add topological sort

Signed-off-by: Mattias Andrée <maandree@operamail.com>

1 files changed, 243 insertions, 0 deletions

diff --git a/src/algorithms/sorting/other/TopologicalSort.java b/src/algorithms/sorting/other/TopologicalSort.java
new file mode 100644
index 0000000..48ff604
--- /dev/null
+++ b/src/algorithms/sorting/other/TopologicalSort.java
@@ -0,0 +1,243 @@
+/**
+ * Copyright © 2014  Mattias Andrée (maandree@member.fsf.org)
+ * 
+ * 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;
+    }
+    
+}
+