/*******************************************************************************
* Copyright (c) 2004, 2016 IBM Corporation and others.
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License v1.0
* which accompanies this distribution, and is available at
* http://www.eclipse.org/legal/epl-v10.html
*
* Contributors:
* IBM Corporation - initial API and implementation
*******************************************************************************/
package org.eclipse.osgi.internal.container;
import java.util.*;
/**
* Borrowed from org.eclipse.core.internal.resources.ComputeProjectOrder
* to be used when computing the stop order.
* Implementation of a sort algorithm for computing the node order. This
* algorithm handles cycles in the node reference graph in a reasonable way.
*
* @since 3.0
*/
public class ComputeNodeOrder {
/*
* Prevent class from being instantiated.
*/
private ComputeNodeOrder() {
// not allowed
}
/**
* A directed graph. Once the vertexes and edges of the graph have been
* defined, the graph can be queried for the depth-first finish time of each
* vertex.
* <p>
* Ref: Cormen, Leiserson, and Rivest <it>Introduction to Algorithms</it>,
* McGraw-Hill, 1990. The depth-first search algorithm is in section 23.3.
* </p>
*/
private static class Digraph {
/**
* struct-like object for representing a vertex along with various
* values computed during depth-first search (DFS).
*/
public static class Vertex {
/**
* White is for marking vertexes as unvisited.
*/
public static final String WHITE = "white"; //$NON-NLS-1$
/**
* Grey is for marking vertexes as discovered but visit not yet
* finished.
*/
public static final String GREY = "grey"; //$NON-NLS-1$
/**
* Black is for marking vertexes as visited.
*/
public static final String BLACK = "black"; //$NON-NLS-1$
/**
* Color of the vertex. One of <code>WHITE</code> (unvisited),
* <code>GREY</code> (visit in progress), or <code>BLACK</code>
* (visit finished). <code>WHITE</code> initially.
*/
public String color = WHITE;
/**
* The DFS predecessor vertex, or <code>null</code> if there is no
* predecessor. <code>null</code> initially.
*/
public Vertex predecessor = null;
/**
* Timestamp indicating when the vertex was finished (became BLACK)
* in the DFS. Finish times are between 1 and the number of
* vertexes.
*/
public int finishTime;
/**
* The id of this vertex.
*/
public Object id;
/**
* Ordered list of adjacent vertexes. In other words, "this" is the
* "from" vertex and the elements of this list are all "to"
* vertexes.
*
* Element type: <code>Vertex</code>
*/
public List<Vertex> adjacent = new ArrayList<>(3);
/**
* Creates a new vertex with the given id.
*
* @param id the vertex id
*/
public Vertex(Object id) {
this.id = id;
}
}
/**
* Ordered list of all vertexes in this graph.
*
* Element type: <code>Vertex</code>
*/
private List<Vertex> vertexList = new ArrayList<>(100);
/**
* Map from id to vertex.
*
* Key type: <code>Object</code>; value type: <code>Vertex</code>
*/
private Map<Object, Vertex> vertexMap = new HashMap<>(100);
/**
* DFS visit time. Non-negative.
*/
private int time;
/**
* Indicates whether the graph has been initialized. Initially
* <code>false</code>.
*/
private boolean initialized = false;
/**
* Indicates whether the graph contains cycles. Initially
* <code>false</code>.
*/
private boolean cycles = false;
/**
* Creates a new empty directed graph object.
* <p>
* After this graph's vertexes and edges are defined with
* <code>addVertex</code> and <code>addEdge</code>, call
* <code>freeze</code> to indicate that the graph is all there, and then
* call <code>idsByDFSFinishTime</code> to read off the vertexes ordered
* by DFS finish time.
* </p>
*/
public Digraph() {
super();
}
/**
* Freezes this graph. No more vertexes or edges can be added to this
* graph after this method is called. Has no effect if the graph is
* already frozen.
*/
public void freeze() {
if (!initialized) {
initialized = true;
// only perform depth-first-search once
DFS();
}
}
/**
* Defines a new vertex with the given id. The depth-first search is
* performed in the relative order in which vertexes were added to the
* graph.
