/**
* Copyright © 2014 Mattias Andrée (m@maandree.se)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
package algorithms.sorting.other;
import java.util.*;
/**
* Topological sorting class. There are a few ways to perform
* a topological sort, this class implements an topological
* sort with advisory dependencies and strict dependencies.
* Dependencies are broken when there are cyclic dependencies,
* but if the dependency is strict rather than advisory, the
* algorithm fails. Additionally, this this, implementation
* uses two input parameters, a map from items to sets of
* dependencies, and a map from items, to a set of strict
* dependencies. The strict dependencies must appear in both
* of the sets, whilst the advisory dependencies must only
* appear in the first set of dependencies. This implemention
* tries to minimise the number of transversially broken
* dependencies. It is advisable to use both hash based maps
* and sets.
*
* @param <T> The data type that has been sorted
*/
public class TopologicalSort<T>
{
/**
* Constructor
*/
private TopologicalSort()
{
/* Do nothing */
}
/**
* List of missing dependencies. There may be duplicates,
* see {@link #missingDependent}.
*/
public ArrayList<T> missingDependency = new ArrayList<T>();
/**
* List of items with missing dependencies. For any give index
* i, the element in {@link #missingDependency} with index i
* is required by the element with index i in this list.
*/
public ArrayList<T> missingDependent = new ArrayList<T>();
/**
* The items in topological order
*/
public ArrayList<T> order = new ArrayList<T>();
/**
* If an items exists as a key in this map it has been used
* to break a cyclic dependency. The associated value of a
* key is a set of all direct dependencies that will appear
* later in the topologically ordered list {@link #order}.
*/
public HashMap<T, HashSet<T>> breaks = new HashMap<T, HashSet<T>>();
/**
* Whether the topological sort was successful, i.e., not
* absolute dependencies needed to be broken. If this value
* is {@code false}, the topologically ordered list and
* the map of cyclic dependency breaks may no be complete.
*/
public boolean successful = false;
/**
* Topolocally sort data.
*
* @param dependencies Map for items to their advisory dependencies, will be modified
* @param absolutes Map for items to their absolute dependencies
* @return A data structure with the result of the topological sort
*/
@SuppressWarnings("unchecked")
public static <T> TopologicalSort<T> tsort(Map<T, Set<T>> dependencies, Map<T, Set<T>> absolutes)
{
TopologicalSort<T> rc = new TopologicalSort<T>();
if (absolutes == null) /* sugar */
absolutes = new HashMap<T, Set<T>>();
/* Find, list and remove missing dependencies */
{
HashMap<T, ArrayList<T>> removed = new HashMap<T, ArrayList<T>>();
for (Map.Entry<T, Set<T>> req_deps : dependencies.entrySet())
{
T req = req_deps.getKey();
for (T dep : req_deps.getValue())
if (dependencies.containsKey(dep) == false)
{
rc.missingDependency.add(dep);
rc.missingDependent.add(req);
if (removed.containsKey(dep) == false)
removed.put(dep, new ArrayList<T>());
removed.get(dep).add(req);
}
}
for (Map.Entry<T, ArrayList<T>> remove_reqs : removed.entrySet())
{
T remove = remove_reqs.getKey();
for (T req : remove_reqs.getValue())
dependencies.get(req).remove(remove);
}
}
/* Sort cyclic graph topologically */
{
ArrayList<T> removed = new ArrayList<T>();
removed.add(null);
while (removed.size() > 0)
{
/* Sort acyclic graph topologically */
while (removed.size() > 0)
{
removed.clear();
/* Report and remove items with no unresolved dependency */
T[] dependencies_ = (T[])(new Object[dependencies.size()]); /* needed to avoid concurrent modification */
int i = 0;
for (T key : dependencies.keySet())
dependencies_[i++] = key;
for (T item : dependencies_)
if (dependencies.get(item).size() == 0)
{
rc.order.add(item);
removed.add(item);
dependencies.remove(item);
}
/* Remove reported items from dependency lists */
for (Map.Entry<T, Set<T>> req_deps : dependencies.entrySet())
{
T req = req_deps.getKey();
Set<T> deps = req_deps.getValue();
for (T old : removed)
if (deps.contains(old))
deps.remove(old);
}
}
/* Break one cycle with as few transversial dependencies as possible */
if (dependencies.size() > 0)
{
T best = null;
HashSet<T> bestBreaks = null;
/* Find best cycle break */
for (Map.Entry<T, Set<T>> item_deps : dependencies.entrySet())
{
T item = item_deps.getKey();
Set<T> queue_ = item_deps.getValue();
Set<T> abs_ = absolutes.get(item);
HashSet<T> abs = new HashSet<T>();
if (abs_ != null)
for (T elem : abs_)
abs.add(elem);
HashSet<T> deps = new HashSet<T>();
T[] queue = (T[])(new Object[queue_.size()]);
int queue_h = 0, queue_t = 0;
for (T elem : queue_)
queue[queue_t++] = elem;
deps.add(item);
boolean bad = false;
while (queue_h != queue_t)
{
T dep = queue[queue_h++];
if (abs.contains(dep))
{
bad = true;
break;
}
if (deps.contains(dep))
continue;
deps.add(dep);
Set<T> extra = dependencies.get(dep);
queue_t -= queue_h;
System.arraycopy(queue, queue_h, queue = (T[])(new Object[queue_t + extra.size()]), 0, queue_t);
queue_h = 0;
for (T elem : extra)
queue[queue_t++] = elem;
if ((extra = absolutes.get(dep)) != null)
for (T elem : extra)
abs.add(elem);
}
if (bad)
continue;
deps.remove(item);
if ((best == null) || (bestBreaks.size() > deps.size()))
{
best = item;
bestBreaks = deps;
}
}
/* List cycle break and remove item */
if (best == null)
return rc;
rc.order.add(best);
rc.breaks.put(best, bestBreaks);
removed.add(best);
dependencies.remove(best);
/* Remove item from dependency lists */
for (Map.Entry<T, Set<T>> item_deps : dependencies.entrySet())
{
T item = item_deps.getKey();
Set<T> deps = item_deps.getValue();
if (deps.contains(item) == false)
deps.remove(best);
}
}
}
}
rc.successful = true;
return rc;
}
}
