public PartitionResultWrapper Partition(LBT lbt, Segment S_l, Segment S_r, PartitionClass P_l, PartitionClass P_r, RelationTreeNode TLEFT, RelationTreeNode BLEFT)
        {
            PartitionResult R = new PartitionResult();

            if (TLEFT != null)
            {
                foreach (Stroke s in TLEFT.strokes)
                {
                    R.TLEFT.strokes.Add(s);
                }
            }
            if (BLEFT != null)
            {
                foreach (Stroke s in BLEFT.strokes)
                {
                    R.BLEFT.strokes.Add(s);
                }
            }

            // Handle no right/left symbol.
            if (S_l == null && S_r == null)
            {
                throw new ArgumentException("Partition:: both passed segments are null.");
            }

            // y-writing-line hack
            if (S_l != null && (S_l.classification[0].symbol == "y" || S_l.classification[0].symbol == "\\log" || S_l.classification[0].symbol == "\\tan"))
            {
                P_l = PartitionClass.Regular;                 // if not already?
                int[] lines = GetCenteredLines(S_l);
                S_l.bb.Top    = lines[0];
                S_l.bb.Bottom = lines[1];
            }

            // Case for no right symbol (and default; symbols at left of current symbol).
            //List< Stroke > SP = S_r == null ? lbt.strokes : lbt.strokes.Where( _s => { if ( _s.aabb.Left < S_r.bb.Left ) { Console.WriteLine( "{0} < {1} (!)", _s.aabb.Left, S_r.bb.Left ); return true; } else { return false; } } ).ToList();
            List <Stroke> SP = new List <Stroke>();

            if (S_r == null)
            {
                SP = lbt.strokes;
            }
            else
            {
                // foreach ( Stroke _s in lbt.strokes ) {
                for (int i = 0; i < lbt.strokes.Count; i++)
                {
                    Stroke _s = lbt.strokes[i];
                    if (_s.aabb.Right /*Left?*/ < S_r.bb.Left)
                    {
                        //Console.WriteLine( "{0} < {1} (!)", _s.aabb.Left, S_r.bb.Left );
                        SP.Add(_s);
                    }
                }
            }

            // Case for no left symbol; switch right to "left" symbol.

            bool noLeft = false;

            if (S_l == null)
            {
                S_l    = S_r;
                SP     = lbt.strokes.Where(_s => _s.aabb.Right < S_r.bb.Left).ToList();
                noLeft = true;
            }

            // HACK.
            bool indexed = S_l != null && (S_l.classification[0].symbol == "\\sum" || S_l.classification[0].symbol == "\\int" ||
                                           S_l.classification[0].symbol == "\\lim");

            foreach (Stroke _s in SP)
            {
                if (S_l != null && !noLeft)
                {
                    bool horOverlap = !(S_l.bb.Right < _s.aabb.Left || _s.aabb.Right < S_l.bb.Left);
                    bool fullContained = S_l.bb.Left <_s.aabb.Left && S_l.bb.Right> _s.aabb.Right &&
                                         S_l.bb.Top <_s.aabb.Top && S_l.bb.Bottom> _s.aabb.Bottom;

                    float midRight = S_l.bb.Top + (S_l.bb.Height / 2);
                    float dtop     = midRight - _s.aabb.Top;
                    float dbottom  = _s.aabb.Bottom - midRight;

                    //float topSpan = Math.Min( Math.Abs( S_l.bb.Top - _s.aabb.Bottom ), Math.Abs( midRight - _s.aabb.Top ) );
                    //float bottomSpan = Math.Min( Math.Abs( S_l.bb.Bottom - _s.aabb.Top ), Math.Abs( midRight - _s.aabb.Bottom ) );

                    // Be lenient here; invalid partitions will be pruned
                    bool added = false;
                    if (P_l == PartitionClass.SquareRoot && fullContained)
                    {
                        R.CONTAINS.strokes.Add(_s);
                        added = true;
                    }
                    else if (/*P_l == PartitionClass.HorLine &&*/ horOverlap)
                    {
                        /*
                         *                      if ( _s.aabb.Bottom <= S_l.bb.Top ) {
                         *                              R.ABOVE.strokes.Add( _s );
                         *                              added = true;
                         *                      } else if ( _s.aabb.Top > S_l.bb.Bottom ) {
                         *                              R.BELOW.strokes.Add( _s );
                         *                              added = true;
                         *                      }
                         */

