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A set of mathematical utilities
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/**
* Copyright (c) 2016, All partners of the iTesla project (http://www.itesla-project.eu/consortium)
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
* SPDX-License-Identifier: MPL-2.0
*/
package com.powsybl.math.graph;
import com.google.common.base.Predicates;
import com.google.common.collect.FluentIterable;
import com.powsybl.commons.PowsyblException;
import gnu.trove.list.array.TIntArrayList;
import gnu.trove.list.linked.TIntLinkedList;
import gnu.trove.set.hash.TIntHashSet;
import java.io.PrintStream;
import java.util.*;
import java.util.concurrent.CopyOnWriteArrayList;
import java.util.concurrent.locks.Lock;
import java.util.concurrent.locks.ReentrantLock;
import java.util.function.Function;
import java.util.function.Predicate;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;
/**
*
* @author Geoffroy Jamgotchian {@literal }
*/
public class UndirectedGraphImpl implements UndirectedGraph {
private static final int VERTICES_CAPACITY = 10;
private static final int EDGES_CAPACITY = 15;
private static final int NEIGHBORS_CAPACITY = 2;
private static final class Vertex {
private E object;
private Vertex() {
}
public E getObject() {
return object;
}
public void setObject(E object) {
this.object = object;
}
}
private static final class Edge {
private final int v1;
private final int v2;
private E object;
private Edge(int v1, int v2, E object) {
this.v1 = v1;
this.v2 = v2;
this.object = object;
}
public int getV1() {
return v1;
}
public int getV2() {
return v2;
}
public E getObject() {
return object;
}
public void setObject(E object) {
this.object = object;
}
@Override
public String toString() {
return object.toString();
}
}
/* vertices */
private final List> vertices = new ArrayList<>(VERTICES_CAPACITY);
/* edges */
private final List> edges = new ArrayList<>(EDGES_CAPACITY);
/* cached adjacency list */
private TIntArrayList[] adjacencyListCache;
private final Lock adjacencyListCacheLock = new ReentrantLock();
private final TIntHashSet availableVertices = new TIntHashSet();
private final TIntLinkedList removedEdges = new TIntLinkedList();
private final List> listeners = new CopyOnWriteArrayList<>();
private final int vertexLimit;
public UndirectedGraphImpl(int vertexLimit) {
if (vertexLimit < 1) {
throw new PowsyblException("Vertex limit should be positive");
}
this.vertexLimit = vertexLimit;
}
private void checkVertex(int v) {
if (v < 0 || v >= vertices.size() || vertices.get(v) == null) {
throw new PowsyblException("Vertex " + v + " not found");
}
}
private void checkEdge(int e) {
if (e < 0 || e >= edges.size() || edges.get(e) == null) {
throw new PowsyblException("Edge " + e + " not found");
}
}
public int addVertex() {
return addVertex(true);
}
@Override
public int addVertex(boolean notify) {
int v;
if (availableVertices.isEmpty()) {
v = vertices.size();
vertices.add(new Vertex<>());
} else {
v = availableVertices.iterator().next();
availableVertices.remove(v);
vertices.set(v, new Vertex<>());
}
invalidateAdjacencyList();
if (notify) {
notifyVertexAdded(v);
}
return v;
}
@Override
public void addVertexIfNotPresent(int v) {
addVertexIfNotPresent(v, true);
}
@Override
public void addVertexIfNotPresent(int v, boolean notify) {
if (v < 0) {
throw new PowsyblException("Invalid vertex " + v);
}
if (v >= this.vertexLimit) {
throw new PowsyblException("Vertex index too high: " + v + ". Limit is " + this.vertexLimit);
}
if (v < vertices.size()) {
if (availableVertices.contains(v)) {
vertices.set(v, new Vertex<>());
availableVertices.remove(v);
invalidateAdjacencyList();
if (notify) {
notifyVertexAdded(v);
}
}
