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#include "nfa.h"

#include <QSet>

#include <limits.h>

NFA NFA::createSingleInputNFA(InputType input)

{

    NFA result;

    result.initialize(2);

    result.addTransition(result.initialState, input, result.finalState);

    return result;

}

NFA NFA::createSymbolNFA(const QString &symbol)

{

    NFA result = NFA::createSingleInputNFA(Epsilon);

    result.states[result.finalState].symbol = symbol;

    return result;

}

void NFA::initialize(int size)

{

    states.resize(size);

    states.fill(State());

    initialState = 0;

    finalState = size - 1;

}

void NFA::addTransition(int from, InputType input, int to)

{

    assertValidState(from);

    assertValidState(to);

    states[from].transitions.insertMulti(input, to);

}

void NFA::copyFrom(const NFA &other, int baseState)

{

    assertValidState(baseState);

    assertValidState(baseState + other.states.count() - 1);

    for (int i = 0; i < other.states.count(); ++i) {

        State s = other.states.at(i);

        for (TransitionMap::Iterator it = s.transitions.begin(),

             end = s.transitions.end(); it != end; ++it)

            *it += baseState;

        states[baseState + i] = s;

    }

}

void NFA::initializeFromPair(const NFA &a, const NFA &b,

                             int *initialA, int *finalA,

                             int *initialB, int *finalB)

{

    initialize(a.states.count() + b.states.count() + 2);

    int baseIdxA = 1;

    int baseIdxB = 1 + a.states.count();

    *initialA = a.initialState + baseIdxA;

    *finalA = a.finalState + baseIdxA;

    *initialB = b.initialState + baseIdxB;

    *finalB = b.finalState + baseIdxB;

    copyFrom(a, baseIdxA);

    copyFrom(b, baseIdxB);

}

NFA NFA::createAlternatingNFA(const NFA &a, const NFA &b)

{

    NFA result;

    int newInitialA, newFinalA,

        newInitialB, newFinalB;

    result.initializeFromPair(a, b, &newInitialA, &newFinalA,

                              &newInitialB, &newFinalB);

    result.addTransition(result.initialState, Epsilon, newInitialA);

    result.addTransition(result.initialState, Epsilon, newInitialB);

    result.addTransition(newFinalA, Epsilon, result.finalState);

    result.addTransition(newFinalB, Epsilon, result.finalState);

    return result;

}

NFA NFA::createConcatenatingNFA(const NFA &a, const NFA &b)

{

    NFA result;

    int initialA, finalA,

        initialB, finalB;

    result.initializeFromPair(a, b, &initialA, &finalA, &initialB, &finalB);

    result.addTransition(result.initialState, Epsilon, initialA);

    result.addTransition(finalA, Epsilon, initialB);

    result.addTransition(finalB, Epsilon, result.finalState);

    return result;

}

NFA NFA::createOptionalNFA(const NFA &a)

{

    NFA result;

    result.initialize(a.states.count() + 2);

    int baseIdxA = 1;

    int initialA = a.initialState + baseIdxA;

    int finalA = a.finalState + baseIdxA;

    result.copyFrom(a, baseIdxA);

    result.addTransition(result.initialState, Epsilon, initialA);

    result.addTransition(result.initialState, Epsilon, result.finalState);

    result.addTransition(finalA, Epsilon, initialA);

    result.addTransition(finalA, Epsilon, result.finalState);

    return result;

}

NFA NFA::createStringNFA(const QByteArray &str)

{

    NFA result;

    foreach (char c, str) {

        NFA ch = NFA::createSingleInputNFA(c);

        if (result.isEmpty())

            result = ch;

        else

            result = NFA::createConcatenatingNFA(result, ch);

    }

    return result;

}

NFA NFA::createSetNFA(const QSet<InputType> &set)

{

    NFA result;

    result.initialize(set.count() + 2);

    int state = 1;

    for (QSet<InputType>::ConstIterator it = set.constBegin(), end = set.constEnd();

         it != end; ++it, ++state) {

        result.addTransition(result.initialState, Epsilon, state);

        result.addTransition(state, *it, result.finalState);

