source: branches/ralph/src/main/java/de/ugoe/cs/autoquest/tasktrees/temporalrelation/SequenceForTaskDetectionRuleAlignment.java @ 1553

//   Copyright 2012 Georg-August-Universität Göttingen, Germany
//
//   Licensed 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 de.ugoe.cs.autoquest.tasktrees.temporalrelation;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.logging.Level;

import de.ugoe.cs.autoquest.tasktrees.alignment.algorithms.NumberSequence;
import de.ugoe.cs.autoquest.tasktrees.taskequality.TaskEquality;
import de.ugoe.cs.autoquest.tasktrees.treeifc.IIteration;
import de.ugoe.cs.autoquest.tasktrees.treeifc.IIterationInstance;
import de.ugoe.cs.autoquest.tasktrees.treeifc.ISelection;
import de.ugoe.cs.autoquest.tasktrees.treeifc.ISelectionInstance;
import de.ugoe.cs.autoquest.tasktrees.treeifc.ISequence;
import de.ugoe.cs.autoquest.tasktrees.treeifc.ISequenceInstance;
import de.ugoe.cs.autoquest.tasktrees.treeifc.ITask;
import de.ugoe.cs.autoquest.tasktrees.treeifc.ITaskBuilder;
import de.ugoe.cs.autoquest.tasktrees.treeifc.ITaskFactory;
import de.ugoe.cs.autoquest.tasktrees.treeifc.ITaskInstance;
import de.ugoe.cs.autoquest.tasktrees.treeifc.ITaskInstanceList;
import de.ugoe.cs.autoquest.tasktrees.treeifc.IUserSession;
import de.ugoe.cs.autoquest.usageprofiles.SymbolMap;
import de.ugoe.cs.autoquest.usageprofiles.Trie;
import de.ugoe.cs.autoquest.usageprofiles.TrieProcessor;
import de.ugoe.cs.util.StopWatch;
import de.ugoe.cs.util.console.Console;

/**
 * <p>
 * This class implements the major rule for creating task trees based on a set of recorded
 * user sessions. For this, it first harmonizes all tasks. This eases later comparison. Then it
 * searches the sessions for iterations and replaces them accordingly. Then it searches for sub
 * sequences being the longest and occurring most often. For each found sub sequence, it replaces
 * the occurrences by creating appropriate {@link ISequence}s. Afterwards, again searches for
 * iterations and then again for sub sequences until no more replacements are done.
 * </p>
 * <p>
 * For determining the longest sequence occurring most often, the implementation uses a 
 * {@link Trie}. The depth of the tree is initially 3. If the algorithm has a longest sequence
 * occurring most often whose length is equal to the depth of the trie, it recalculates the trie
 * with an increased depth. 
 * </p>
 * 
 * @author Patrick Harms
 */
class SequenceForTaskDetectionRuleAlignment implements ISessionScopeRule {
    
    /**
     * <p>
     * the task factory to be used for creating substructures for the temporal
     * relationships identified during rul application
     * </p>
     */
    private ITaskFactory taskFactory;
    /**
     * <p>
     * the task builder to be used for creating substructures for the temporal relationships
     * identified during rule application
     * </p>
     */
    private ITaskBuilder taskBuilder;

    /**
     * <p>
     * the task handling strategy to be used for comparing tasks for preparation, i.e., before
     * the tasks are harmonized
     * </p>
     */
    private TaskHandlingStrategy preparationTaskHandlingStrategy;
    
    /**
     * <p>
     * the task handling strategy to be used for comparing tasks during iteration detection an trie
     * generation, i.e., after the tasks are harmonized 
     * </p>
     */
    private TaskHandlingStrategy identityTaskHandlingStrategy;;
    
    
    private ArrayList<NumberSequence> numberseqs;
    
    /**
     * <p>
     * instantiates the rule and initializes it with a task equality to be considered when
     * comparing tasks as well as a task factory and builder to be used for creating task
     * structures.
     * </p>
     * 
     * @param minimalTaskEquality the task equality to be considered when comparing tasks
     * @param taskFactory         the task factory to be used for creating substructures
     * @param taskBuilder         the task builder to be used for creating substructures
     */
    
   
    SequenceForTaskDetectionRuleAlignment(TaskEquality minimalTaskEquality,
                                 ITaskFactory taskFactory,
                                 ITaskBuilder taskBuilder)
    {
        this.taskFactory = taskFactory;
        this.taskBuilder = taskBuilder;
        
        this.preparationTaskHandlingStrategy = new TaskHandlingStrategy(minimalTaskEquality);
        this.identityTaskHandlingStrategy = new TaskHandlingStrategy(TaskEquality.IDENTICAL);
        
