lucene/core/src/java/org/apache/lucene/util/fst/Util.java

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.lucene.util.fst;


import org.apache.lucene.util.BytesRef;
import org.apache.lucene.util.BytesRefBuilder;
import org.apache.lucene.util.IntsRef;
import org.apache.lucene.util.IntsRefBuilder;
import org.apache.lucene.util.fst.FST.Arc;
import org.apache.lucene.util.fst.FST.BytesReader;

import java.io.IOException;
import java.io.Writer;
import java.util.ArrayList;
import java.util.BitSet;
import java.util.Comparator;
import java.util.Iterator;
import java.util.List;
import java.util.TreeSet;

import static org.apache.lucene.util.fst.FST.Arc.BitTable;

/** Static helper methods.
 *
 * @lucene.experimental */
public final class Util {
  private Util() {
  }

  /** Looks up the output for this input, or null if the
   *  input is not accepted. */
  public static<T> T get(FST<T> fst, IntsRef input) throws IOException {

    // TODO: would be nice not to alloc this on every lookup
    final FST.Arc<T> arc = fst.getFirstArc(new FST.Arc<T>());

    final BytesReader fstReader = fst.getBytesReader();

    // Accumulate output as we go
    T output = fst.outputs.getNoOutput();
    for(int i=0;i<input.length;i++) {
      if (fst.findTargetArc(input.ints[input.offset + i], arc, arc, fstReader) == null) {
        return null;
      }
      output = fst.outputs.add(output, arc.output());
    }

    if (arc.isFinal()) {
      return fst.outputs.add(output, arc.nextFinalOutput());
    } else {
      return null;
    }
  }

  // TODO: maybe a CharsRef version for BYTE2

  /** Looks up the output for this input, or null if the
   *  input is not accepted */
  public static<T> T get(FST<T> fst, BytesRef input) throws IOException {
    assert fst.inputType == FST.INPUT_TYPE.BYTE1;

    final BytesReader fstReader = fst.getBytesReader();

    // TODO: would be nice not to alloc this on every lookup
    final FST.Arc<T> arc = fst.getFirstArc(new FST.Arc<>());

    // Accumulate output as we go
    T output = fst.outputs.getNoOutput();
    for(int i=0;i<input.length;i++) {
      if (fst.findTargetArc(input.bytes[i+input.offset] & 0xFF, arc, arc, fstReader) == null) {
        return null;
      }
      output = fst.outputs.add(output, arc.output());
    }

    if (arc.isFinal()) {
      return fst.outputs.add(output, arc.nextFinalOutput());
    } else {
      return null;
    }
  }

  /** Reverse lookup (lookup by output instead of by input),
   *  in the special case when your FSTs outputs are
   *  strictly ascending.  This locates the input/output
   *  pair where the output is equal to the target, and will
   *  return null if that output does not exist.
   *
   *  <p>NOTE: this only works with {@code FST<Long>}, only
   *  works when the outputs are ascending in order with
   *  the inputs.
   *  For example, simple ordinals (0, 1,
   *  2, ...), or file offsets (when appending to a file)
   *  fit this. */
  @Deprecated
  public static IntsRef getByOutput(FST<Long> fst, long targetOutput) throws IOException {

    final BytesReader in = fst.getBytesReader();

    // TODO: would be nice not to alloc this on every lookup
    FST.Arc<Long> arc = fst.getFirstArc(new FST.Arc<Long>());
    
    FST.Arc<Long> scratchArc = new FST.Arc<>();

    final IntsRefBuilder result = new IntsRefBuilder();
    return getByOutput(fst, targetOutput, in, arc, scratchArc, result);
  }
    
  /** 
   * Expert: like {@link Util#getByOutput(FST, long)} except reusing 
   * BytesReader, initial and scratch Arc, and result.
   */
  @Deprecated
  public static IntsRef getByOutput(FST<Long> fst, long targetOutput, BytesReader in, Arc<Long> arc, Arc<Long> scratchArc, IntsRefBuilder result) throws IOException {
    long output = arc.output();
    int upto = 0;

