
}
/**
* Returns a view of {@code graph} with the direction (if any) of every edge reversed. All other
* properties remain intact, and further updates to {@code graph} will be reflected in the view.
*/
public static ValueGraph transpose(ValueGraph graph) {
if (!graph.isDirected()) {
return graph; // the transpose of an undirected graph is an identical graph
}
if (graph instanceof TransposedValueGraph) {
return ((TransposedValueGraph) graph).graph;
}
return new TransposedValueGraph(graph);
}
private static class TransposedValueGraph extends AbstractValueGraph {
private final ValueGraph graph;
TransposedValueGraph(ValueGraph graph) {
this.graph = graph;
}
@Override
public Set nodes() {
return graph.nodes();
}
/**
* Defer to {@link AbstractGraph#edges()} (based on {@link #successors(Object)}) for full
* edges() implementation.
*/
@Override
protected long edgeCount() {
return graph.edges().size();
}
@Override
public boolean isDirected() {
return graph.isDirected();
}
@Override
public boolean allowsSelfLoops() {
return graph.allowsSelfLoops();
}
@Override
public ElementOrder nodeOrder() {
return graph.nodeOrder();
}
@Override
public Set adjacentNodes(Object node) {
return graph.adjacentNodes(node);
}
@Override
public Set predecessors(Object node) {
return graph.successors(node); // transpose
}
@Override
public Set successors(Object node) {
return graph.predecessors(node); // transpose
}
@Override
public V edgeValue(Object nodeU, Object nodeV) {
return graph.edgeValue(nodeV, nodeU); // transpose
}
@Override
public V edgeValueOrDefault(Object nodeU, Object nodeV, @Nullable V defaultValue) {
return graph.edgeValueOrDefault(nodeV, nodeU, defaultValue); // transpose
}
}
/**
* Returns a view of {@code network} with the direction (if any) of every edge reversed. All other
* properties remain intact, and further updates to {@code network} will be reflected in the view.
*/
public static Network transpose(Network network) {
if (!network.isDirected()) {
return network; // the transpose of an undirected network is an identical network
}
if (network instanceof TransposedNetwork) {
return ((TransposedNetwork) network).network;
}
return new TransposedNetwork(network);
}
private static class TransposedNetwork extends AbstractNetwork {
private final Network network;
TransposedNetwork(Network network) {
this.network = network;
}
@Override
public Set nodes() {
return network.nodes();
}
@Override
public Set edges() {
return network.edges();
}
@Override
public boolean isDirected() {
return network.isDirected();
}
@Override
public boolean allowsParallelEdges() {
return network.allowsParallelEdges();
}
@Override
public boolean allowsSelfLoops() {
return network.allowsSelfLoops();
}
@Override
public ElementOrder nodeOrder() {
return network.nodeOrder();
}
@Override
public ElementOrder edgeOrder() {
return network.edgeOrder();
}
@Override
public Set adjacentNodes(Object node) {
return network.adjacentNodes(node);
}
@Override
public Set predecessors(Object node) {
return network.successors(node); // transpose
}
@Override
public Set successors(Object node) {
return network.predecessors(node); // transpose
}
@Override
public Set incidentEdges(Object node) {
return network.incidentEdges(node);
}
@Override
public Set inEdges(Object node) {
return network.outEdges(node); // transpose
}
@Override
public Set outEdges(Object node) {
return network.inEdges(node); // transpose
}
@Override
public EndpointPair incidentNodes(Object edge) {
EndpointPair endpointPair = network.incidentNodes(edge);
return EndpointPair.of(network, endpointPair.nodeV(), endpointPair.nodeU()); // transpose
}
@Override
public Set adjacentEdges(Object edge) {
return network.adjacentEdges(edge);
}
@Override
public Set edgesConnecting(Object nodeU, Object nodeV) {
return network.edgesConnecting(nodeV, nodeU); // transpose
}
}
// Graph copy methods
/**
* Returns the subgraph of {@code graph} induced by {@code nodes}. This subgraph is a new graph
* that contains all of the nodes in {@code nodes}, and all of the {@link Graph#edges() edges}
* from {@code graph} for which both nodes are contained by {@code nodes}.