    }

    /* (non-Javadoc)
     * @see java.lang.Object#toString()
     */
    @Override
    public String toString() {
        return "SequenceForTaskDetectionRuleAlignment";
    }

    /* (non-Javadoc)
     * @see de.ugoe.cs.autoquest.tasktrees.temporalrelation.ISessionScopeRule#apply(java.util.List)
     */
    @Override
    public RuleApplicationResult apply(List<IUserSession> sessions) {
        RuleApplicationData appData = new RuleApplicationData(sessions);
        numberseqs = new ArrayList<NumberSequence>();
        
        // this is the real rule application. Loop while something is replaced.
        harmonizeEventTaskInstancesModel(appData);
        
        
        //Hier mein kram hin
        /*do {
            System.out.println();
            
            appData.getStopWatch().start("whole loop");
            detectAndReplaceIterations(appData);

            appData.getStopWatch().start("task replacement");
            detectAndReplaceTasks(appData);
            appData.getStopWatch().stop("task replacement");
            appData.getStopWatch().stop("whole loop");
            
            //((TaskTreeNodeComparator) taskComparator).getStopWatch().dumpStatistics(System.out);
            //((TaskTreeNodeComparator) taskComparator).getStopWatch().reset();
            
            appData.getStopWatch().dumpStatistics(System.out);
            appData.getStopWatch().reset();
            
        }
        while (appData.detectedAndReplacedTasks());*/
        
        Console.println
            ("created " + appData.getResult().getNewlyCreatedTasks().size() +
             " new tasks and " + appData.getResult().getNewlyCreatedTaskInstances().size() +
             " appropriate instances\n");
        
        if ((appData.getResult().getNewlyCreatedTasks().size() > 0) ||
            (appData.getResult().getNewlyCreatedTaskInstances().size() > 0))
        {
            appData.getResult().setRuleApplicationStatus(RuleApplicationStatus.FINISHED);
        }
        
        return appData.getResult();
    }

    /**
     * <p>
     * harmonizes the event task instances by unifying tasks. This is done, as initially the
     * event tasks being equal with respect to the considered task equality are distinct objects.
     * The comparison of these distinct objects is more time consuming than comparing the object
     * references.
     * </p>
     *
     * @param appData the rule application data combining all data used for applying this rule
     */
    private void harmonizeEventTaskInstancesModel(RuleApplicationData appData) {
        Console.traceln(Level.INFO, "harmonizing task model of event task instances");
        appData.getStopWatch().start("harmonizing event tasks");

        SymbolMap<ITaskInstance, ITask> uniqueTasks =
            preparationTaskHandlingStrategy.createSymbolMap();
        TaskInstanceComparator comparator = preparationTaskHandlingStrategy.getTaskComparator();
        
        int unifiedTasks = 0;
        ITask task;
        List<IUserSession> sessions = appData.getSessions();
        int sessionNo = 0;
        for (IUserSession session : sessions) {
            Console.traceln(Level.FINE, "handling " + (++sessionNo) + ". " + session);
                NumberSequence templist = new NumberSequence(session.size()) ;
            
            for (int i = 0; i < session.size(); i++) {
                ITaskInstance taskInstance = session.get(i); 
                task = uniqueTasks.getValue(taskInstance);
                
                if (task == null) {
                    uniqueTasks.addSymbol(taskInstance, taskInstance.getTask());
                    templist.getSequence()[i]=taskInstance.getTask().getId();
                }
                else {
                    taskBuilder.setTask(taskInstance, task);
                        templist.getSequence()[i]=task.getId();
                    unifiedTasks++;
                }
            }
            
            comparator.clearBuffers();
        }
        
        appData.getStopWatch().stop("harmonizing event tasks");
        Console.traceln(Level.INFO, "harmonized " + unifiedTasks + " task occurrences (still " +
                        uniqueTasks.size() + " different tasks)");

        appData.getStopWatch().dumpStatistics(System.out);
        appData.getStopWatch().reset();
    }

    /**
     * <p>
     * searches for direct iterations of single tasks in all sequences and replaces them with
     * {@link IIteration}s, respectively appropriate instances. Also all single occurrences of
     * a task that is iterated somewhen are replaced with iterations to have again an efficient
     * way for task comparisons. 
     * </p>
     * 
     * @param appData the rule application data combining all data used for applying this rule
     */
    private void detectAndReplaceIterations(RuleApplicationData appData) {
        Console.traceln(Level.FINE, "detecting iterations");
        appData.getStopWatch().start("detecting iterations");
        