    //System.out.println("reverseLookup output=" + targetOutput);

    while(true) {
      //System.out.println("loop: output=" + output + " upto=" + upto + " arc=" + arc);
      if (arc.isFinal()) {
        final long finalOutput = output + arc.nextFinalOutput();
        //System.out.println("  isFinal finalOutput=" + finalOutput);
        if (finalOutput == targetOutput) {
          result.setLength(upto);
          //System.out.println("    found!");
          return result.get();
        } else if (finalOutput > targetOutput) {
          //System.out.println("    not found!");
          return null;
        }
      }

      if (FST.targetHasArcs(arc)) {
        //System.out.println("  targetHasArcs");
        result.grow(1+upto);
        
        fst.readFirstRealTargetArc(arc.target(), arc, in);

        if (arc.bytesPerArc() != 0 && arc.nodeFlags() == FST.ARCS_FOR_BINARY_SEARCH) {

          int low = 0;
          int high = arc.numArcs() -1;
          int mid = 0;
          //System.out.println("bsearch: numArcs=" + arc.numArcs + " target=" + targetOutput + " output=" + output);
          boolean exact = false;
          while (low <= high) {
            mid = (low + high) >>> 1;
            in.setPosition(arc.posArcsStart());
            in.skipBytes(arc.bytesPerArc() *mid);
            final byte flags = in.readByte();
            fst.readLabel(in);
            final long minArcOutput;
            if ((flags & FST.BIT_ARC_HAS_OUTPUT) != 0) {
              final long arcOutput = fst.outputs.read(in);
              minArcOutput = output + arcOutput;
            } else {
              minArcOutput = output;
            }
            //System.out.println("  cycle mid=" + mid + " output=" + minArcOutput);
            if (minArcOutput == targetOutput) {
              exact = true;
              break;
            } else if (minArcOutput < targetOutput) {
              low = mid + 1;
            } else {
              high = mid - 1;
            }
          }

          int idx;
          if (high == -1) {
            return null;
          } else if (exact) {
            idx = mid;
          } else {
            idx = low - 1;
          }

          fst.readArcByIndex(arc, in, idx);
          result.setIntAt(upto++, arc.label());
          output += arc.output();

        } else {

          FST.Arc<Long> prevArc = null;

          while(true) {
            //System.out.println("    cycle label=" + arc.label + " output=" + arc.output);

            // This is the min output we'd hit if we follow
            // this arc:
            final long minArcOutput = output + arc.output();

            if (minArcOutput == targetOutput) {
              // Recurse on this arc:
              //System.out.println("  match!  break");
              output = minArcOutput;
              result.setIntAt(upto++, arc.label());
              break;
            } else if (minArcOutput > targetOutput) {
              if (prevArc == null) {
                // Output doesn't exist
                return null;
              } else {
                // Recurse on previous arc:
                arc.copyFrom(prevArc);
                result.setIntAt(upto++, arc.label());
                output += arc.output();
                //System.out.println("    recurse prev label=" + (char) arc.label + " output=" + output);
                break;
              }
            } else if (arc.isLast()) {
              // Recurse on this arc:
              output = minArcOutput;
              //System.out.println("    recurse last label=" + (char) arc.label + " output=" + output);
              result.setIntAt(upto++, arc.label());
              break;
            } else {
              // Read next arc in this node:
              prevArc = scratchArc;
              prevArc.copyFrom(arc);
              //System.out.println("      after copy label=" + (char) prevArc.label + " vs " + (char) arc.label);
              fst.readNextRealArc(arc, in);
            }
          }
        }
      } else {
        //System.out.println("  no target arcs; not found!");
        return null;
      }
    }    
  }

  /** Represents a path in TopNSearcher.
   *
   *  @lucene.experimental
   */
  public static class FSTPath<T> {
    /** Holds the last arc appended to this path */
    public FST.Arc<T> arc;
    /** Holds cost plus any usage-specific output: */
    public T output;
    public final IntsRefBuilder input;
    public final float boost;
    public final CharSequence context;

    // Custom int payload for consumers; the NRT suggester uses this to record if this path has already enumerated a surface form
    public int payload;

    FSTPath(T output, FST.Arc<T> arc, IntsRefBuilder input, float boost, CharSequence context, int payload) {
      this.arc = new FST.Arc<T>().copyFrom(arc);
      this.output = output;
      this.input = input;
      this.boost = boost;
      this.context = context;
      this.payload = payload;
    }

