A (fairly) general purpose implementation of Dijkstra's shortest path

algorithm.


git-svn-id: https://samskivert.googlecode.com/svn/trunk@1537 6335cc39-0255-0410-8fd6-9bcaacd3b74c

projects/samskivert/src/java/com/samskivert/util/ShortestPath.java

@@ -0,0 +1,142 @@
+//
+// samskivert library - useful routines for java programs
+// Copyright (C) 2001-2004 Michael Bayne
+// 
+// This library is free software; you can redistribute it and/or modify it
+// under the terms of the GNU Lesser General Public License as published
+// by the Free Software Foundation; either version 2.1 of the License, or
+// (at your option) any later version.
+//
+// This library 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
+// Lesser General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+package com.samskivert.util;
+
+import java.util.ArrayList;
+import java.util.HashMap;
+import java.util.HashSet;
+import java.util.Iterator;
+import java.util.List;
+
+/**
+ * Implements Dijkstra's algorithm for finding the shortest path between
+ * two nodes in a weighted graph. The code assumes that the caller
+ * represents their nodes and edges as objects which can be compared and
+ * hashed (via {@link Object#equals} and {@link Object#hashCode}) other
+ * necessary information is obtained through a special interface {@link
+ * Graph} implemented by the caller to enumerate edges and compute
+ * weights.
+ */
+public class ShortestPath
+{
+    /** A caller must implement this interface to provide the information
+     * needed to define the graph and compute the shortest path. */
+    public interface Graph
+    {
+        /** Enumerates all nodes in the graph. */
+        public Iterator enumerateNodes ();
+
+        /** Returns the list of the edges for the specified node. */
+        public List getEdges (Object node);
+
+        /** Returns the weight associated with the supplied edge in the
+         * direction established by the supplied starting node. */
+        public int computeWeight (Object edge, Object start);
+
+        /** Returns the node opposite the supplied node on the supplied edge. */
+        public Object getOpposite (Object edge, Object node);
+    }
+
+    /**
+     * Computes the shortest path between the specified starting and
+     * ending nodes using Dijkstra's algorithm. This implementation
+     * assumes that the graph is properly formed and may behave strangely
+     * or throw an exception if provided with an invalid graph.
+     *
+     * @return a list of the edges that must be followed to traverse from
+     * the starting node to the ending node. This list may be empty if the
+     * graph is improperly formed.
+     */
+    public static List compute (Graph graph, Object start, Object end)
+    {
+        HashMap nodes = new HashMap();
+        HashSet relaxed = new HashSet();
+        SortableArrayList uptight = new SortableArrayList();
+
+        // initialize our searching info
+        for (Iterator iter = graph.enumerateNodes(); iter.hasNext(); ) {
+            NodeInfo info = new NodeInfo();
+            info.node = iter.next();
+            if (info.node == start) {
+                info.weightTo = 0;
+            }
+            uptight.add(info);
+            nodes.put(info.node, info);
+        }
+        uptight.sort();
+
+        // now execute the main part of the search
+        while (uptight.size() > 0) {
+            // remove the cheapest known node
+            NodeInfo info = (NodeInfo)uptight.remove(uptight.size()-1);
+            // make a note that it is now relaxed
+            relaxed.add(info.node);
+            // relax its uptight neighbors
+            List edges = graph.getEdges(info.node);
+            for (int ii = 0, ll = edges.size(); ii < ll; ii++) {
+                Object edge = edges.get(ii);
+                Object onode = graph.getOpposite(edge, info.node);
+                if (relaxed.contains(onode)) {
+                    continue;
+                }
+                // if the path through this node to its neighbor is
+                // cheaper than the existing known shortest path, update
+                // the neighbor to reflect this new shorter path
+                NodeInfo oinfo = (NodeInfo)nodes.get(onode);
+                int weight = graph.computeWeight(edge, info.node);
+                if (oinfo.weightTo > info.weightTo + weight) {
+                    oinfo.weightTo = info.weightTo + weight;
+                    oinfo.edgeTo = edge;
+                }
+            }
+            // now resort the uptight list
+            uptight.sort();
+        }
+
+        // now trace the path from the final node back to the start
+        ArrayList path = new ArrayList();
+        NodeInfo info = (NodeInfo)nodes.get(end);
+        while (info.edgeTo != null) {
+            path.add(0, info.edgeTo);
+            info = (NodeInfo)nodes.get(
+                graph.getOpposite(info.edgeTo, info.node));
+        }
+        return path;
+    }
+
+    /** Used to maintain information during the shortest path search. */
+    protected static final class NodeInfo
+        implements Comparable
+    {
+        /** The node for which we're representing information. */
+        public Object node;
+
+        /** The cumulative weight to this node from the source. */
+        public int weightTo = Integer.MAX_VALUE / 4;
+
+        /** The edge followed to reach this node along the shortest path. */
+        public Object edgeTo;
+
+        /** We order ourselves by the cumulative weight to this node. */
+        public int compareTo (Object o)
+        {
+            return ((NodeInfo)o).weightTo - weightTo;
+        }
+    }
+}