        List<IUserSession> sessions = appData.getSessions();
        
        Set<ITask> iteratedTasks = searchIteratedTasks(sessions);
        
        if (iteratedTasks.size() > 0) {
            replaceIterationsOf(iteratedTasks, sessions, appData);
        }
        
        appData.getStopWatch().stop("detecting iterations");
        Console.traceln(Level.INFO, "replaced " + iteratedTasks.size() + " iterated tasks");
    }

    /**
     * <p>
     * searches the provided sessions for task iterations. If a task is iterated, it is added
     * to the returned set.
     * </p>
     * 
     * @param the session to search for iterations in
     * 
     * @return a set of tasks being iterated somewhere
     */
    private Set<ITask> searchIteratedTasks(List<IUserSession> sessions) {
        Set<ITask> iteratedTasks = new HashSet<ITask>();
        for (IUserSession session : sessions) {
            for (int i = 0; i < (session.size() - 1); i++) {
                // we prepared the task instances to refer to unique tasks, if they are treated
                // as equal. Therefore, we just compare the identity of the tasks of the task
                // instances
                if (session.get(i).getTask() == session.get(i + 1).getTask()) {
                    iteratedTasks.add(session.get(i).getTask());
                }
            }
        }
        
        return iteratedTasks;
    }

    /**
     * <p>
     * replaces all occurrences of all tasks provided in the set with iterations
     * </p>
     *
     * @param iteratedTasks the tasks to be replaced with iterations
     * @param sessions      the sessions in which the tasks are to be replaced
     * @param appData       the rule application data combining all data used for applying this rule
     */
    private void replaceIterationsOf(Set<ITask>          iteratedTasks,
                                     List<IUserSession>  sessions,
                                     RuleApplicationData appData)
    {
        Map<ITask, IIteration> iterations = new HashMap<ITask, IIteration>();
        Map<IIteration, List<IIterationInstance>> iterationInstances =
                new HashMap<IIteration, List<IIterationInstance>>();
            
        for (ITask iteratedTask : iteratedTasks) {
            IIteration iteration = taskFactory.createNewIteration();
            iterations.put(iteratedTask, iteration);
            iterationInstances.put(iteration, new LinkedList<IIterationInstance>());
        }
        
        IIterationInstance iterationInstance;
        
        for (IUserSession session : sessions) {
            int index = 0;
            iterationInstance = null;

            while (index < session.size()) {
                // we prepared the task instances to refer to unique tasks, if they are treated
                // as equal. Therefore, we just compare the identity of the tasks of the task
                // instances
                ITask currentTask = session.get(index).getTask();
                IIteration iteration = iterations.get(currentTask);
                if (iteration != null) {
                    if ((iterationInstance == null) || (iterationInstance.getTask() != iteration))
                    {
                        iterationInstance = taskFactory.createNewTaskInstance(iteration);
                        iterationInstances.get(iteration).add(iterationInstance);
                        taskBuilder.addTaskInstance(session, index, iterationInstance);
                        index++;
                    }
                    
                    taskBuilder.addChild(iterationInstance, session.get(index));
                    taskBuilder.removeTaskInstance(session, index);
                }
                else {
                    if (iterationInstance != null) {
                        iterationInstance = null;
                    }
                    index++;
                }
            }
        }
        
        for (Map.Entry<IIteration, List<IIterationInstance>> entry : iterationInstances.entrySet())
        {
            harmonizeIterationInstancesModel(entry.getKey(), entry.getValue());
        }
    }

    /**
     * <p>
     * TODO clarify why this is done
     * </p>
     */
    private void harmonizeIterationInstancesModel(IIteration               iteration,
                                                  List<IIterationInstance> iterationInstances)
    {
        List<ITask> iteratedTaskVariants = new LinkedList<ITask>();
        TaskInstanceComparator comparator = preparationTaskHandlingStrategy.getTaskComparator();
        
        // merge the lexically different variants of iterated task to a unique list 
        for (IIterationInstance iterationInstance : iterationInstances) {
            for (ITaskInstance executionVariant : iterationInstance) {
                ITask candidate = executionVariant.getTask();
            
                boolean found = false;
                for (ITask taskVariant : iteratedTaskVariants) {
                    if (comparator.areLexicallyEqual(taskVariant, candidate)) {
                        taskBuilder.setTask(executionVariant, taskVariant);
                        found = true;
                        break;
                    }
                }
                
                if (!found) {
                    iteratedTaskVariants.add(candidate);
                }
            }
        }
        