    FSTPath<T> newPath(T output, IntsRefBuilder input) {
      return new FSTPath<>(output, this.arc, input, this.boost, this.context, this.payload);
    }

    @Override
    public String toString() {
      return "input=" + input.get() + " output=" + output + " context=" + context + " boost=" + boost + " payload=" + payload;
    }
  }

  /** Compares first by the provided comparator, and then
   *  tie breaks by path.input. */
  private static class TieBreakByInputComparator<T> implements Comparator<FSTPath<T>> {
    private final Comparator<T> comparator;

    TieBreakByInputComparator(Comparator<T> comparator) {
      this.comparator = comparator;
    }

    @Override
    public int compare(FSTPath<T> a, FSTPath<T> b) {
      int cmp = comparator.compare(a.output, b.output);
      if (cmp == 0) {
        return a.input.get().compareTo(b.input.get());
      } else {
        return cmp;
      }
    }
  }

  /** Utility class to find top N shortest paths from start
   *  point(s). */
  public static class TopNSearcher<T> {

    private final FST<T> fst;
    private final BytesReader bytesReader;
    private final int topN;
    private final int maxQueueDepth;

    private final FST.Arc<T> scratchArc = new FST.Arc<>();
    
    private final Comparator<T> comparator;
    private final Comparator<FSTPath<T>> pathComparator;

    TreeSet<FSTPath<T>> queue;

    /**
     * Creates an unbounded TopNSearcher
     * @param fst the {@link org.apache.lucene.util.fst.FST} to search on
     * @param topN the number of top scoring entries to retrieve
     * @param maxQueueDepth the maximum size of the queue of possible top entries
     * @param comparator the comparator to select the top N
     */
    public TopNSearcher(FST<T> fst, int topN, int maxQueueDepth, Comparator<T> comparator) {
      this(fst, topN, maxQueueDepth, comparator, new TieBreakByInputComparator<>(comparator));
    }

    public TopNSearcher(FST<T> fst, int topN, int maxQueueDepth, Comparator<T> comparator,
                        Comparator<FSTPath<T>> pathComparator) {
      this.fst = fst;
      this.bytesReader = fst.getBytesReader();
      this.topN = topN;
      this.maxQueueDepth = maxQueueDepth;
      this.comparator = comparator;
      this.pathComparator = pathComparator;
      queue = new TreeSet<>(pathComparator);
    }

    // If back plus this arc is competitive then add to queue:
    protected void addIfCompetitive(FSTPath<T> path) {

      assert queue != null;

      T output = fst.outputs.add(path.output, path.arc.output());

      if (queue.size() == maxQueueDepth) {
        FSTPath<T> bottom = queue.last();
        int comp = pathComparator.compare(path, bottom);
        if (comp > 0) {
          // Doesn't compete
          return;
        } else if (comp == 0) {
          // Tie break by alpha sort on the input:
          path.input.append(path.arc.label());
          final int cmp = bottom.input.get().compareTo(path.input.get());
          path.input.setLength(path.input.length() - 1);

          // We should never see dups:
          assert cmp != 0;

          if (cmp < 0) {
            // Doesn't compete
            return;
          }
        }
        // Competes
      }
      // else ... Queue isn't full yet, so any path we hit competes:

      // copy over the current input to the new input
      // and add the arc.label to the end
      IntsRefBuilder newInput = new IntsRefBuilder();
      newInput.copyInts(path.input.get());
      newInput.append(path.arc.label());

      FSTPath<T> newPath = path.newPath(output, newInput);
      if (acceptPartialPath(newPath)) {
        queue.add(newPath);
        if (queue.size() == maxQueueDepth+1) {
          queue.pollLast();
        }
      }
    }

    public void addStartPaths(FST.Arc<T> node, T startOutput, boolean allowEmptyString, IntsRefBuilder input) throws IOException {
      addStartPaths(node, startOutput, allowEmptyString, input, 0, null, -1);
    }

    /** Adds all leaving arcs, including 'finished' arc, if
     *  the node is final, from this node into the queue.  */
    public void addStartPaths(FST.Arc<T> node, T startOutput, boolean allowEmptyString, IntsRefBuilder input,
                              float boost, CharSequence context, int payload) throws IOException {