                        // "less strict" constraints on top/bottom
                        if (_s.aabb.Top < S_l.bb.Top && _s.aabb.Bottom <= S_l.bb.Bottom)
                        {
                            R.ABOVE.strokes.Add(_s);
                            added = true;
                        }
                        else if (_s.aabb.Bottom > S_l.bb.Bottom && _s.aabb.Top >= S_l.bb.Top)
                        {
                            R.BELOW.strokes.Add(_s);
                            added = true;
                        }
                    }
                    else if (dtop > dbottom)
                    {
                        R.SUPER.strokes.Add(_s);
                        added = true;
                    }
                    else
                    {
                        R.SUBSC.strokes.Add(_s);
                        added = true;
                    }
#if DEBUG
                    if (!added)
                    {
                        Console.Error.WriteLine("Stroke ({0}) did not get partitioned in {1}.", _s, S_l);
                    }
#endif
                }
                else
                {
                    // HACK** There is nothing at left. Create TLEFT/BLEFT regions.
                    double midPoint = (S_r.bb.Top + S_r.bb.Bottom) / 2.0;
                    if (_s.aabb.Bottom <= midPoint)
                    {
                        R.TLEFT.strokes.Add(_s);
                    }
                    else if (_s.aabb.Top > midPoint)
                    {
                        R.BLEFT.strokes.Add(_s);
                    }
                }
            }

            // split SUPER/SUBSC by finding maximum gap location
            if (S_l != null && S_r != null)
            {
                float super_gap = MaximumGapLocation(R.SUPER.strokes, S_l, S_r);
                float subsc_gap = MaximumGapLocation(R.SUBSC.strokes, S_l, S_r);

                // super
                foreach (Stroke s in R.SUPER.strokes)
                {
                    if (s.aabb.Left > super_gap)
                    {
                        R.TLEFT.strokes.Add(s);
                    }
                }
                foreach (Stroke s in R.TLEFT.strokes)
                {
                    if (R.SUPER.strokes.Contains(s))
                    {
                        R.SUPER.strokes.Remove(s);
                    }
                }

                // subsc
                foreach (Stroke s in R.SUBSC.strokes)
                {
                    if (s.aabb.Left > subsc_gap)
                    {
                        R.BLEFT.strokes.Add(s);
                    }
                }
                foreach (Stroke s in R.BLEFT.strokes)
                {
                    if (R.SUBSC.strokes.Contains(s))
                    {
                        R.SUBSC.strokes.Remove(s);
                    }
                }
            }

            // if nosupersub, add super/sub to TLEFT/BLEFT
            if (P_l == PartitionClass.HorLine)
            {
                foreach (Stroke s in R.SUPER.strokes)
                {
                    R.TLEFT.strokes.Add(s);
                }
                R.SUPER.strokes.Clear();

                foreach (Stroke s in R.SUBSC.strokes)
                {
                    R.BLEFT.strokes.Add(s);
                }
                R.SUBSC.strokes.Clear();
            }

            // Create LBTs.
            R.ABOVE.lbt    = new LBT(R.ABOVE.strokes, LBT.DefaultAdjacentCriterion);
            R.BELOW.lbt    = new LBT(R.BELOW.strokes, LBT.DefaultAdjacentCriterion);
            R.CONTAINS.lbt = new LBT(R.CONTAINS.strokes, LBT.DefaultAdjacentCriterion);
            R.SUPER.lbt    = new LBT(R.SUPER.strokes, LBT.DefaultAdjacentCriterion);
            R.SUBSC.lbt    = new LBT(R.SUBSC.strokes, LBT.DefaultAdjacentCriterion);
            R.TLEFT.lbt    = new LBT(R.TLEFT.strokes, LBT.DefaultAdjacentCriterion);
            R.BLEFT.lbt    = new LBT(R.BLEFT.strokes, LBT.DefaultAdjacentCriterion);

            // combine above/super/tleft and below/subsc/bleft for horline
            if (indexed)
            {
                if (R.ABOVE.strokes.Count > 0 && (R.SUPER.strokes.Count > 0 || R.TLEFT.strokes.Count > 0))
                {
                    foreach (Stroke s in R.SUPER.strokes)
                    {
                        R.ABOVE.strokes.Add(s);
                    }
                    R.SUPER.strokes.Clear();
                    R.SUPER.lbt = new LBT(R.SUPER.strokes, LBT.DefaultAdjacentCriterion);

                    foreach (Stroke s in R.TLEFT.strokes)
                    {
                        R.ABOVE.strokes.Add(s);
                    }
                    R.TLEFT.strokes.Clear();
                    R.TLEFT.lbt = new LBT(R.TLEFT.strokes, LBT.DefaultAdjacentCriterion);