} else {
for (int i = vertices.size(); i < v; i++) {
vertices.add(null);
availableVertices.add(i);
}
vertices.add(new Vertex<>());
invalidateAdjacencyList();
if (notify) {
notifyVertexAdded(v);
}
}
}
@Override
public boolean vertexExists(int v) {
if (v < 0) {
throw new PowsyblException("Invalid vertex " + v);
}
return v < vertices.size() && vertices.get(v) != null;
}
private V removeVertexInternal(int v, boolean notify) {
V obj = vertices.get(v).getObject();
if (v == vertices.size() - 1) {
vertices.remove(v);
cleanVertices(v - 1);
} else {
vertices.set(v, null);
availableVertices.add(v);
}
if (notify) {
notifyVertexRemoved(v, obj);
}
return obj;
}
@Override
public V removeVertex(int v) {
return removeVertex(v, true);
}
@Override
public V removeVertex(int v, boolean notify) {
checkVertex(v);
for (Edge e : edges) {
if (e != null && (e.getV1() == v || e.getV2() == v)) {
throw new PowsyblException("An edge is connected to vertex " + v);
}
}
V obj = removeVertexInternal(v, notify);
invalidateAdjacencyList();
return obj;
}
private void cleanVertices(int v) {
for (int i = v; i >= 0; i--) {
if (!availableVertices.contains(i)) {
return;
}
availableVertices.remove(i);
vertices.remove(i);
}
}
@Override
public int getVertexCount() {
return vertices.size() - availableVertices.size();
}
@Override
public void removeAllVertices() {
removeAllVertices(true);
}
@Override
public void removeAllVertices(boolean notify) {
if (!edges.isEmpty()) {
throw new PowsyblException("Cannot remove all vertices because there is still some edges in the graph");
}
vertices.clear();
availableVertices.clear();
invalidateAdjacencyList();
if (notify) {
notifyAllVerticesRemoved();
}
}
@Override
public int addEdge(int v1, int v2, E obj) {
return addEdge(v1, v2, obj, true);
}
@Override
public int addEdge(int v1, int v2, E obj, boolean notify) {
checkVertex(v1);
checkVertex(v2);
int e;
Edge edge = new Edge<>(v1, v2, obj);
if (removedEdges.isEmpty()) {
e = edges.size();
edges.add(edge);
} else {
e = removedEdges.removeAt(0);
edges.set(e, edge);
}
invalidateAdjacencyList();
if (notify) {
notifyEdgeAdded(e, obj);
}
return e;
}
private E removeEdgeInternal(int e, boolean notify) {
E obj = edges.get(e).getObject();
if (notify) {
notifyEdgeBeforeRemoval(e, obj);
}
if (e == edges.size() - 1) {
edges.remove(e);
} else {
edges.set(e, null);
removedEdges.add(e);
}
if (notify) {
notifyEdgeRemoved(e, obj);
}
return obj;
}
@Override
public E removeEdge(int e) {
return removeEdge(e, true);
}
@Override
public E removeEdge(int e, boolean notify) {
checkEdge(e);
E obj = removeEdgeInternal(e, notify);
invalidateAdjacencyList();
return obj;
}
@Override
public void removeAllEdges() {
removeAllEdges(true);
}
@Override
public void removeAllEdges(boolean notify) {
Collection allEdges = edges.stream().filter(Objects::nonNull).map(Edge::getObject).collect(Collectors.toList());
if (notify) {
notifyAllEdgesBeforeRemoval(allEdges);
}
edges.clear();
removedEdges.clear();
invalidateAdjacencyList();
if (notify) {
notifyAllEdgesRemoved(allEdges);
}
}
@Override
public int getEdgeCount() {
return edges.size() - removedEdges.size();
}
@Override
public int[] getVertices() {
TIntArrayList t = new TIntArrayList(vertices.size());
for (int i = 0; i < vertices.size(); i++) {
if (vertices.get(i) != null) {
t.add(i);
}
}
return t.toArray();
}
@Override
public int[] getEdges() {
TIntArrayList t = new TIntArrayList(getEdgeCount());
for (int e = 0; e < edges.size(); e++) {
if (edges.get(e) != null) {
t.add(e);
}
}
return t.toArray();
}
@Override
public int getVertexCapacity() {
return vertices.size();
}
@Override
public Iterable getVerticesObj() {
return FluentIterable.from(vertices)
.filter(Predicates.notNull())
.transform(Vertex::getObject);