*
* @throws IllegalArgumentException if any element in {@code nodes} is not a node in the graph
*/
public static MutableGraph inducedSubgraph(Graph graph, Iterable nodes) {
MutableGraph subgraph = GraphBuilder.from(graph).build();
for (N node : nodes) {
subgraph.addNode(node);
}
for (N node : subgraph.nodes()) {
for (N successorNode : graph.successors(node)) {
if (subgraph.nodes().contains(successorNode)) {
subgraph.putEdge(node, successorNode);
}
}
}
return subgraph;
}
/**
* Returns the subgraph of {@code graph} induced by {@code nodes}. This subgraph is a new graph
* that contains all of the nodes in {@code nodes}, and all of the {@link Graph#edges() edges}
* (and associated edge values) from {@code graph} for which both nodes are contained by {@code
* nodes}.
*
* @throws IllegalArgumentException if any element in {@code nodes} is not a node in the graph
*/
public static MutableValueGraph inducedSubgraph(
ValueGraph graph, Iterable nodes) {
MutableValueGraph subgraph = ValueGraphBuilder.from(graph).build();
for (N node : nodes) {
subgraph.addNode(node);
}
for (N node : subgraph.nodes()) {
for (N successorNode : graph.successors(node)) {
if (subgraph.nodes().contains(successorNode)) {
subgraph.putEdgeValue(node, successorNode, graph.edgeValue(node, successorNode));
}
}
}
return subgraph;
}
/**
* Returns the subgraph of {@code network} induced by {@code nodes}. This subgraph is a new graph
* that contains all of the nodes in {@code nodes}, and all of the {@link Network#edges() edges}
* from {@code network} for which the {@link Network#incidentNodes(Object) incident nodes} are
* both contained by {@code nodes}.
*
* @throws IllegalArgumentException if any element in {@code nodes} is not a node in the graph
*/
public static MutableNetwork inducedSubgraph(
Network network, Iterable nodes) {
MutableNetwork subgraph = NetworkBuilder.from(network).build();
for (N node : nodes) {
subgraph.addNode(node);
}
for (N node : subgraph.nodes()) {
for (E edge : network.outEdges(node)) {
N successorNode = network.incidentNodes(edge).adjacentNode(node);
if (subgraph.nodes().contains(successorNode)) {
subgraph.addEdge(node, successorNode, edge);
}
}
}
return subgraph;
}
/** Creates a mutable copy of {@code graph} with the same nodes and edges. */
public static MutableGraph copyOf(Graph graph) {
MutableGraph copy = GraphBuilder.from(graph).expectedNodeCount(graph.nodes().size()).build();
for (N node : graph.nodes()) {
copy.addNode(node);
}
for (EndpointPair edge : graph.edges()) {
copy.putEdge(edge.nodeU(), edge.nodeV());
}
return copy;
}
/** Creates a mutable copy of {@code graph} with the same nodes, edges, and edge values. */
public static MutableValueGraph copyOf(ValueGraph graph) {
MutableValueGraph copy =
ValueGraphBuilder.from(graph).expectedNodeCount(graph.nodes().size()).build();
for (N node : graph.nodes()) {
copy.addNode(node);
}
for (EndpointPair edge : graph.edges()) {
copy.putEdgeValue(edge.nodeU(), edge.nodeV(), graph.edgeValue(edge.nodeU(), edge.nodeV()));
}
return copy;
}
/** Creates a mutable copy of {@code network} with the same nodes and edges. */
public static MutableNetwork copyOf(Network network) {
MutableNetwork copy =
NetworkBuilder.from(network)
.expectedNodeCount(network.nodes().size())
.expectedEdgeCount(network.edges().size())
.build();
for (N node : network.nodes()) {
copy.addNode(node);
}
for (E edge : network.edges()) {
EndpointPair endpointPair = network.incidentNodes(edge);
copy.addEdge(endpointPair.nodeU(), endpointPair.nodeV(), edge);
}
return copy;
}
@CanIgnoreReturnValue
static int checkNonNegative(int value) {
checkArgument(value >= 0, "Not true that %s is non-negative.", value);
return value;
}
@CanIgnoreReturnValue
static int checkPositive(int value) {
checkArgument(value > 0, "Not true that %s is positive.", value);
return value;
}
@CanIgnoreReturnValue
static long checkNonNegative(long value) {
checkArgument(value >= 0, "Not true that %s is non-negative.", value);
return value;
}
@CanIgnoreReturnValue
static long checkPositive(long value) {
checkArgument(value > 0, "Not true that %s is positive.", value);
return value;
}
/**
* An enum representing the state of a node during DFS. {@code PENDING} means that the node is on
* the stack of the DFS, while {@code COMPLETE} means that the node and all its successors have
* been already explored. Any node that has not been explored will not have a state at all.
*/
private enum NodeVisitState {
PENDING,
COMPLETE
}
}