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/*
* Copyright (C) 2017 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.base.Preconditions.checkNotNull;
import com.google.common.annotations.Beta;
import com.google.common.collect.AbstractIterator;
import com.google.common.collect.ImmutableSet;
import com.google.errorprone.annotations.DoNotMock;
import java.util.ArrayDeque;
import java.util.Deque;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Set;
import org.checkerframework.checker.nullness.compatqual.NullableDecl;
/**
* An object that can traverse the nodes that are reachable from a specified (set of) start node(s)
* using a specified {@link SuccessorsFunction}.
*
* There are two entry points for creating a {@code Traverser}: {@link
* #forTree(SuccessorsFunction)} and {@link #forGraph(SuccessorsFunction)}. You should choose one
* based on your answers to the following questions:
*
*
* - Is there only one path to any node that's reachable from any start node? (If so, the graph
* to be traversed is a tree or forest even if it is a subgraph of a graph which is neither.)
*
- Are the node objects' implementations of {@code equals()}/{@code hashCode()} recursive?
*
*
* If your answers are:
*
*
* - (1) "no" and (2) "no", use {@link #forGraph(SuccessorsFunction)}.
*
- (1) "yes" and (2) "yes", use {@link #forTree(SuccessorsFunction)}.
*
- (1) "yes" and (2) "no", you can use either, but {@code forTree()} will be more efficient.
*
- (1) "no" and (2) "yes", neither will work, but if you transform your node
* objects into a non-recursive form, you can use {@code forGraph()}.
*
*
* @author Jens Nyman
* @param Node parameter type
* @since 23.1
*/
@Beta
@DoNotMock(
"Call forGraph or forTree, passing a lambda or a Graph with the desired edges (built with"
+ " GraphBuilder)")
public abstract class Traverser {
private final SuccessorsFunction successorFunction;
private Traverser(SuccessorsFunction successorFunction) {
this.successorFunction = checkNotNull(successorFunction);
}
/**
* Creates a new traverser for the given general {@code graph}.
*
* Traversers created using this method are guaranteed to visit each node reachable from the
* start node(s) at most once.
*
*
If you know that no node in {@code graph} is reachable by more than one path from the start
* node(s), consider using {@link #forTree(SuccessorsFunction)} instead.
*
*
Performance notes
*
*
* - Traversals require O(n) time (where n is the number of nodes reachable from
* the start node), assuming that the node objects have O(1) {@code equals()} and
* {@code hashCode()} implementations. (See the
* notes on element objects for more information.)
*
- While traversing, the traverser will use O(n) space (where n is the number
* of nodes that have thus far been visited), plus O(H) space (where H is the
* number of nodes that have been seen but not yet visited, that is, the "horizon").
*
*
* @param graph {@link SuccessorsFunction} representing a general graph that may have cycles.
*/
public static Traverser forGraph(final SuccessorsFunction graph) {
return new Traverser(graph) {
@Override
Traversal newTraversal() {
return Traversal.inGraph(graph);
}
};
}
/**
* Creates a new traverser for a directed acyclic graph that has at most one path from the start
* node(s) to any node reachable from the start node(s), and has no paths from any start node to
* any other start node, such as a tree or forest.
*
* {@code forTree()} is especially useful (versus {@code forGraph()}) in cases where the data
* structure being traversed is, in addition to being a tree/forest, also defined recursively.
* This is because the {@code forTree()}-based implementations don't keep track of visited nodes,
* and therefore don't need to call `equals()` or `hashCode()` on the node objects; this saves
* both time and space versus traversing the same graph using {@code forGraph()}.
*
*
Providing a graph to be traversed for which there is more than one path from the start
* node(s) to any node may lead to:
*
*
* - Traversal not terminating (if the graph has cycles)
*
- Nodes being visited multiple times (if multiple paths exist from any start node to any
* node reachable from any start node)
*
*
* Performance notes
*
*
* - Traversals require O(n) time (where n is the number of nodes reachable from
* the start node).
*
- While traversing, the traverser will use O(H) space (where H is the number
* of nodes that have been seen but not yet visited, that is, the "horizon").
*
*
* Examples (all edges are directed facing downwards)
*
*
The graph below would be valid input with start nodes of {@code a, f, c}. However, if {@code
* b} were also a start node, then there would be multiple paths to reach {@code e} and
* {@code h}.
*
*
{@code
* a b c
* / \ / \ |
* / \ / \ |
* d e f g
* |
* |
* h
* }
*
* .
*
*
The graph below would be a valid input with start nodes of {@code a, f}. However, if {@code
* b} were a start node, there would be multiple paths to {@code f}.