}
@Override
public Stream getVertexObjectStream() {
return vertices.stream().filter(Objects::nonNull).map(Vertex::getObject);
}
@Override
public V getVertexObject(int v) {
checkVertex(v);
return vertices.get(v).getObject();
}
@Override
public void setVertexObject(int v, V obj) {
setVertexObject(v, obj, true);
}
@Override
public void setVertexObject(int v, V obj, boolean notify) {
checkVertex(v);
vertices.get(v).setObject(obj);
if (notify) {
notifyVertexObjectSet(v, obj);
}
}
@Override
public int getEdgeVertex1(int e) {
checkEdge(e);
return edges.get(e).getV1();
}
@Override
public List getEdgeObjectsConnectedToVertex(int v) {
return getEdgeObjectConnectedToVertexStream(v).collect(Collectors.toList());
}
@Override
public Stream getEdgeObjectConnectedToVertexStream(int v) {
return getEdgeConnectedToVertexStream(v).mapToObj(this::getEdgeObject);
}
@Override
public List getEdgesConnectedToVertex(int v) {
return getEdgeConnectedToVertexStream(v).boxed().collect(Collectors.toList());
}
@Override
public IntStream getEdgeConnectedToVertexStream(int v) {
checkVertex(v);
TIntArrayList[] adjacencyList = getAdjacencyList();
TIntArrayList adjacentEdges = adjacencyList[v];
return IntStream.range(0, adjacentEdges.size()).map(adjacentEdges::getQuick);
}
@Override
public int getEdgeVertex2(int e) {
checkEdge(e);
return edges.get(e).getV2();
}
@Override
public Iterable getEdgesObject() {
return FluentIterable.from(edges)
.filter(Predicates.notNull())
.transform(Edge::getObject);
}
@Override
public Stream getEdgeObjectStream() {
return edges.stream().filter(Objects::nonNull).map(Edge::getObject);
}
@Override
public E getEdgeObject(int e) {
checkEdge(e);
return edges.get(e).getObject();
}
@Override
public List getEdgeObjects(int v1, int v2) {
checkVertex(v1);
checkVertex(v2);
List edgeObjects = new ArrayList<>(1);
TIntArrayList[] adjacencyList = getAdjacencyList();
TIntArrayList adjacentEdges = adjacencyList[v1];
for (int i = 0; i < adjacentEdges.size(); i++) {
int e = adjacentEdges.getQuick(i);
Edge edge = edges.get(e);
if (edge.getV1() == v1 && edge.getV2() == v2
|| edge.getV1() == v2 && edge.getV2() == v1) {
edgeObjects.add(edge.getObject());
}
}
return edgeObjects;
}
/**
* Create the adjacency list of this graph.
* @return the adjacency list as a {@link TIntArrayList} of {@link TIntArrayList}.
*/
private TIntArrayList[] getAdjacencyList() {
adjacencyListCacheLock.lock();
try {
if (adjacencyListCache == null) {
adjacencyListCache = new TIntArrayList[vertices.size()];
for (int v = 0; v < vertices.size(); v++) {
Vertex vertex = vertices.get(v);
if (vertex != null) {
adjacencyListCache[v] = new TIntArrayList(NEIGHBORS_CAPACITY);
}
}
for (int e = 0; e < edges.size(); e++) {
Edge edge = edges.get(e);
if (edge != null) {
int v1 = edge.getV1();
int v2 = edge.getV2();
adjacencyListCache[v1].add(e);
adjacencyListCache[v2].add(e);
}
}
}
return adjacencyListCache;
} finally {
adjacencyListCacheLock.unlock();
}
}
/**
* Invalidate the adjacency list.
*/
private void invalidateAdjacencyList() {
adjacencyListCache = null;
}
private void traverseVertex(int vToTraverse, boolean[] vEncountered, Deque edgesToTraverse,
TIntArrayList[] adjacencyList, TraversalType traversalType) {
if (vEncountered[vToTraverse]) {
return;
}
vEncountered[vToTraverse] = true;
TIntArrayList adjacentEdges = adjacencyList[vToTraverse];
for (int i = 0; i < adjacentEdges.size(); i++) {
// For depth-first traversal, we're going to poll the last element added in the deque. Hence, edges have to
// be added in reverse order, otherwise the depth-first traversal will be "on the right side" instead of
// "on the left side" of the tree. That is, it would always go deeper taking with last neighbour of visited vertex.