        // if there are more than one lexically different variant of iterated tasks, adapt the
        // iteration model to be a selection of different variants. In this case also adapt
        // the generated iteration instances to correctly contain selection instances. If there
        // is only one variant of an iterated task, simply set this as the marked task of the
        // iteration. In this case, the instances can be preserved as is
        if (iteratedTaskVariants.size() > 1) {
            ISelection selection = taskFactory.createNewSelection();
            
            for (ITask variant : iteratedTaskVariants) {
                taskBuilder.addChild(selection, variant);
            }
            
            taskBuilder.setMarkedTask(iteration, selection);
            
            for (IIterationInstance instance : iterationInstances) {
                for (int i = 0; i < instance.size(); i++) {
                    ISelectionInstance selectionInstance =
                        taskFactory.createNewTaskInstance(selection);
                    taskBuilder.setChild(selectionInstance, instance.get(i));
                    taskBuilder.setTaskInstance(instance, i, selectionInstance);
                }
            }
        }
        else {
            taskBuilder.setMarkedTask(iteration, iteratedTaskVariants.get(0));
        }
    }

    /**
     * TODO go on commenting
     * @param appData the rule application data combining all data used for applying this rule
     */
    private void detectAndReplaceTasks(RuleApplicationData appData) {
        Console.traceln(Level.FINE, "detecting and replacing tasks");
        appData.getStopWatch().start("detecting tasks");
        
        getSequencesOccuringMostOften(appData);

        appData.getStopWatch().stop("detecting tasks");
        appData.getStopWatch().start("replacing tasks");
        
        replaceSequencesOccurringMostOften(appData);
        
        appData.getStopWatch().stop("replacing tasks");
        Console.traceln(Level.INFO, "detected and replaced " + appData.getLastFoundTasks().size() +
                        " tasks occuring " + appData.getLastFoundTasks().getOccurrenceCount() +
                        " times");
    }

    /**
     * @param appData the rule application data combining all data used for applying this rule
     */
    private void getSequencesOccuringMostOften(RuleApplicationData appData) {
        Console.traceln(Level.FINE, "determining most prominent tasks");

        Tasks tasks;
        boolean createNewTrie = (appData.getLastTrie() == null) ||
            appData.detectedAndReplacedTasks(); // tree has changed
        
        do {
            if (createNewTrie) {
                createNewTrie(appData);
            }
            
            MaxCountAndLongestTasksFinder finder = new MaxCountAndLongestTasksFinder();
            appData.getLastTrie().process(finder);
        
            tasks = finder.getFoundTasks();
            
            createNewTrie = false;
            
            for (List<ITaskInstance> task : tasks) {
                if (task.size() >= appData.getTrainedSequenceLength()) {
                    // Trie must be recreated with a longer sequence length to be sure that
                    // the found sequences occurring most often are found in their whole length
                    appData.setTrainedSequenceLength(appData.getTrainedSequenceLength() + 1);
                    createNewTrie = true;
                    break;
                }
            }
        }
        while (createNewTrie);
        
        // create a normal trie for comparison
        /*System.out.println("creating test trie for comparison");
        
        appData.getStopWatch().start("testtrie");
        Trie<ITaskInstance> trie = new Trie<ITaskInstance>(identityTaskComparator);
        
        for (IUserSession session : appData.getSessions()) {
            trie.train(session.getExecutedTasks(), appData.getTrainedSequenceLength());
        }
        
        appData.getStopWatch().stop("testtrie");
        
        MaxCountAndLongestTasksFinder finder = new MaxCountAndLongestTasksFinder();
        trie.process(finder);

        boolean allTasksEqual = finder.getFoundTasks().size() == tasks.size();
        
        allTasksEqual &= finder.getFoundTasks().occurrenceCount == tasks.occurrenceCount;
        
        for (List<ITaskInstance> task1 : finder.getFoundTasks()) {
            boolean foundTask = false;
            for (List<ITaskInstance> task2 : tasks) {
                boolean tasksEqual = false;
                if (task1.size() == task2.size()) {
                    tasksEqual = true;
                    for (int i = 0; i < task1.size(); i++) {
                        if (!identityTaskComparator.equals(task1.get(i).getTask(), task2.get(i).getTask()))
                        {
                            tasksEqual = false;
                        }
                    }
                }
                
                if (tasksEqual) {
                    foundTask = true;
                    break;
                }
            }
            
            if (!foundTask) {
                System.out.println("different is " + task1);
                allTasksEqual = false;
                break;
            }
        }
        
        if (!allTasksEqual) {
            System.out.println(finder.getFoundTasks());
            System.out.println(tasks);
            
            throw new IllegalArgumentException("both tries calculated different subsequences");
        }
        