*
* @param id the id of the vertex
* @exception IllegalArgumentException if the vertex id is
* already defined or if the graph is frozen
*/
public void addVertex(Object id) throws IllegalArgumentException {
if (initialized) {
throw new IllegalArgumentException();
}
Vertex vertex = new Vertex(id);
Object existing = vertexMap.put(id, vertex);
// nip problems with duplicate vertexes in the bud
if (existing != null) {
throw new IllegalArgumentException();
}
vertexList.add(vertex);
}
/**
* Adds a new directed edge between the vertexes with the given ids.
* Vertexes for the given ids must be defined beforehand with
* <code>addVertex</code>. The depth-first search is performed in the
* relative order in which adjacent "to" vertexes were added to a given
* "from" index.
*
* @param fromId the id of the "from" vertex
* @param toId the id of the "to" vertex
* @exception IllegalArgumentException if either vertex is undefined or
* if the graph is frozen
*/
public void addEdge(Object fromId, Object toId) throws IllegalArgumentException {
if (initialized) {
throw new IllegalArgumentException();
}
Vertex fromVertex = vertexMap.get(fromId);
Vertex toVertex = vertexMap.get(toId);
// ignore edges when one of the vertices is unknown
if (fromVertex == null || toVertex == null)
return;
fromVertex.adjacent.add(toVertex);
}
/**
* Returns the ids of the vertexes in this graph ordered by depth-first
* search finish time. The graph must be frozen.
*
* @param increasing <code>true</code> if objects are to be arranged
* into increasing order of depth-first search finish time, and
* <code>false</code> if objects are to be arranged into decreasing
* order of depth-first search finish time
* @return the list of ids ordered by depth-first search finish time
* (element type: <code>Object</code>)
* @exception IllegalArgumentException if the graph is not frozen
*/
public List<Object> idsByDFSFinishTime(boolean increasing) {
if (!initialized) {
throw new IllegalArgumentException();
}
int len = vertexList.size();
Object[] r = new Object[len];
for (Iterator<Vertex> allV = vertexList.iterator(); allV.hasNext();) {
Vertex vertex = allV.next();
int f = vertex.finishTime;
// note that finish times start at 1, not 0
if (increasing) {
r[f - 1] = vertex.id;
} else {
r[len - f] = vertex.id;
}
}
return Arrays.asList(r);
}
/**
* Returns whether the graph contains cycles. The graph must be frozen.
*
* @return <code>true</code> if this graph contains at least one cycle,
* and <code>false</code> if this graph is cycle free
* @exception IllegalArgumentException if the graph is not frozen
*/
public boolean containsCycles() {
if (!initialized) {
throw new IllegalArgumentException();
}
return cycles;
}
/**
* Returns the non-trivial components of this graph. A non-trivial
* component is a set of 2 or more vertexes that were traversed
* together. The graph must be frozen.
*
* @return the possibly empty list of non-trivial components, where
* each component is an array of ids (element type:
* <code>Object[]</code>)
* @exception IllegalArgumentException if the graph is not frozen
*/
public List<Object[]> nonTrivialComponents() {
if (!initialized) {
throw new IllegalArgumentException();
}
// find the roots of each component
// Map<Vertex,List<Object>> components
Map<Vertex, List<Object>> components = new HashMap<>();
for (Iterator<Vertex> it = vertexList.iterator(); it.hasNext();) {
Vertex vertex = it.next();
if (vertex.predecessor == null) {
// this vertex is the root of a component
// if component is non-trivial we will hit a child
} else {
// find the root ancestor of this vertex
Vertex root = vertex;
while (root.predecessor != null) {
root = root.predecessor;
}
List<Object> component = components.get(root);
if (component == null) {
component = new ArrayList<>(2);
component.add(root.id);
components.put(root, component);
}
component.add(vertex.id);
}
}
List<Object[]> result = new ArrayList<>(components.size());
for (Iterator<List<Object>> it = components.values().iterator(); it.hasNext();) {
List<Object> component = it.next();
if (component.size() > 1) {
result.add(component.toArray());
}
}
return result;
}
// /**
// * Performs a depth-first search of this graph and records interesting
// * info with each vertex, including DFS finish time. Employs a recursive
// * helper method <code>DFSVisit</code>.