*
*
{@code
* a b
* / \ / \
* / \ / \
* c d e
* \ /
* \ /
* f
* }
*
* Note on binary trees
*
*
This method can be used to traverse over a binary tree. Given methods {@code
* leftChild(node)} and {@code rightChild(node)}, this method can be called as
*
*
{@code
* Traverser.forTree(node -> ImmutableList.of(leftChild(node), rightChild(node)));
* }
*
* @param tree {@link SuccessorsFunction} representing a directed acyclic graph that has at most
* one path between any two nodes
*/
public static Traverser forTree(final SuccessorsFunction tree) {
if (tree instanceof BaseGraph) {
checkArgument(((BaseGraph) tree).isDirected(), "Undirected graphs can never be trees.");
}
if (tree instanceof Network) {
checkArgument(((Network) tree).isDirected(), "Undirected networks can never be trees.");
}
return new Traverser(tree) {
@Override
Traversal newTraversal() {
return Traversal.inTree(tree);
}
};
}
/**
* Returns an unmodifiable {@code Iterable} over the nodes reachable from {@code startNode}, in
* the order of a breadth-first traversal. That is, all the nodes of depth 0 are returned, then
* depth 1, then 2, and so on.
*
* Example: The following graph with {@code startNode} {@code a} would return nodes in
* the order {@code abcdef} (assuming successors are returned in alphabetical order).
*
*
{@code
* b ---- a ---- d
* | |
* | |
* e ---- c ---- f
* }
*
* The behavior of this method is undefined if the nodes, or the topology of the graph, change
* while iteration is in progress.
*
*
The returned {@code Iterable} can be iterated over multiple times. Every iterator will
* compute its next element on the fly. It is thus possible to limit the traversal to a certain
* number of nodes as follows:
*
*
{@code
* Iterables.limit(Traverser.forGraph(graph).breadthFirst(node), maxNumberOfNodes);
* }
*
* See Wikipedia for more
* info.
*
* @throws IllegalArgumentException if {@code startNode} is not an element of the graph
*/
public final Iterable breadthFirst(N startNode) {
return breadthFirst(ImmutableSet.of(startNode));
}
/**
* Returns an unmodifiable {@code Iterable} over the nodes reachable from any of the {@code
* startNodes}, in the order of a breadth-first traversal. This is equivalent to a breadth-first
* traversal of a graph with an additional root node whose successors are the listed {@code
* startNodes}.
*
* @throws IllegalArgumentException if any of {@code startNodes} is not an element of the graph
* @see #breadthFirst(Object)
* @since 24.1
*/
public final Iterable breadthFirst(Iterable startNodes) {
final ImmutableSet validated = validate(startNodes);
return new Iterable() {
@Override
public Iterator iterator() {
return newTraversal().breadthFirst(validated.iterator());
}
};
}
/**
* Returns an unmodifiable {@code Iterable} over the nodes reachable from {@code startNode}, in
* the order of a depth-first pre-order traversal. "Pre-order" implies that nodes appear in the
* {@code Iterable} in the order in which they are first visited.
*
* Example: The following graph with {@code startNode} {@code a} would return nodes in
* the order {@code abecfd} (assuming successors are returned in alphabetical order).
*
*
{@code
* b ---- a ---- d
* | |
* | |
* e ---- c ---- f
* }
*
* The behavior of this method is undefined if the nodes, or the topology of the graph, change
* while iteration is in progress.
*
*
The returned {@code Iterable} can be iterated over multiple times. Every iterator will
* compute its next element on the fly. It is thus possible to limit the traversal to a certain
* number of nodes as follows:
*
*
{@code
* Iterables.limit(
* Traverser.forGraph(graph).depthFirstPreOrder(node), maxNumberOfNodes);
* }
*
* See Wikipedia for more info.
*
* @throws IllegalArgumentException if {@code startNode} is not an element of the graph
*/
public final Iterable depthFirstPreOrder(N startNode) {
return depthFirstPreOrder(ImmutableSet.of(startNode));
}
/**
* Returns an unmodifiable {@code Iterable} over the nodes reachable from any of the {@code
* startNodes}, in the order of a depth-first pre-order traversal. This is equivalent to a
* depth-first pre-order traversal of a graph with an additional root node whose successors are
* the listed {@code startNodes}.
*
* @throws IllegalArgumentException if any of {@code startNodes} is not an element of the graph
* @see #depthFirstPreOrder(Object)
* @since 24.1
*/
public final Iterable depthFirstPreOrder(Iterable startNodes) {
final ImmutableSet validated = validate(startNodes);
return new Iterable() {
@Override
public Iterator iterator() {
return newTraversal().preOrder(validated.iterator());
}
};
}
/**
* Returns an unmodifiable {@code Iterable} over the nodes reachable from {@code startNode}, in
* the order of a depth-first post-order traversal. "Post-order" implies that nodes appear in the
* {@code Iterable} in the order in which they are visited for the last time.
*
* Example: The following graph with {@code startNode} {@code a} would return nodes in
* the order {@code fcebda} (assuming successors are returned in alphabetical order).
*
*
{@code
* b ---- a ---- d
* | |
* | |
* e ---- c ---- f
* }
*
* The behavior of this method is undefined if the nodes, or the topology of the graph, change
* while iteration is in progress.
*
*
The returned {@code Iterable} can be iterated over multiple times. Every iterator will
* compute its next element on the fly. It is thus possible to limit the traversal to a certain
* number of nodes as follows:
*
*
{@code
* Iterables.limit(
* Traverser.forGraph(graph).depthFirstPostOrder(node), maxNumberOfNodes);
* }
*
* See Wikipedia for more info.