        /*TrieStatisticsDumper dumper = new TrieStatisticsDumper();
        appData.getLastTrie().process(dumper);
        dumper.dumpCounters();*/
        
        appData.setLastFoundTasks(tasks);

        Console.traceln(Level.FINE, "found " + appData.getLastFoundTasks().size() + " tasks " +
                        "occurring " + appData.getLastFoundTasks().getOccurrenceCount() + " times");
    }

    /**
     * @param appData the rule application data combining all data used for applying this rule
     */
    private void createNewTrie(RuleApplicationData appData) {
        Console.traceln(Level.FINER, "training trie with a maximum sequence length of " +
                        appData.getTrainedSequenceLength());

        appData.getStopWatch().start("training trie");
        
        // we prepared the task instances to refer to unique tasks, if they are treated
        // as equal. Therefore, we just compare the identity of the tasks of the task
        // instances
        appData.setLastTrie(new TaskInstanceTrie(identityTaskHandlingStrategy));
    
        appData.getLastTrie().trainSessions
            (appData.getSessions(), appData.getTrainedSequenceLength());
        
        appData.getStopWatch().stop("training trie");
    }

    /**
     * @param appData the rule application data combining all data used for applying this rule
     */
    private void replaceSequencesOccurringMostOften(RuleApplicationData appData) {
        appData.detectedAndReplacedTasks(false);

        if ((appData.getLastFoundTasks().size() > 0) &&
            (appData.getLastFoundTasks().getOccurrenceCount() > 1))
        {
            Console.traceln(Level.FINER, "replacing tasks occurrences");

            for (List<ITaskInstance> task : appData.getLastFoundTasks()) {
                ISequence sequence = taskFactory.createNewSequence();
                
                Console.traceln(Level.FINEST, "replacing " + sequence.getId() + ": " + task);

                List<ISequenceInstance> sequenceInstances =
                    replaceTaskOccurrences(task, appData.getSessions(), sequence);
                
                harmonizeSequenceInstancesModel(sequence, sequenceInstances,task.size());
                appData.detectedAndReplacedTasks
                    (appData.detectedAndReplacedTasks() || (sequenceInstances.size() > 0));

                if (sequenceInstances.size() < appData.getLastFoundTasks().getOccurrenceCount()) {
                    Console.traceln(Level.FINE, sequence.getId() + ": replaced task only " +
                                    sequenceInstances.size() + " times instead of expected " +
                                    appData.getLastFoundTasks().getOccurrenceCount());
                }
            }
        }
        
    }

    /**
     *
     */
    private void harmonizeSequenceInstancesModel(ISequence               sequence,
                                                 List<ISequenceInstance> sequenceInstances,
                                                 int                     sequenceLength)
    {
        TaskInstanceComparator comparator = preparationTaskHandlingStrategy.getTaskComparator();
        
        // ensure for each subtask that lexically different variants are preserved
        for (int subTaskIndex = 0; subTaskIndex < sequenceLength; subTaskIndex++) {
            List<ITask> subTaskVariants = new LinkedList<ITask>();
            
            for (ISequenceInstance sequenceInstance : sequenceInstances) {
                ITask candidate = sequenceInstance.get(subTaskIndex).getTask();
                
                boolean found = false;
                
                for (int i = 0; i < subTaskVariants.size(); i++) {
                    if (comparator.areLexicallyEqual(subTaskVariants.get(i), candidate)) {
                        taskBuilder.setTask
                            (sequenceInstance.get(subTaskIndex), subTaskVariants.get(i));
                        
                        found = true;
                        break;
                    }
                }
                
                if (!found) {
                    subTaskVariants.add(candidate);
                }
            }
            
            // if there are more than one lexically different variant of the sub task at
            // the considered position, adapt the sequence model at that position to have
            // a selection of the different variants. In this case also adapt the
            // generated sequence instances to correctly contain selection instances. If
            // there is only one variant of sub tasks at the given position, simply set
            // this variant as the sub task of the selection. In this case, the instances
            // can be preserved as is
            if (subTaskVariants.size() > 1) {
                ISelection selection = taskFactory.createNewSelection();
                
                for (ITask variant : subTaskVariants) {
                    taskBuilder.addChild(selection, variant);
                }
                
                taskBuilder.addChild(sequence, selection);
                
                for (ISequenceInstance instance : sequenceInstances) {
                    ISelectionInstance selectionInstance =
                        taskFactory.createNewTaskInstance(selection);
                    taskBuilder.setChild(selectionInstance, instance.get(subTaskIndex));
                    taskBuilder.setTaskInstance(instance, subTaskIndex, selectionInstance);
                }
            }
            else if (subTaskVariants.size() == 1) {
                taskBuilder.addChild(sequence, subTaskVariants.get(0));
            }
        }
    }