    }

    /*

    foreach (InputType input, set) {

        NFA ch = NFA::createSingleInputNFA(input);

        if (result.isEmpty())

            result = ch;

        else

            result = NFA::createAlternatingNFA(result, ch);

    }

    */

    return result;

}

NFA NFA::createZeroOrOneNFA(const NFA &a)

{

    NFA epsilonNFA = createSingleInputNFA(Epsilon);

    return NFA::createAlternatingNFA(a, epsilonNFA);

}

NFA NFA::applyQuantity(const NFA &a, int minOccurrences, int maxOccurrences)

{

    NFA result = a;

    NFA epsilonNFA = createSingleInputNFA(Epsilon);

    if (minOccurrences == 0) {

        result = NFA::createAlternatingNFA(result, epsilonNFA);

    } else {

        minOccurrences--;

    }

    maxOccurrences--;

    for (int i = 0; i < minOccurrences; ++i)

        result = NFA::createConcatenatingNFA(result, a);

    for (int i = minOccurrences; i < maxOccurrences; ++i)

        result = NFA::createConcatenatingNFA(result, NFA::createAlternatingNFA(a, epsilonNFA));

    return result;

}

void NFA::debug()

{

    qDebug() << "NFA has" << states.count() << "states";

    qDebug() << "initial state is" << initialState;

    qDebug() << "final state is" << finalState;

    for (int i = 0; i < states.count(); ++i) {

        const State &s = states.at(i);

        for (TransitionMap::ConstIterator it = s.transitions.constBegin(),

             end = s.transitions.constEnd(); it != end; ++it)

            qDebug() << "transition from state" << i << "to" << it.value() << "through"

                     << (it.key() == Epsilon ? QString("Epsilon") : QString(char(it.key())));

        if (!s.symbol.isEmpty())

            qDebug() << "State" << i << "leads to symbol" << s.symbol;

    }

}

// helper

typedef QSet<int> DFAState;

// that's a bad hash, but it's good enough for us

// and it allows us to use the nice QHash API :)

inline uint qHash(const DFAState &state)

{

    uint val = 0;

    foreach (int s, state)

        val |= qHash(s);

    return val;

}

DFA NFA::toDFA() const

{

    DFA result;

    result.reserve(states.count());

    QHash<QString, int> symbolReferenceCounts;

    {

        QSet<int> symbolStates;

        for (int i = 0; i < states.count(); ++i)

            if (!states.at(i).symbol.isEmpty())

                symbolStates.insert(i);

        QHash<int, QString> epsilonStates;

        for (int i = 0; i < states.count(); ++i) {

            const State &s = states.at(i);

            for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();

                 transition != end; ++transition)

                if (transition.key() == Epsilon && symbolStates.contains(transition.value()))

                    epsilonStates.insert(i, states.at(transition.value()).symbol);

        }

        int lastCount;

        do {

            lastCount = epsilonStates.count();

            for (int i = 0; i < states.count(); ++i) {

                const State &s = states.at(i);

                for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();

                     transition != end; ++transition)

                    if (transition.key() == Epsilon && epsilonStates.contains(transition.value()))

                        epsilonStates.insert(i, epsilonStates.value(transition.value()));

            }

        } while (lastCount != epsilonStates.count());

        for (int i = 0; i < states.count(); ++i) {

            const State &s = states.at(i);

            for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();

                 transition != end; ++transition) {

                if (transition.key() == Epsilon)

                    continue;

                if (symbolStates.contains(transition.value())) {

                    const QString symbol = states.at(transition.value()).symbol;

                    symbolReferenceCounts[symbol]++;

                } else if (epsilonStates.contains(transition.value())) {

                    const QString symbol = epsilonStates.value(transition.value());

                    symbolReferenceCounts[symbol]++;

                }

            }

        }

        /*

        for (QHash<QString, int>::ConstIterator symIt = symbolReferenceCounts.constBegin(), symEnd = symbolReferenceCounts.constEnd();

             symIt != symEnd; ++symIt)

            qDebug() << "symbol" << symIt.key() << "is reached" << symIt.value() << "times";

            */

    }

    QSet<InputType> validInput;

    foreach (const State &s, states)

        for (TransitionMap::ConstIterator it = s.transitions.constBegin(),

             end = s.transitions.constEnd(); it != end; ++it)

            if (it.key() != Epsilon)

                validInput.insert(it.key());

    // A DFA state can consist of multiple NFA states.