int iEdge = switch (traversalType) {
case DEPTH_FIRST -> adjacentEdges.size() - i - 1;
case BREADTH_FIRST -> i;
};
int adjacentEdgeIndex = adjacentEdges.getQuick(iEdge);
boolean flippedEdge = edges.get(adjacentEdgeIndex).v1 != vToTraverse;
edgesToTraverse.add(new DirectedEdge(adjacentEdgeIndex, flippedEdge));
}
}
/**
* Record to store which edge has to be traversed and in which direction
* @param index index of the edge within the edges list
* @param flippedDirection if true, edge.getNode2() has already been visited, otherwise it's edge.getNode1()
*/
private record DirectedEdge(int index, boolean flippedDirection) {
}
@Override
public boolean traverse(int v, TraversalType traversalType, Traverser traverser, boolean[] encounteredVertices) {
checkVertex(v);
Objects.requireNonNull(traverser);
Objects.requireNonNull(encounteredVertices);
if (encounteredVertices.length < vertices.size()) {
throw new PowsyblException("Encountered array is too small");
}
boolean[] encounteredEdges = new boolean[edges.size()];
TIntArrayList[] adjacencyList = getAdjacencyList();
boolean keepGoing = true;
Deque edgesToTraverse = new ArrayDeque<>();
traverseVertex(v, encounteredVertices, edgesToTraverse, adjacencyList, traversalType);
while (!edgesToTraverse.isEmpty() && keepGoing) {
DirectedEdge directedEdge = switch (traversalType) {
case DEPTH_FIRST -> edgesToTraverse.pollLast();
case BREADTH_FIRST -> edgesToTraverse.pollFirst();
};
if (!encounteredEdges[directedEdge.index]) {
encounteredEdges[directedEdge.index] = true;
Edge edge = edges.get(directedEdge.index);
int vOrigin = directedEdge.flippedDirection ? edge.getV2() : edge.getV1();
int vDest = directedEdge.flippedDirection ? edge.getV1() : edge.getV2();
TraverseResult traverserResult = traverser.traverse(vOrigin, directedEdge.index, vDest);
switch (traverserResult) {
case CONTINUE -> traverseVertex(vDest, encounteredVertices, edgesToTraverse, adjacencyList, traversalType);
case TERMINATE_TRAVERSER -> keepGoing = false; // the whole traversing needs to stop
case TERMINATE_PATH -> {
// Path ends on edge e before reaching vDest, continuing with next edge in the deque
}
}
}
}
return keepGoing;
}
@Override
public boolean traverse(int v, TraversalType traversalType, Traverser traverser) {
boolean[] encountered = new boolean[vertices.size()];
Arrays.fill(encountered, false);
return traverse(v, traversalType, traverser, encountered);
}
@Override
public boolean traverse(int[] startingVertices, TraversalType traversalType, Traverser traverser) {
boolean[] encountered = new boolean[vertices.size()];
Arrays.fill(encountered, false);
for (int startingVertex : startingVertices) {
if (!encountered[startingVertex] && !traverse(startingVertex, traversalType, traverser, encountered)) {
return false;
}
}
return true;
}
/**
* {@inheritDoc}
*
* This method allocates a {@link List} of {@link TIntArrayList} to store the paths, a {@link BitSet} to store the encountered vertices
* and calls {@link #findAllPaths(int, Predicate, Predicate, TIntArrayList, BitSet, List)}.
*
* In the output, the paths are sorted by size considering the number of switches in each path.
*/
@Override
public List findAllPaths(int from, Predicate pathComplete, Predicate pathCancelled) {
return findAllPaths(from, pathComplete, pathCancelled, Comparator.comparing(TIntArrayList::size));
}
/**
* {@inheritDoc}
*
* This method allocates a {@link List} of {@link TIntArrayList} to store the paths, a {@link BitSet} to store the encountered vertices
* and calls {@link #findAllPaths(int, Predicate, Predicate, TIntArrayList, BitSet, List)}.
* In the output, the paths are sorted by using the given comparator.