    /**
     * @param tree
     */
    private List<ISequenceInstance> replaceTaskOccurrences(List<ITaskInstance> task,
                                                           List<IUserSession>  sessions,
                                                           ISequence           temporalTaskModel)
    {
        List<ISequenceInstance> sequenceInstances = new LinkedList<ISequenceInstance>();
        
        for (IUserSession session : sessions) {
            int index = -1;
                
            do {
                index = getSubListIndex(session, task, ++index);

                if (index > -1) {
                    sequenceInstances.add
                        (RuleUtils.createNewSubSequenceInRange
                             (session, index, index + task.size() - 1, temporalTaskModel,
                              taskFactory, taskBuilder));
                }
            }
            while (index > -1);
        }
        
        return sequenceInstances;
    }

    /**
     * @param trie
     * @param object
     * @return
     */
    private int getSubListIndex(ITaskInstanceList   list,
                                List<ITaskInstance> subList,
                                int                 startIndex)
    {
        boolean matchFound;
        int result = -1;
        
        for (int i = startIndex; i <= list.size() - subList.size(); i++) {
            matchFound = true;
            
            for (int j = 0; j < subList.size(); j++) {
                // we prepared the task instances to refer to unique tasks, if they are treated
                // as equal. Therefore, we just compare the identity of the tasks of the task
                // instances
                if (list.get(i + j).getTask() != subList.get(j).getTask()) {
                    matchFound = false;
                    break;
                }
            }
            
            if (matchFound) {
                result = i;
                break;
            }
        }
        
        return result;
    }

    /**
     * @param trie
     * @param object
     * @return
     */
    private int getSubListIndex(List<ITaskInstance> list,
                                List<ITaskInstance> subList,
                                int                 startIndex)
    {
        boolean matchFound;
        int result = -1;
        
        for (int i = startIndex; i <= list.size() - subList.size(); i++) {
            matchFound = true;
            
            for (int j = 0; j < subList.size(); j++) {
                // we prepared the task instances to refer to unique tasks, if they are treated
                // as equal. Therefore, we just compare the identity of the tasks of the task
                // instances
                if (list.get(i + j) != subList.get(j)) {
                    matchFound = false;
                    break;
                }
            }
            
            if (matchFound) {
                result = i;
                break;
            }
        }
        
        return result;
    }
    
    /**
     * @author Patrick Harms
     */
    private class MaxCountAndLongestTasksFinder implements TrieProcessor<ITaskInstance> {
        
        /**
         * 
         */
        private int currentCount;
        
        /**
         * 
         */
        private List<List<ITaskInstance>> foundTasks = new LinkedList<List<ITaskInstance>>();

        /**
         *
         */
        public MaxCountAndLongestTasksFinder() {
            super();
            this.currentCount = 0;
        }

        /* (non-Javadoc)
         * @see de.ugoe.cs.autoquest.usageprofiles.TrieProcessor#process(java.util.List, int)
         */
        @Override
        public TrieProcessor.Result process(List<ITaskInstance> foundTask, int count) {
            if (foundTask.size() < 2) {
                // ignore single tasks
                return TrieProcessor.Result.CONTINUE;
            }
            
            if (count < 2) {
                // ignore singular occurrences
                return TrieProcessor.Result.SKIP_NODE;
            }

            if (this.currentCount > count) {
                // ignore this children of this task, as they may have only smaller counts than
                // the already found tasks
                return TrieProcessor.Result.SKIP_NODE;
            }
            
            if (this.currentCount < count) {
                // the provided task occurs more often that all tasks found so far.
                // clear all found tasks and use the new count as the one searched for
                foundTasks.clear();
                this.currentCount = count;
            }
            
            if (this.currentCount == count) {
                // the task is of interest. Sort it into the other found tasks so that
                // the longest come first
                boolean added = false;
                for (int i = 0; i < foundTasks.size(); i++) {
                    if (foundTasks.get(i).size() < foundTask.size()) {
                        // defensive copy
                        foundTasks.add(i, new LinkedList<ITaskInstance>(foundTask)); // defensive copy
                        added = true;
                        break;
                    }
                }
                
                if (!added) {
                    foundTasks.add(new LinkedList<ITaskInstance>(foundTask)); // defensive copy
                }
            }
            
            return TrieProcessor.Result.CONTINUE;
        }

        /**
         *  @return
         */
        public Tasks getFoundTasks() {
            removePermutationsOfShorterTasks();
            return new Tasks(currentCount, foundTasks);
        }