      // De-dup NO_OUTPUT since it must be a singleton:
      if (startOutput.equals(fst.outputs.getNoOutput())) {
        startOutput = fst.outputs.getNoOutput();
      }

      FSTPath<T> path = new FSTPath<>(startOutput, node, input, boost, context, payload);
      fst.readFirstTargetArc(node, path.arc, bytesReader);

      // Bootstrap: find the min starting arc
      while (true) {
        if (allowEmptyString || path.arc.label() != FST.END_LABEL) {
          addIfCompetitive(path);
        }
        if (path.arc.isLast()) {
          break;
        }
        fst.readNextArc(path.arc, bytesReader);
      }
    }

    public TopResults<T> search() throws IOException {

      final List<Result<T>> results = new ArrayList<>();

      final BytesReader fstReader = fst.getBytesReader();
      final T NO_OUTPUT = fst.outputs.getNoOutput();

      // TODO: we could enable FST to sorting arcs by weight
      // as it freezes... can easily do this on first pass
      // (w/o requiring rewrite)

      // TODO: maybe we should make an FST.INPUT_TYPE.BYTE0.5!?
      // (nibbles)
      int rejectCount = 0;

      // For each top N path:
      while (results.size() < topN) {

        FSTPath<T> path;

        if (queue == null) {
          // Ran out of paths
          break;
        }

        // Remove top path since we are now going to
        // pursue it:
        path = queue.pollFirst();

        if (path == null) {
          // There were less than topN paths available:
          break;
        }
        //System.out.println("pop path=" + path + " arc=" + path.arc.output);

        if (acceptPartialPath(path) == false) {
          continue;
        }

        if (path.arc.label() == FST.END_LABEL) {
          // Empty string!
          path.input.setLength(path.input.length() - 1);
          results.add(new Result<>(path.input.get(), path.output));
          continue;
        }

        if (results.size() == topN-1 && maxQueueDepth == topN) {
          // Last path -- don't bother w/ queue anymore:
          queue = null;
        }

        // We take path and find its "0 output completion",
        // ie, just keep traversing the first arc with
        // NO_OUTPUT that we can find, since this must lead
        // to the minimum path that completes from
        // path.arc.

        // For each input letter:
        while (true) {

          fst.readFirstTargetArc(path.arc, path.arc, fstReader);

          // For each arc leaving this node:
          boolean foundZero = false;
          boolean arcCopyIsPending = false;
          while(true) {
            // tricky: instead of comparing output == 0, we must
            // express it via the comparator compare(output, 0) == 0
            if (comparator.compare(NO_OUTPUT, path.arc.output()) == 0) {
              if (queue == null) {
                foundZero = true;
                break;
              } else if (!foundZero) {
                arcCopyIsPending = true;
                foundZero = true;
              } else {
                addIfCompetitive(path);
              }
            } else if (queue != null) {
              addIfCompetitive(path);
            }
            if (path.arc.isLast()) {
              break;
            }
            if (arcCopyIsPending) {
              scratchArc.copyFrom(path.arc);
              arcCopyIsPending = false;
            }
            fst.readNextArc(path.arc, fstReader);
          }

          assert foundZero;

          if (queue != null && !arcCopyIsPending) {
            path.arc.copyFrom(scratchArc);
          }

          if (path.arc.label() == FST.END_LABEL) {
            // Add final output:
            path.output = fst.outputs.add(path.output, path.arc.output());
            if (acceptResult(path)) {
              results.add(new Result<>(path.input.get(), path.output));
            } else {
              rejectCount++;
            }
            break;
          } else {
            path.input.append(path.arc.label());
            path.output = fst.outputs.add(path.output, path.arc.output());
            if (acceptPartialPath(path) == false) {
              break;
            }
          }
        }
      }
      return new TopResults<>(rejectCount + topN <= maxQueueDepth, results);
    }

    protected boolean acceptResult(FSTPath<T> path) {
      return acceptResult(path.input.get(), path.output);
    }

    /** Override this to prevent considering a path before it's complete */
    protected boolean acceptPartialPath(FSTPath<T> path) {
      return true;
    }

    protected boolean acceptResult(IntsRef input, T output) {
      return true;
    }
  }