                    R.ABOVE.strokes.Sort((s1, s2) => int.Parse(s1.stroke_id) - int.Parse(s2.stroke_id));
                    R.ABOVE.lbt = new LBT(R.ABOVE.strokes, LBT.DefaultAdjacentCriterion);
                }
                if (R.BELOW.strokes.Count > 0 && (R.SUBSC.strokes.Count > 0 || R.BLEFT.strokes.Count > 0))
                {
                    foreach (Stroke s in R.SUBSC.strokes)
                    {
                        R.BELOW.strokes.Add(s);
                    }
                    R.SUBSC.strokes.Clear();
                    R.SUBSC.lbt = new LBT(R.SUBSC.strokes, LBT.DefaultAdjacentCriterion);

                    foreach (Stroke s in R.BLEFT.strokes)
                    {
                        R.BELOW.strokes.Add(s);
                    }
                    R.BLEFT.strokes.Clear();
                    R.BLEFT.lbt = new LBT(R.BLEFT.strokes, LBT.DefaultAdjacentCriterion);

                    R.BELOW.strokes.Sort((s1, s2) => int.Parse(s1.stroke_id) - int.Parse(s2.stroke_id));
                    R.BELOW.lbt = new LBT(R.BELOW.strokes, LBT.DefaultAdjacentCriterion);
                }
            }


            //Console.WriteLine("SUPER STROKES: {0}",R.SUPER.lbt.strokes.Count);

            return(new PartitionResultWrapper(R, UpdateLBT(new Segment {
                strokes = SP
            }, lbt)));
            //lbt = UpdateLBT( new Segment { strokes = SP }, lbt ) };
        }
        public void applyRules(List <ParseTreeNode> arg_nlist)
        {
#if DEBUG
            Console.WriteLine("[applyRules] entered.");
            treeRoot.ShowTree(4, null);
            Console.WriteLine("Min Required Strokes: " + minRequiredStrokes);
            Console.WriteLine("Call: " + apply_rule_counter);
#else
            //Console.Write(apply_rule_counter);
            //Console.Write('\r');
#endif
            // increment counter
            apply_rule_counter++;
            if (arg_nlist.Count == 0)
            {
                return;
            }
            if (unusedStrokes < 1 && arg_nlist[0] != ParseTreeNode.EndOfBaseline && !(arg_nlist[0] is RelationTreeNode))
            {
                return;
            }

            // if ( unusedStrokes > 0 && !( arg_nlist[ 0 ].GetType().Equals( typeof( ParseTreeNode ) ) ) ) return;

            List <ParseTreeNode> nlist = new List <ParseTreeNode>(arg_nlist);
            ParseTreeNode        n     = nlist[0];
            nlist.RemoveAt(0);

            if (n == ParseTreeNode.EndOfBaseline)
            {
                // END-OF-BASELINE CASE


                PartitionResultWrapper pr = attachSymbol(currentSymbol.symbol.lbt, null);

                // continue only if valid partition made
                if (pr != null)
                {
                    if (nlist.Count == 0 && unusedStrokes == 0 && unusedInputStrokes == 0)
                    {
#if DEBUG
                        Console.WriteLine("***ACCEPT***");
#endif
                        acceptCurrentParseTree();
                    }

                    int nodes_added = nlist.Count;

                    if (pr.result != null && pr.result.ABOVE.lbt.strokes.Count != 0)
                    {
                        nlist.Add(pr.result.ABOVE);
                    }
                    if (pr.result != null && pr.result.BELOW.lbt.strokes.Count != 0)
                    {
                        nlist.Add(pr.result.BELOW);
                    }
                    if (pr.result != null && pr.result.CONTAINS.lbt.strokes.Count != 0)
                    {
                        nlist.Add(pr.result.CONTAINS);
                    }
                    if (pr.result != null && pr.result.SUBSC.lbt.strokes.Count != 0)
                    {
                        nlist.Add(pr.result.SUBSC);
                    }
                    if (pr.result != null && pr.result.SUPER.lbt.strokes.Count != 0)
                    {
                        nlist.Add(pr.result.SUPER);
                    }