// * <p>
// * Although this method is not used, it is the basis of the
// * non-recursive <code>DFS</code> method.
// * </p>
// */
// private void recursiveDFS() {
// // initialize
// // all vertex.color initially Vertex.WHITE;
// // all vertex.predecessor initially null;
// time = 0;
// for (Iterator allV = vertexList.iterator(); allV.hasNext();) {
// Vertex nextVertex = (Vertex) allV.next();
// if (nextVertex.color == Vertex.WHITE) {
// DFSVisit(nextVertex);
// }
// }
// }
//
// /**
// * Helper method. Performs a depth first search of this graph.
// *
// * @param vertex the vertex to visit
// */
// private void DFSVisit(Vertex vertex) {
// // mark vertex as discovered
// vertex.color = Vertex.GREY;
// List adj = vertex.adjacent;
// for (Iterator allAdjacent=adj.iterator(); allAdjacent.hasNext();) {
// Vertex adjVertex = (Vertex) allAdjacent.next();
// if (adjVertex.color == Vertex.WHITE) {
// // explore edge from vertex to adjVertex
// adjVertex.predecessor = vertex;
// DFSVisit(adjVertex);
// } else if (adjVertex.color == Vertex.GREY) {
// // back edge (grey vertex means visit in progress)
// cycles = true;
// }
// }
// // done exploring vertex
// vertex.color = Vertex.BLACK;
// time++;
// vertex.finishTime = time;
// }
/**
* Performs a depth-first search of this graph and records interesting
* info with each vertex, including DFS finish time. Does not employ
* recursion.
*/
private void DFS() {
// state machine rendition of the standard recursive DFS algorithm
int state;
final int NEXT_VERTEX = 1;
final int START_DFS_VISIT = 2;
final int NEXT_ADJACENT = 3;
final int AFTER_NEXTED_DFS_VISIT = 4;
// use precomputed objects to avoid garbage
final Integer NEXT_VERTEX_OBJECT = Integer.valueOf(NEXT_VERTEX);
final Integer AFTER_NEXTED_DFS_VISIT_OBJECT = Integer.valueOf(AFTER_NEXTED_DFS_VISIT);
// initialize
// all vertex.color initially Vertex.WHITE;
// all vertex.predecessor initially null;
time = 0;
// for a stack, append to the end of an array-based list
List<Object> stack = new ArrayList<>(Math.max(1, vertexList.size()));
Iterator<Vertex> allAdjacent = null;
Vertex vertex = null;
Iterator<Vertex> allV = vertexList.iterator();
state = NEXT_VERTEX;
nextStateLoop: while (true) {
switch (state) {
case NEXT_VERTEX :
// on entry, "allV" contains vertexes yet to be visited
if (!allV.hasNext()) {
// all done
break nextStateLoop;
}
Vertex nextVertex = allV.next();
if (nextVertex.color == Vertex.WHITE) {
stack.add(NEXT_VERTEX_OBJECT);
vertex = nextVertex;
state = START_DFS_VISIT;
continue nextStateLoop;
}
state = NEXT_VERTEX;
continue nextStateLoop;
case START_DFS_VISIT :
// on entry, "vertex" contains the vertex to be visited
// top of stack is return code
// mark the vertex as discovered
vertex.color = Vertex.GREY;
allAdjacent = vertex.adjacent.iterator();
state = NEXT_ADJACENT;
continue nextStateLoop;
case NEXT_ADJACENT :
// on entry, "allAdjacent" contains adjacent vertexes to
// be visited; "vertex" contains vertex being visited
if (allAdjacent.hasNext()) {
Vertex adjVertex = allAdjacent.next();
if (adjVertex.color == Vertex.WHITE) {
// explore edge from vertex to adjVertex
adjVertex.predecessor = vertex;
stack.add(allAdjacent);
stack.add(vertex);
stack.add(AFTER_NEXTED_DFS_VISIT_OBJECT);
vertex = adjVertex;
state = START_DFS_VISIT;
continue nextStateLoop;
}
if (adjVertex.color == Vertex.GREY) {
// back edge (grey means visit in progress)