*
*/
public List findAllPaths(int from, Predicate pathComplete, Predicate pathCancelled, Comparator comparator) {
Objects.requireNonNull(pathComplete);
List paths = new ArrayList<>();
BitSet encountered = new BitSet(vertices.size());
TIntArrayList path = new TIntArrayList(1);
findAllPaths(from, pathComplete, pathCancelled, path, encountered, paths);
// sort paths by size according to the given comparator
paths.sort(comparator);
return paths;
}
/**
* This method is called by {@link #findAllPaths(int, Predicate, Predicate, TIntArrayList, BitSet, List)} each time a vertex is traversed.
* The path is added to the paths list if it's complete, otherwise this method calls the {@link #findAllPaths(int, Predicate, Predicate, TIntArrayList, BitSet, List)}
* to continue the recursion.
*
* @param e the index of the current edge.
* @param v1or2 the index of the current vertex.
* @param pathComplete a function that returns true when the target vertex is found.
* @param pathCancelled pathCanceled a function that returns true when the edge must not be traversed.
* @param path a list that contains the traversed edges.
* @param encountered a BitSet that contains the traversed vertex.
* @param paths a list that contains the complete paths.
* @return true if the path is complete, false otherwise.
*/
private boolean findAllPaths(int e, int v1or2, Predicate pathComplete, Predicate pathCancelled,
TIntArrayList path, BitSet encountered, List paths) {
if (encountered.get(v1or2)) {
return false;
}
Vertex obj1or2 = vertices.get(v1or2);
path.add(e);
if (Boolean.TRUE.equals(pathComplete.test(obj1or2.getObject()))) {
paths.add(path);
return true;
} else {
findAllPaths(v1or2, pathComplete, pathCancelled, path, encountered, paths);
return false;
}
}
/**
* This method is called by {@link #findAllPaths(int, Predicate, Predicate)} or {@link #findAllPaths(int, int, Predicate, Predicate, TIntArrayList, BitSet, List)}.
* For each adjacent edges for which the pathCanceled returns {@literal false}, traverse the other vertex calling {@link #findAllPaths(int, int, Predicate, Predicate, TIntArrayList, BitSet, List)}.
*
* @param v the current vertex
* @param pathComplete a function that returns true when the target vertex is found.
* @param pathCancelled a function that returns true when the edge must not be traversed.
* @param path a list that contains the traversed edges.
* @param encountered a BitSet that contains the traversed vertex.
* @param paths a list that contains the complete paths.
*/
private void findAllPaths(int v, Predicate pathComplete, Predicate pathCancelled,
TIntArrayList path, BitSet encountered, List paths) {
checkVertex(v);
encountered.set(v, true);
TIntArrayList[] adjacencyList = getAdjacencyList();
TIntArrayList adjacentEdges = adjacencyList[v];
for (int i = 0; i < adjacentEdges.size(); i++) {
int e = adjacentEdges.getQuick(i);
Edge edge = edges.get(e);
if (pathCancelled != null && pathCancelled.test(edge.getObject())) {
continue;
}
int v1 = edge.getV1();
int v2 = edge.getV2();
TIntArrayList path2;
BitSet encountered2;
if (i < adjacentEdges.size() - 1) {
path2 = new TIntArrayList(path);
encountered2 = new BitSet(vertices.size());
encountered2.or(encountered);
} else {
path2 = path;
encountered2 = encountered;
}
if (v == v2) {
findAllPaths(e, v1, pathComplete, pathCancelled, path2, encountered2, paths);
} else if (v == v1) {
findAllPaths(e, v2, pathComplete, pathCancelled, path2, encountered2, paths);
} else {
throw new IllegalStateException();
}
}
}
@Override
public void addListener(UndirectedGraphListener l) {
listeners.add(l);
}
@Override
public void removeListener(UndirectedGraphListener l) {
listeners.remove(l);
}
private void notifyVertexAdded(int v) {
for (UndirectedGraphListener l : listeners) {
l.vertexAdded(v);
}
}
private void notifyVertexObjectSet(int v, V obj) {
for (UndirectedGraphListener l : listeners) {
l.vertexObjectSet(v, obj);
}
}