  /** Holds a single input (IntsRef) + output, returned by
   *  {@link #shortestPaths shortestPaths()}. */
  public final static class Result<T> {
    public final IntsRef input;
    public final T output;
    public Result(IntsRef input, T output) {
      this.input = input;
      this.output = output;
    }
  }


  /**
   * Holds the results for a top N search using {@link TopNSearcher}
   */
  public static final class TopResults<T> implements Iterable<Result<T>> {

    /**
     * <code>true</code> iff this is a complete result ie. if
     * the specified queue size was large enough to find the complete list of results. This might
     * be <code>false</code> if the {@link TopNSearcher} rejected too many results.
     */
    public final boolean isComplete;
    /**
     * The top results
     */
    public final List<Result<T>> topN;

    TopResults(boolean isComplete, List<Result<T>> topN) {
      this.topN = topN;
      this.isComplete = isComplete;
    }

    @Override
    public Iterator<Result<T>> iterator() {
      return topN.iterator();
    }
  }


  /** Starting from node, find the top N min cost 
   *  completions to a final node. */
  public static <T> TopResults<T> shortestPaths(FST<T> fst, FST.Arc<T> fromNode, T startOutput, Comparator<T> comparator, int topN,
                                                 boolean allowEmptyString) throws IOException {

    // All paths are kept, so we can pass topN for
    // maxQueueDepth and the pruning is admissible:
    TopNSearcher<T> searcher = new TopNSearcher<>(fst, topN, topN, comparator);

    // since this search is initialized with a single start node 
    // it is okay to start with an empty input path here
    searcher.addStartPaths(fromNode, startOutput, allowEmptyString, new IntsRefBuilder());
    return searcher.search();
  } 

  /**
   * Dumps an {@link FST} to a GraphViz's <code>dot</code> language description
   * for visualization. Example of use:
   * 
   * <pre class="prettyprint">
   * PrintWriter pw = new PrintWriter(&quot;out.dot&quot;);
   * Util.toDot(fst, pw, true, true);
   * pw.close();
   * </pre>
   * 
   * and then, from command line:
   * 
   * <pre>
   * dot -Tpng -o out.png out.dot
   * </pre>
   * 
   * <p>
   * Note: larger FSTs (a few thousand nodes) won't even
   * render, don't bother.
   * 
   * @param sameRank
   *          If <code>true</code>, the resulting <code>dot</code> file will try
   *          to order states in layers of breadth-first traversal. This may
   *          mess up arcs, but makes the output FST's structure a bit clearer.
   * 
   * @param labelStates
   *          If <code>true</code> states will have labels equal to their offsets in their
   *          binary format. Expands the graph considerably. 
   * 
   * @see <a href="http://www.graphviz.org/">graphviz project</a>
   */
  public static <T> void toDot(FST<T> fst, Writer out, boolean sameRank, boolean labelStates) 
    throws IOException {    
    final String expandedNodeColor = "blue";

    // This is the start arc in the automaton (from the epsilon state to the first state 
    // with outgoing transitions.
    final FST.Arc<T> startArc = fst.getFirstArc(new FST.Arc<>());

    // A queue of transitions to consider for the next level.
    final List<FST.Arc<T>> thisLevelQueue = new ArrayList<>();

    // A queue of transitions to consider when processing the next level.
    final List<FST.Arc<T>> nextLevelQueue = new ArrayList<>();
    nextLevelQueue.add(startArc);
    //System.out.println("toDot: startArc: " + startArc);
    
    // A list of states on the same level (for ranking).
    final List<Integer> sameLevelStates = new ArrayList<>();

    // A bitset of already seen states (target offset).
    final BitSet seen = new BitSet();
    seen.set((int) startArc.target());

    // Shape for states.
    final String stateShape = "circle";
    final String finalStateShape = "doublecircle";

    // Emit DOT prologue.
    out.write("digraph FST {\n");
    out.write("  rankdir = LR; splines=true; concentrate=true; ordering=out; ranksep=2.5; \n");

    if (!labelStates) {
      out.write("  node [shape=circle, width=.2, height=.2, style=filled]\n");      
    }

    emitDotState(out, "initial", "point", "white", "");

    final T NO_OUTPUT = fst.outputs.getNoOutput();
    final BytesReader r = fst.getBytesReader();

    // final FST.Arc<T> scratchArc = new FST.Arc<>();