cycles = true;
}
state = NEXT_ADJACENT;
continue nextStateLoop;
}
// done exploring vertex
vertex.color = Vertex.BLACK;
time++;
vertex.finishTime = time;
state = ((Integer) stack.remove(stack.size() - 1)).intValue();
continue nextStateLoop;
case AFTER_NEXTED_DFS_VISIT :
// on entry, stack contains "vertex" and "allAjacent"
vertex = (Vertex) stack.remove(stack.size() - 1);
@SuppressWarnings("unchecked")
Iterator<Vertex> unchecked = (Iterator<Vertex>) stack.remove(stack.size() - 1);
allAdjacent = unchecked;
state = NEXT_ADJACENT;
continue nextStateLoop;
}
}
}
}
/**
* Sorts the given list of projects in a manner that honors the given
* project reference relationships. That is, if project A references project
* B, then the resulting order will list B before A if possible. For graphs
* that do not contain cycles, the result is the same as a conventional
* topological sort. For graphs containing cycles, the order is based on
* ordering the strongly connected components of the graph. This has the
* effect of keeping each knot of projects together without otherwise
* affecting the order of projects not involved in a cycle. For a graph G,
* the algorithm performs in O(|G|) space and time.
* <p>
* When there is an arbitrary choice, vertexes are ordered as supplied.
* Arranged projects in descending alphabetical order generally results in
* an order that builds "A" before "Z" when there are no other constraints.
* </p>
* <p> Ref: Cormen, Leiserson, and Rivest <it>Introduction to
* Algorithms</it>, McGraw-Hill, 1990. The strongly-connected-components
* algorithm is in section 23.5.
* </p>
*
* @param objects a list of projects (element type:
* <code>IProject</code>)
* @param references a list of project references [A,B] meaning that A
* references B (element type: <code>IProject[]</code>)
* @return an object describing the resulting project order
*/
public static Object[][] computeNodeOrder(Object[] objects, Object[][] references) {
// Step 1: Create the graph object.
final Digraph g1 = new Digraph();
// add vertexes
for (int i = 0; i < objects.length; i++)
g1.addVertex(objects[i]);
// add edges
for (int i = 0; i < references.length; i++)
// create an edge from q to p
// to cause q to come before p in eventual result
g1.addEdge(references[i][1], references[i][0]);
g1.freeze();
// Step 2: Create the transposed graph. This time, define the vertexes
// in decreasing order of depth-first finish time in g1
// interchange "to" and "from" to reverse edges from g1
final Digraph g2 = new Digraph();
// add vertexes
List<Object> resortedVertexes = g1.idsByDFSFinishTime(false);
for (Iterator<Object> it = resortedVertexes.iterator(); it.hasNext();)
g2.addVertex(it.next());
// add edges
for (int i = 0; i < references.length; i++)
g2.addEdge(references[i][0], references[i][1]);
g2.freeze();
// Step 3: Return the vertexes in increasing order of depth-first finish
// time in g2
List<Object> sortedProjectList = g2.idsByDFSFinishTime(true);
Object[] orderedNodes = new Object[sortedProjectList.size()];
sortedProjectList.toArray(orderedNodes);
Object[][] knots;
boolean hasCycles = g2.containsCycles();
if (hasCycles) {
List<Object[]> knotList = g2.nonTrivialComponents();
knots = knotList.toArray(new Object[knotList.size()][]);
} else {
knots = new Object[0][];
}
for (int i = 0; i < orderedNodes.length; i++)
objects[i] = orderedNodes[i];
return knots;
}
}