                    // add BLEFT/TLEFT
                    //if ( pr.result != null && pr.result.BLEFT.lbt.strokes.Count != 0 ) nlist.Add( pr.result.BLEFT );
                    //if ( pr.result != null && pr.result.TLEFT.lbt.strokes.Count != 0 ) nlist.Add( pr.result.TLEFT );

                    nodes_added         = nlist.Count - nodes_added;
                    minRequiredStrokes += nodes_added;

                    applyRules(nlist);
                }
                else
                {
#if DEBUG
                    Console.WriteLine("**BACKTRACK: end-of-baseline, invalid partition");
#endif
                }
            }
            else if (n is RelationTreeNode)
            {
                // handle relation nodes by adding new parse tree node
                RelationTreeNode rtn = n as RelationTreeNode;
                ParseTreeNode    ptn = new ParseTreeNode();
                ptn.strokes  = rtn.strokes;
                ptn.nodeType = rtn.nodeType;
                // increment here for new production
                ptn.lbt = rtn.lbt;
                rtn.children.Clear();                 // remove all before
                rtn.children.Add(ptn);
                parse(ptn.lbt, ptn, nlist);
            }
            else if (n.nodeType.StartsWith("*"))
            {             // if n generates terminal symbols
                List <LexerResult> C = SelectCandidateSymbols(n.nodeType);
                //candidateSymbols = C;
                foreach (LexerResult c in C)
                {
                    PartitionResultWrapper pr = attachSymbol(currentSymbol == null ? initLBT : currentSymbol.symbol.lbt, c);
                    if (pr != null)
                    {
                        pushCurrentState();

                        // update current state
                        currentSymbol       = new PreviousSymbol(c, n, null, null, true);
                        unusedStrokes      -= currentSymbol.symbol.segment.strokes.Count;
                        unusedInputStrokes -= currentSymbol.symbol.segment.strokes.Count;
                        // remove one of the min required strokes for the current token
                        minRequiredStrokes -= 1;

                        // prune by  number of strokes left
                        if (unusedInputStrokes < minRequiredStrokes)
                        {
                            popCurrentState();
                            return;                             // continue;
                        }

                        List <string> layoutClasses = grammar.GetLayoutClassesFromTerminal(c.segment.classification[0].symbol);

                        if (layoutClasses.Count == 0)
                        {
                            continue;
                        }

                        candidateSymbols = new List <LexerResult>();
                        foreach (string layoutClass in layoutClasses)
                        {
                            List <LexerResult> res = lexer.Next(c.lbt, c.segment, layoutClass, MAX_NEIGHBORS);
                            foreach (LexerResult r in res)
                            {
                                if (!candidateSymbols.Contains(r))
                                {
                                    candidateSymbols.Add(r);
                                }
                            }
                        }


                        if (candidateSymbols.Count == 0 && !nlist.Contains(ParseTreeNode.EndOfBaseline))
                        {
                            nlist.Insert(0, ParseTreeNode.EndOfBaseline);
                        }
                        // not end of baseline, so prune and backtrack if necessary
                        else if (nlist.Count > 0 && (nlist[0] is RelationTreeNode == false))
                        {
                            // prune candidates based on the current node type
                            foreach (LexerResult lr in candidateSymbols)
                            {
                                for (int k = 0; k < lr.segment.classification.Count; k++)
                                {
                                    if (grammar.NonTerminalCanGenerateTerminal(nlist[0].nodeType, lr.segment.classification[k].symbol) == false)
                                    {
                                        lr.segment.classification.RemoveAt(k--);
                                    }
                                }
                            }
                            // remove candidate symbols which contain no symbol alternatives
                            for (int k = 0; k < candidateSymbols.Count; k++)
                            {
                                if (candidateSymbols[k].segment.classification.Count == 0)
                                {
                                    candidateSymbols.RemoveAt(k--);
                                }
                            }

                            // no valid symbols given the grammar, so bbreak out early
                            if (candidateSymbols.Count == 0)
                            {
                                popCurrentState();
                                return;                                 // continue;
                            }
                        }

                        SymbolTreeNode nc = new SymbolTreeNode(c);
                        n.children.Add(nc);

                        /*
                         * if ( nlist.Count == 0 && unusedStrokes == 0 ) {
                         *      if ( unusedInputStrokes == 0 ) acceptCurrentParseTree();
                         * } else {
                         */
                        // append relation nodes to the END