    {
      final String stateColor;
      if (fst.isExpandedTarget(startArc, r)) {
        stateColor = expandedNodeColor;
      } else {
        stateColor = null;
      }

      final boolean isFinal;
      final T finalOutput;
      if (startArc.isFinal()) {
        isFinal = true;
        finalOutput = startArc.nextFinalOutput() == NO_OUTPUT ? null : startArc.nextFinalOutput();
      } else {
        isFinal = false;
        finalOutput = null;
      }
      
      emitDotState(out, Long.toString(startArc.target()), isFinal ? finalStateShape : stateShape, stateColor, finalOutput == null ? "" : fst.outputs.outputToString(finalOutput));
    }

    out.write("  initial -> " + startArc.target() + "\n");

    int level = 0;

    while (!nextLevelQueue.isEmpty()) {
      // we could double buffer here, but it doesn't matter probably.
      //System.out.println("next level=" + level);
      thisLevelQueue.addAll(nextLevelQueue);
      nextLevelQueue.clear();

      level++;
      out.write("\n  // Transitions and states at level: " + level + "\n");
      while (!thisLevelQueue.isEmpty()) {
        final FST.Arc<T> arc = thisLevelQueue.remove(thisLevelQueue.size() - 1);
        //System.out.println("  pop: " + arc);
        if (FST.targetHasArcs(arc)) {
          // scan all target arcs
          //System.out.println("  readFirstTarget...");

          final long node = arc.target();

          fst.readFirstRealTargetArc(arc.target(), arc, r);

          //System.out.println("    firstTarget: " + arc);

          while (true) {

            //System.out.println("  cycle arc=" + arc);
            // Emit the unseen state and add it to the queue for the next level.
            if (arc.target() >= 0 && !seen.get((int) arc.target())) {

              /*
              boolean isFinal = false;
              T finalOutput = null;
              fst.readFirstTargetArc(arc, scratchArc);
              if (scratchArc.isFinal() && fst.targetHasArcs(scratchArc)) {
                // target is final
                isFinal = true;
                finalOutput = scratchArc.output == NO_OUTPUT ? null : scratchArc.output;
                System.out.println("dot hit final label=" + (char) scratchArc.label);
              }
              */
              final String stateColor;
              if (fst.isExpandedTarget(arc, r)) {
                stateColor = expandedNodeColor;
              } else {
                stateColor = null;
              }

              final String finalOutput;
              if (arc.nextFinalOutput() != null && arc.nextFinalOutput() != NO_OUTPUT) {
                finalOutput = fst.outputs.outputToString(arc.nextFinalOutput());
              } else {
                finalOutput = "";
              }

              emitDotState(out, Long.toString(arc.target()), stateShape, stateColor, finalOutput);
              // To see the node address, use this instead:
              //emitDotState(out, Integer.toString(arc.target), stateShape, stateColor, String.valueOf(arc.target));
              seen.set((int) arc.target());
              nextLevelQueue.add(new FST.Arc<T>().copyFrom(arc));
              sameLevelStates.add((int) arc.target());
            }

            String outs;
            if (arc.output() != NO_OUTPUT) {
              outs = "/" + fst.outputs.outputToString(arc.output());
            } else {
              outs = "";
            }

            if (!FST.targetHasArcs(arc) && arc.isFinal() && arc.nextFinalOutput() != NO_OUTPUT) {
              // Tricky special case: sometimes, due to
              // pruning, the builder can [sillily] produce
              // an FST with an arc into the final end state
              // (-1) but also with a next final output; in
              // this case we pull that output up onto this
              // arc
              outs = outs + "/[" + fst.outputs.outputToString(arc.nextFinalOutput()) + "]";
            }

            final String arcColor;
            if (arc.flag(FST.BIT_TARGET_NEXT)) {
              arcColor = "red";
            } else {
              arcColor = "black";
            }

            assert arc.label() != FST.END_LABEL;
            out.write("  " + node + " -> " + arc.target() + " [label=\"" + printableLabel(arc.label()) + outs + "\"" + (arc.isFinal() ? " style=\"bold\"" : "" ) + " color=\"" + arcColor + "\"]\n");
                   
            // Break the loop if we're on the last arc of this state.
            if (arc.isLast()) {
              //System.out.println("    break");
              break;
            }
            fst.readNextRealArc(arc, r);
          }
        }
      }