*
* @throws IllegalArgumentException if {@code startNode} is not an element of the graph
*/
public final Iterable depthFirstPostOrder(N startNode) {
return depthFirstPostOrder(ImmutableSet.of(startNode));
}
/**
* Returns an unmodifiable {@code Iterable} over the nodes reachable from any of the {@code
* startNodes}, in the order of a depth-first post-order traversal. This is equivalent to a
* depth-first post-order traversal of a graph with an additional root node whose successors are
* the listed {@code startNodes}.
*
* @throws IllegalArgumentException if any of {@code startNodes} is not an element of the graph
* @see #depthFirstPostOrder(Object)
* @since 24.1
*/
public final Iterable depthFirstPostOrder(Iterable startNodes) {
final ImmutableSet validated = validate(startNodes);
return new Iterable() {
@Override
public Iterator iterator() {
return newTraversal().postOrder(validated.iterator());
}
};
}
abstract Traversal newTraversal();
@SuppressWarnings("CheckReturnValue")
private ImmutableSet validate(Iterable startNodes) {
ImmutableSet copy = ImmutableSet.copyOf(startNodes);
for (N node : copy) {
successorFunction.successors(node); // Will throw if node doesn't exist
}
return copy;
}
/**
* Abstracts away the difference between traversing a graph vs. a tree. For a tree, we just take
* the next element from the next non-empty iterator; for graph, we need to loop through the next
* non-empty iterator to find first unvisited node.
*/
private abstract static class Traversal {
final SuccessorsFunction successorFunction;
Traversal(SuccessorsFunction successorFunction) {
this.successorFunction = successorFunction;
}
static Traversal inGraph(SuccessorsFunction graph) {
final Set visited = new HashSet<>();
return new Traversal(graph) {
@Override
N visitNext(Deque> horizon) {
Iterator top = horizon.getFirst();
while (top.hasNext()) {
N element = checkNotNull(top.next());
if (visited.add(element)) {
return element;
}
}
horizon.removeFirst();
return null;
}
};
}
static Traversal inTree(SuccessorsFunction tree) {
return new Traversal(tree) {
@Override
N visitNext(Deque> horizon) {
Iterator top = horizon.getFirst();
if (top.hasNext()) {
return checkNotNull(top.next());
}
horizon.removeFirst();
return null;
}
};
}
final Iterator breadthFirst(Iterator startNodes) {
return topDown(startNodes, InsertionOrder.BACK);
}
final Iterator preOrder(Iterator startNodes) {
return topDown(startNodes, InsertionOrder.FRONT);
}
/**
* In top-down traversal, an ancestor node is always traversed before any of its descendant
* nodes. The traversal order among descendant nodes (particularly aunts and nieces) are
* determined by the {@code InsertionOrder} parameter: nieces are placed at the FRONT before
* aunts for pre-order; while in BFS they are placed at the BACK after aunts.
*/
private Iterator topDown(Iterator startNodes, final InsertionOrder order) {
final Deque> horizon = new ArrayDeque<>();
horizon.add(startNodes);
return new AbstractIterator() {
@Override
protected N computeNext() {
do {
N next = visitNext(horizon);
if (next != null) {
Iterator successors = successorFunction.successors(next).iterator();
if (successors.hasNext()) {
// BFS: horizon.addLast(successors)
// Pre-order: horizon.addFirst(successors)
order.insertInto(horizon, successors);
}
return next;
}
} while (!horizon.isEmpty());
return endOfData();
}
};
}
final Iterator postOrder(Iterator startNodes) {
final Deque ancestorStack = new ArrayDeque<>();
final Deque> horizon = new ArrayDeque<>();
horizon.add(startNodes);
return new AbstractIterator() {
@Override
protected N computeNext() {
for (N next = visitNext(horizon); next != null; next = visitNext(horizon)) {
Iterator successors = successorFunction.successors(next).iterator();
if (!successors.hasNext()) {
return next;
}
horizon.addFirst(successors);
ancestorStack.push(next);
}
return ancestorStack.isEmpty() ? endOfData() : ancestorStack.pop();
}
};
}
/**
* Visits the next node from the top iterator of {@code horizon} and returns the visited node.
* Null is returned to indicate reaching the end of the top iterator.
*
* For example, if horizon is {@code [[a, b], [c, d], [e]]}, {@code visitNext()} will return
* {@code [a, b, null, c, d, null, e, null]} sequentially, encoding the topological structure.
* (Note, however, that the callers of {@code visitNext()} often insert additional iterators
* into {@code horizon} between calls to {@code visitNext()}. This causes them to receive
* additional values interleaved with those shown above.)
*/
@NullableDecl
abstract N visitNext(Deque> horizon);
}
/** Poor man's method reference for {@code Deque::addFirst} and {@code Deque::addLast}. */
private enum InsertionOrder {
FRONT {
@Override
void insertInto(Deque deque, T value) {
deque.addFirst(value);
}
},
BACK {
@Override
void insertInto(Deque deque, T value) {
deque.addLast(value);
}
};
abstract void insertInto(Deque deque, T value);
}
}