private void notifyVertexRemoved(int v, V obj) {
for (UndirectedGraphListener l : listeners) {
l.vertexRemoved(v, obj);
}
}
private void notifyAllVerticesRemoved() {
for (UndirectedGraphListener l : listeners) {
l.allVerticesRemoved();
}
}
private void notifyEdgeAdded(int e, E obj) {
for (UndirectedGraphListener l : listeners) {
l.edgeAdded(e, obj);
}
}
private void notifyEdgeRemoved(int e, E obj) {
for (UndirectedGraphListener l : listeners) {
l.edgeRemoved(e, obj);
}
}
private void notifyEdgeBeforeRemoval(int e, E obj) {
for (UndirectedGraphListener l : listeners) {
l.edgeBeforeRemoval(e, obj);
}
}
private void notifyAllEdgesBeforeRemoval(Collection obj) {
for (UndirectedGraphListener l : listeners) {
l.allEdgesBeforeRemoval(obj);
}
}
private void notifyAllEdgesRemoved(Collection obj) {
for (UndirectedGraphListener l : listeners) {
l.allEdgesRemoved(obj);
}
}
@Override
public void print(PrintStream out, Function vertexToString, Function edgeToString) {
out.append("Vertices:").append(System.lineSeparator());
for (int v = 0; v < vertices.size(); v++) {
Vertex vertex = vertices.get(v);
if (vertex != null) {
String str = vertexToString == null ? Objects.toString(vertex.getObject()) : vertexToString.apply(vertex.getObject());
out.append(Integer.toString(v)).append(": ")
.append(str)
.append(System.lineSeparator());
}
}
out.append("Edges:").append(System.lineSeparator());
for (int e = 0; e < edges.size(); e++) {
Edge edge = edges.get(e);
if (edge != null) {
String str = edgeToString == null ? Objects.toString(edge.getObject()) : edgeToString.apply(edge.getObject());
out.append(Integer.toString(e)).append(": ")
.append(Integer.toString(edge.getV1())).append("<->")
.append(Integer.toString(edge.getV2())).append(" ")
.append(str).append(System.lineSeparator());
}
}
}
private void removeIsolatedVertices(int v, TIntArrayList[] adjacencyList, boolean notify) {
Vertex vertex = vertices.get(v);
if (vertex != null && vertex.getObject() == null) {
TIntArrayList adjacentEdges = adjacencyList[v];
if (adjacentEdges.isEmpty()) {
removeVertexInternal(v, notify);
adjacencyList[v] = null;
if (!adjacentEdges.isEmpty()) {
int e = adjacentEdges.getQuick(0);
removeDanglingEdgeAndPropagate(e, v, adjacencyList, notify);
}
}
}
}
private void removeDanglingEdgeAndPropagate(int edgeToRemove, int vFrom, TIntArrayList[] adjacencyList, boolean notify) {
Edge edge = edges.get(edgeToRemove);
int v1 = edge.getV1();
int v2 = edge.getV2();
int vTo = v1 == vFrom ? v2 : v1;
// updating adjacency list of vFrom & vTo is not done here, as:
// - vFrom adjacency list has been set to null when vertex vFrom has been removed
// - vTo adjacency list is updated hereafter
removeEdgeInternal(edgeToRemove, notify);
Vertex vertex = vertices.get(vTo);
TIntArrayList adjacentEdges = adjacencyList[vTo];
if (vertex == null || vertex.getObject() != null || adjacentEdges.size() > 2) {
// propagation stops: update adjacency list of vertex
adjacentEdges.remove(edgeToRemove);
return;
}
// propagate: we know that one of the neighbours (vFrom) of this vertex has been removed, hence:
// - if only one adjacent edge, this is a newly isolated vertex
// - if only two adjacent edges, this is a newly dangling vertex
removeVertexInternal(vTo, notify);
adjacencyList[vTo] = null;
// find the other edge to remove if dangling vertex
if (adjacentEdges.size() == 2) {
int otherEdgeToRemove = adjacentEdges.getQuick(0) == edgeToRemove
? adjacentEdges.getQuick(1)
: adjacentEdges.getQuick(0);
removeDanglingEdgeAndPropagate(otherEdgeToRemove, vTo, adjacencyList, notify);
}
}
@Override
public void removeIsolatedVertices() {
removeIsolatedVertices(true);
}
@Override
public void removeIsolatedVertices(boolean notify) {
TIntArrayList[] adjacencyList = getAdjacencyList();
for (int v = 0; v < vertices.size(); v++) {
removeIsolatedVertices(v, adjacencyList, notify);
}
}
}
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