                        List <RelationTreeNode> nlist_rels = new List <RelationTreeNode>();
                        if (pr.result != null && pr.result.ABOVE.lbt.strokes.Count != 0)
                        {
                            nlist_rels.Add(pr.result.ABOVE);
                        }
                        if (pr.result != null && pr.result.BELOW.lbt.strokes.Count != 0)
                        {
                            nlist_rels.Add(pr.result.BELOW);
                        }
                        if (pr.result != null && pr.result.CONTAINS.lbt.strokes.Count != 0)
                        {
                            nlist_rels.Add(pr.result.CONTAINS);
                        }
                        if (pr.result != null && pr.result.SUBSC.lbt.strokes.Count != 0)
                        {
                            nlist_rels.Add(pr.result.SUBSC);
                        }
                        if (pr.result != null && pr.result.SUPER.lbt.strokes.Count != 0)
                        {
                            nlist_rels.Add(pr.result.SUPER);
                        }
                        //if ( pr.result != null && pr.result.BLEFT.lbt.strokes.Count != 0 ) nlist_rels.Add( pr.result.BLEFT );
                        //if ( pr.result != null && pr.result.TLEFT.lbt.strokes.Count != 0 ) nlist_rels.Add( pr.result.TLEFT );
                        foreach (RelationTreeNode rtn in nlist_rels)
                        {
                            nlist.Add(rtn);
                        }

                        minRequiredStrokes += nlist_rels.Count;

                        applyRules(nlist);
                        //}

                        if (nlist.Count > 0 && nlist[0] == ParseTreeNode.EndOfBaseline)
                        {
                            nlist.RemoveAt(0);                                                                                           // !
                        }
                        // remove any leftover relation nodes
                        n.children.Remove(nc);
                        List <ParseTreeNode> n_children_tmp = new List <ParseTreeNode>(n.children);
                        for (int i = 0; i < n_children_tmp.Count; i++)
                        {
                            if (n_children_tmp[i] is RelationTreeNode)
                            {
                                n.children.Remove(n_children_tmp[i]);
                            }
                        }

                        foreach (RelationTreeNode rtn in nlist_rels)
                        {
                            nlist.Remove(rtn);
                        }
                        popCurrentState();
                    }
                }
            }
            else
            {
                // NONTERMINALS
                //n.lexResult.segment.classification[0].symbol;
                List <string[]> productions = grammar.GetProductions(n.nodeType);
                if (productions == null)
                {
#if DEBUG
                    Console.Error.WriteLine("Error: invalid nonterminal ({0}).", n.nodeType);
#endif
                    return;
                }

                // remove one for the token we are replacing with productions
                minRequiredStrokes--;

                foreach (string[] production in productions)
                {
                    minRequiredStrokes += production.Length;

                    // prune by  number of strokes left
                    if (unusedInputStrokes < minRequiredStrokes)
                    {
                        minRequiredStrokes -= production.Length;
                        continue;
                    }

                    // prune based on the candidate symbols and the first rule in production
                    bool candidate_can_be_generated = false;
                    foreach (LexerResult lr in candidateSymbols)
                    {
                        foreach (Classification csf in lr.segment.classification)
                        {
                            if (grammar.NonTerminalCanGenerateTerminal(production[0], csf.symbol))
                            {
                                candidate_can_be_generated = true;
                                break;
                            }
                        }
                        if (candidate_can_be_generated)
                        {
                            break;
                        }
                    }

                    if (!candidate_can_be_generated)
                    {
                        minRequiredStrokes -= production.Length;
                        continue;
                    }


                    List <ParseTreeNode> nodes = new List <ParseTreeNode>();
                    foreach (string p in production)
                    {
                        ParseTreeNode n0 = new ParseTreeNode();
                        n0.nodeType  = p;
                        n0.lexResult = null;
                        nodes.Add(n0);
                        n.children.Add(n0);
                    }

                    for (int i = nodes.Count - 1; i >= 0; i--)
                    {
                        nlist.Insert(0, nodes[i]);
                    }
                    applyRules(nlist);

                    // restore min required strokes
                    minRequiredStrokes -= production.Length;

                    foreach (ParseTreeNode node in nodes)
                    {
                        n.children.Remove(node);
                        nlist.Remove(node);
                    }
                }
                minRequiredStrokes++;
            }
        }