        /**
         *
         */
        private void removePermutationsOfShorterTasks() {
            // now iterate the sorted list and for each task remove all other tasks that are shorter
            // (i.e. come later in the sorted list) and that represent a subpart of the task
            for (int i = 0; i < foundTasks.size(); i++) {
                for (int j = i + 1; j < foundTasks.size();) {
                    if (foundTasks.get(j).size() < foundTasks.get(i).size()) {
                        // found a task that is a potential subtask. Check for this and remove the
                        // subtask if needed
                        List<ITaskInstance> longTask = foundTasks.get(i);
                        List<ITaskInstance> shortTask = foundTasks.get(j);
                        
                        if (getSubListIndex(longTask, shortTask, 0) > -1) {
                            foundTasks.remove(j);
                        }
                        else {
                            j++;
                        }
                    }
                    else {
                        j++;
                    }
                }
            }
        }

    }
    
//    /**
//     * @author Patrick Harms
//     */
//    private class TrieStatisticsDumper implements TrieProcessor<ITaskInstance> {
//        
//        /**
//         * 
//         */
//        private Map<Integer, Integer> counters = new HashMap<Integer, Integer>();
//        
//        /* (non-Javadoc)
//         * @see de.ugoe.cs.autoquest.usageprofiles.TrieProcessor#process(java.util.List, int)
//         */
//        @Override
//        public TrieProcessor.Result process(List<ITaskInstance> subsequence, int count) {
//            if (subsequence.size() == 1) {
//                Integer value = counters.get(count);
//                
//                if (value == null) {
//                    value = 0;
//                }
//                
//                counters.put(count, value + 1);
//                
//                return TrieProcessor.Result.CONTINUE;
//            }
//            else {
//                // ignore singular occurrences
//                return TrieProcessor.Result.SKIP_NODE;
//            }
//        }
//
//        /**
//         *  @return
//         */
//        public void dumpCounters() {
//            int dumpedCounters = 0;
//            
//            int count = 1;
//            while (dumpedCounters < counters.size()) {
//                Integer value = counters.get(count++);
//                if (value != null) {
//                    System.out.println(value + " symbols occurred " + count + " times");
//                    dumpedCounters++;
//                }
//            }
//        }
//
//    }
    
    /**
     * 
     */
    private static class RuleApplicationData {
        
        /**
         * 
         */
        private List<IUserSession> sessions;
        
        /**
         * 
         */
        private TaskInstanceTrie lastTrie;
        
        /**
         * default and minimum trained sequence length is 3
         */
        private int trainedSequenceLength = 3;
        
        /**
         * 
         */
        private Tasks lastFoundTasks = new Tasks(Integer.MAX_VALUE, null);
        
        /**
         * 
         */
        private boolean detectedAndReplacedTasks;
        
        /**
         * 
         */
        private RuleApplicationResult result = new RuleApplicationResult();
        
        /**
         * 
         */
        private StopWatch stopWatch = new StopWatch();
        
        /**
         * 
         */
        private RuleApplicationData(List<IUserSession> sessions) {
            this.sessions = sessions;
        }

        /**
         * @return the tree
         */
        private List<IUserSession> getSessions() {
            return sessions;
        }

        /**
         * @param lastTrie the lastTrie to set
         */
        private void setLastTrie(TaskInstanceTrie lastTrie) {
            this.lastTrie = lastTrie;
        }

        /**
         * @return the lastTrie
         */
        private TaskInstanceTrie getLastTrie() {
            return lastTrie;
        }

        /**
         * @param trainedSequenceLength the trainedSequenceLength to set
         */
        private void setTrainedSequenceLength(int trainedSequenceLength) {
            this.trainedSequenceLength = trainedSequenceLength;
        }

        /**
         * @return the trainedSequenceLength
         */
        private int getTrainedSequenceLength() {
            return trainedSequenceLength;
        }

        /**
         * @param lastFoundSequences the lastFoundSequences to set
         */
        private void setLastFoundTasks(Tasks lastFoundSequences) {
            this.lastFoundTasks = lastFoundSequences;
        }