      // Emit state ranking information.
      if (sameRank && sameLevelStates.size() > 1) {
        out.write("  {rank=same; ");
        for (int state : sameLevelStates) {
          out.write(state + "; ");
        }
        out.write(" }\n");
      }
      sameLevelStates.clear();                
    }

    // Emit terminating state (always there anyway).
    out.write("  -1 [style=filled, color=black, shape=doublecircle, label=\"\"]\n\n");
    out.write("  {rank=sink; -1 }\n");
    
    out.write("}\n");
    out.flush();
  }

  /**
   * Emit a single state in the <code>dot</code> language. 
   */
  private static void emitDotState(Writer out, String name, String shape,
      String color, String label) throws IOException {
    out.write("  " + name 
        + " [" 
        + (shape != null ? "shape=" + shape : "") + " "
        + (color != null ? "color=" + color : "") + " "
        + (label != null ? "label=\"" + label + "\"" : "label=\"\"") + " "
        + "]\n");
  }

  /**
   * Ensures an arc's label is indeed printable (dot uses US-ASCII). 
   */
  private static String printableLabel(int label) {
    // Any ordinary ascii character, except for " or \, are
    // printed as the character; else, as a hex string:
    if (label >= 0x20 && label <= 0x7d && label != 0x22 && label != 0x5c) {  // " OR \
      return Character.toString((char) label);
    }
    return "0x" + Integer.toHexString(label);
  }

  /** Just maps each UTF16 unit (char) to the ints in an
   *  IntsRef. */
  public static IntsRef toUTF16(CharSequence s, IntsRefBuilder scratch) {
    final int charLimit = s.length();
    scratch.setLength(charLimit);
    scratch.grow(charLimit);
    for (int idx = 0; idx < charLimit; idx++) {
      scratch.setIntAt(idx, (int) s.charAt(idx));
    }
    return scratch.get();
  }    

  /** Decodes the Unicode codepoints from the provided
   *  CharSequence and places them in the provided scratch
   *  IntsRef, which must not be null, returning it. */
  public static IntsRef toUTF32(CharSequence s, IntsRefBuilder scratch) {
    int charIdx = 0;
    int intIdx = 0;
    final int charLimit = s.length();
    while(charIdx < charLimit) {
      scratch.grow(intIdx+1);
      final int utf32 = Character.codePointAt(s, charIdx);
      scratch.setIntAt(intIdx, utf32);
      charIdx += Character.charCount(utf32);
      intIdx++;
    }
    scratch.setLength(intIdx);
    return scratch.get();
  }

  /** Decodes the Unicode codepoints from the provided
   *  char[] and places them in the provided scratch
   *  IntsRef, which must not be null, returning it. */
  public static IntsRef toUTF32(char[] s, int offset, int length, IntsRefBuilder scratch) {
    int charIdx = offset;
    int intIdx = 0;
    final int charLimit = offset + length;
    while(charIdx < charLimit) {
      scratch.grow(intIdx+1);
      final int utf32 = Character.codePointAt(s, charIdx, charLimit);
      scratch.setIntAt(intIdx, utf32);
      charIdx += Character.charCount(utf32);
      intIdx++;
    }
    scratch.setLength(intIdx);
    return scratch.get();
  }

  /** Just takes unsigned byte values from the BytesRef and
   *  converts into an IntsRef. */
  public static IntsRef toIntsRef(BytesRef input, IntsRefBuilder scratch) {
    scratch.clear();
    for(int i=0;i<input.length;i++) {
      scratch.append(input.bytes[i+input.offset] & 0xFF);
    }
    return scratch.get();
  }

  /** Just converts IntsRef to BytesRef; you must ensure the
   *  int values fit into a byte. */
  public static BytesRef toBytesRef(IntsRef input, BytesRefBuilder scratch) {
    scratch.grow(input.length);
    for(int i=0;i<input.length;i++) {
      int value = input.ints[i+input.offset];
      // NOTE: we allow -128 to 255
      assert value >= Byte.MIN_VALUE && value <= 255: "value " + value + " doesn't fit into byte";
      scratch.setByteAt(i, (byte) value);
    }
    scratch.setLength(input.length);
    return scratch.get();
  }

  // Uncomment for debugging:

  /*
  public static <T> void dotToFile(FST<T> fst, String filePath) throws IOException {
    Writer w = new OutputStreamWriter(new FileOutputStream(filePath));
    toDot(fst, w, true, true);
    w.close();
  }
  */

  /**
   * Reads the first arc greater or equal than the given label into the provided
   * arc in place and returns it iff found, otherwise return <code>null</code>.
   * 
   * @param label the label to ceil on
   * @param fst the fst to operate on
   * @param follow the arc to follow reading the label from
   * @param arc the arc to read into in place
   * @param in the fst's {@link BytesReader}
   */
  public static <T> Arc<T> readCeilArc(int label, FST<T> fst, Arc<T> follow, Arc<T> arc, BytesReader in) throws IOException {
    if (label == FST.END_LABEL) {
      return FST.readEndArc(follow, arc);
    }
    if (!FST.targetHasArcs(follow)) {
      return null;
    }
    fst.readFirstTargetArc(follow, arc, in);
    if (arc.bytesPerArc() != 0 && arc.label() != FST.END_LABEL) {
      if (arc.nodeFlags() == FST.ARCS_FOR_DIRECT_ADDRESSING) {
        // Fixed length arcs in a direct addressing node.
        int targetIndex = label - arc.label();
        if (targetIndex >= arc.numArcs()) {
          return null;
        } else if (targetIndex < 0) {
          return arc;
        } else {
          if (BitTable.isBitSet(targetIndex, arc, in)) {
            fst.readArcByDirectAddressing(arc, in, targetIndex);
            assert arc.label() == label;
          } else {
            int ceilIndex = BitTable.nextBitSet(targetIndex, arc, in);
            assert ceilIndex != -1;
            fst.readArcByDirectAddressing(arc, in, ceilIndex);
            assert arc.label() > label;
          }
          return arc;
        }
      }
      // Fixed length arcs in a binary search node.
      int idx = binarySearch(fst, arc, label);
      if (idx >= 0) {
        return fst.readArcByIndex(arc, in, idx);
      }
      idx = -1 - idx;
      if (idx == arc.numArcs()) {
        // DEAD END!
        return null;
      }
      return fst.readArcByIndex(arc, in , idx);
    }

    // Variable length arcs in a linear scan list,
    // or special arc with label == FST.END_LABEL.
    fst.readFirstRealTargetArc(follow.target(), arc, in);

    while (true) {
      // System.out.println("  non-bs cycle");
      // TODO: we should fix this code to not have to create
      // object for the output of every arc we scan... only
      // for the matching arc, if found
      if (arc.label() >= label) {
        // System.out.println("    found!");
        return arc;
      } else if (arc.isLast()) {
        return null;
      } else {
        fst.readNextRealArc(arc, in);
      }
    }
  }

  /**
   * Perform a binary search of Arcs encoded as a packed array
   * @param fst the FST from which to read
   * @param arc the starting arc; sibling arcs greater than this will be searched. Usually the first arc in the array.
   * @param targetLabel the label to search for
   * @param <T> the output type of the FST
   * @return the index of the Arc having the target label, or if no Arc has the matching label, {@code -1 - idx)},
   * where {@code idx} is the index of the Arc with the next highest label, or the total number of arcs
   * if the target label exceeds the maximum.
   * @throws IOException when the FST reader does
   */
  static <T> int binarySearch(FST<T> fst, FST.Arc<T> arc, int targetLabel) throws IOException {
    assert arc.nodeFlags() == FST.ARCS_FOR_BINARY_SEARCH : "Arc is not encoded as packed array for binary search (nodeFlags=" + arc.nodeFlags() + ")";
    BytesReader in = fst.getBytesReader();
    int low = arc.arcIdx();
    int mid = 0;
    int high = arc.numArcs() -1;
    while (low <= high) {
      mid = (low + high) >>> 1;
      in.setPosition(arc.posArcsStart());
      in.skipBytes(arc.bytesPerArc() * mid + 1);
      final int midLabel = fst.readLabel(in);
      final int cmp = midLabel - targetLabel;
      if (cmp < 0) {
        low = mid + 1;
      } else if (cmp > 0) {
        high = mid - 1;
      } else {
        return mid;
      }
    }
    return -1 - low;
  }
}