        /**
         * @return the lastFoundSequences
         */
        private Tasks getLastFoundTasks() {
            return lastFoundTasks;
        }

        /**
         *
         */
        private void detectedAndReplacedTasks(boolean detectedAndReplacedTasks) {
            this.detectedAndReplacedTasks = detectedAndReplacedTasks;
        }

        /**
         *
         */
        private boolean detectedAndReplacedTasks() {
            return detectedAndReplacedTasks;
        }
        
        /**
         * @return the result
         */
        private RuleApplicationResult getResult() {
            return result;
        }

        /**
         * @return the stopWatch
         */
        private StopWatch getStopWatch() {
            return stopWatch;
        }

    }
    

    /**
     * @author Patrick Harms
     */
    private static class Tasks implements Iterable<List<ITaskInstance>> {
        
        /**
         * 
         */
        private int occurrenceCount;
        
        /**
         * 
         */
        private List<List<ITaskInstance>> sequences;

        /**
         * @param occurrenceCount
         * @param sequences
         */
        private Tasks(int occurrenceCount, List<List<ITaskInstance>> sequences) {
            super();
            this.occurrenceCount = occurrenceCount;
            this.sequences = sequences;
        }

        /**
         * @return
         */
        private int getOccurrenceCount() {
            return occurrenceCount;
        }

        /**
         * @return
         */
        private int size() {
            return this.sequences.size();
        }

        /**
         * 
         */

        /* (non-Javadoc)
         * @see java.lang.Iterable#iterator()
         */
        @Override
        public Iterator<List<ITaskInstance>> iterator() {
            return this.sequences.iterator();
        }

        /* (non-Javadoc)
         * @see java.lang.Object#toString()
         */
        @Override
        public String toString() {
            StringBuffer result = new StringBuffer();
            result.append(this.occurrenceCount);
            result.append(" occurrences:\n");
            
            for (List<ITaskInstance> task : sequences) {
                result.append(task);
                result.append("\n");
            }
            
            return result.toString();
        }

    }
    
    // methods for internal testing
//    private void checkMatchingOfSessions(List<List<Event>>  flattenedSessions,
//                                         List<IUserSession> sessions,
//                                         String             when)
//    {
//        List<List<Event>> currentFlattenedSessions = flattenSessions(sessions);
//        if (flattenedSessions.size() != currentFlattenedSessions.size()) {
//            System.out.println("################## number of sessions changed after " + when);
//        }
//        else {
//            for (int i = 0; i < flattenedSessions.size(); i++) {
//                List<Event> expected = flattenedSessions.get(i);
//                List<Event> current = currentFlattenedSessions.get(i);
//            
//                if (expected.size() != current.size()) {
//                    System.out.println
//                        ("################## length of session " + i + " changed after " + when);
//                }
//                else {
//                    for (int j = 0; j < expected.size(); j++) {
//                        if (!expected.get(j).equals(current.get(j))) {
//                            System.out.println("################## event " + j + " of session " +
//                                               i + " changed after " + when);
//                        }
//                    }
//                }
//            }     
//        }
//    }
//
//    private List<List<Event>> flattenSessions(List<IUserSession> sessions) {
//        List<List<Event>> flattenedSessions = new ArrayList<List<Event>>();
//        for (IUserSession session : sessions) {
//            List<Event> flattenedUserSession = new ArrayList<Event>();
//            flatten(session, flattenedUserSession);
//            flattenedSessions.add(flattenedUserSession);
//        }
//
//        return flattenedSessions;
//    }
//
//    private void flatten(IUserSession iUserSession, List<Event> flattenedUserSession) {
//        for (ITaskInstance instance : iUserSession) {
//            flatten(instance, flattenedUserSession);
//        }
//    }
//
//    private void flatten(ITaskInstance instance, List<Event> flattenedUserSession) {
//        if (instance instanceof ITaskInstanceList) {
//            for (ITaskInstance child : (ITaskInstanceList) instance) {
//                flatten(child, flattenedUserSession);
//            }
//        }
//        else if (instance instanceof ISelectionInstance) {
//            flatten(((ISelectionInstance) instance).getChild(), flattenedUserSession);
//        }
//        else if (instance instanceof IOptionalInstance) {
//            flatten(((IOptionalInstance) instance).getChild(), flattenedUserSession);
//        }
//        else if (instance instanceof IEventTaskInstance) {
//            flattenedUserSession.add(((IEventTaskInstance) instance).getEvent());
//        }
//    }

}