    // the dfaStateMap maps from these to the actual

    // state index within the resulting DFA vector

    QHash<DFAState, int> dfaStateMap;

    QStack<DFAState> pendingDFAStates;

    DFAState startState = epsilonClosure(QSet<int>() << initialState);

    result.resize(1);

    dfaStateMap.insert(startState, 0);

    pendingDFAStates.push(startState);

    while (!pendingDFAStates.isEmpty()) {

        DFAState state = pendingDFAStates.pop();

//        qDebug() << "processing" << state << "from the stack of pending states";

        foreach (InputType input, validInput) {

            QSet<int> reachableStates;

            foreach (int nfaState, state) {

                const TransitionMap &transitions = states.at(nfaState).transitions;

                TransitionMap::ConstIterator it = transitions.find(input);

                while (it != transitions.constEnd() && it.key() == input) {

                    reachableStates.insert(it.value());

                    ++it;

                }

            }

            if (reachableStates.isEmpty())

                continue;

//            qDebug() << "can reach" << reachableStates << "from input" << char(input);

            QSet<int> closure = epsilonClosure(reachableStates);

//            qDebug() << "closure is" << closure;

            if (!dfaStateMap.contains(closure)) {

                int dfaState = result.count();

                result.append(State());

                QString symbol;

                int refCount = INT_MAX;

                foreach (int nfaState, closure)

                    if (!states.at(nfaState).symbol.isEmpty()) {

//                        qDebug() << "closure also contains symbol" << states.at(nfaState).symbol;

                        QString candidate = states.at(nfaState).symbol;

                        int candidateRefCount =symbolReferenceCounts.value(candidate, INT_MAX);

                        if (candidateRefCount < refCount) {

                            refCount = candidateRefCount;

                            symbol = candidate;

                        }

                    }

                if (!symbol.isEmpty())

                    result.last().symbol = symbol;

                dfaStateMap.insert(closure, dfaState);

                Q_ASSERT(!pendingDFAStates.contains(closure));

                pendingDFAStates.prepend(closure);

            }

            result[dfaStateMap.value(state)].transitions.insert(input, dfaStateMap.value(closure));

        }

    }

    return result;

}

QSet<int> NFA::epsilonClosure(const QSet<int> &initialClosure) const

{

    QSet<int> closure = initialClosure;

    closure.reserve(closure.count() * 4);

    QStack<int> stateStack;

    stateStack.resize(closure.count());

    qCopy(closure.constBegin(), closure.constEnd(), stateStack.begin());

    while (!stateStack.isEmpty()) {

        int t = stateStack.pop();

        const TransitionMap &transitions = states.at(t).transitions;

        TransitionMap::ConstIterator it = transitions.find(Epsilon);

        while (it != transitions.constEnd() && it.key() == Epsilon) {

            const int u = it.value();

            if (!closure.contains(u)) {

                closure.insert(u);

                stateStack.push(u);

            }

            ++it;

        }

    }

    return closure;

}

void NFA::setTerminationSymbol(const QString &symbol)

{

    states[finalState].symbol = symbol;

}

void DFA::debug() const

{

    qDebug() << "DFA has" << count() << "states";

    for (int i = 0; i < count(); ++i) {

        const State &s = at(i);

        if (s.transitions.isEmpty()) {

            qDebug() << "State" << i << "has no transitions";

        } else {

            for (TransitionMap::ConstIterator it = s.transitions.constBegin(),

                 end = s.transitions.constEnd(); it != end; ++it)

                qDebug() << "transition from state" << i << "to" << it.value() << "through"

                         << (it.key() == Epsilon ? QString("Epsilon") : QString(char(it.key())));

        }

        if (!s.symbol.isEmpty())

            qDebug() << "State" << i << "leads to symbol" << s.symbol;

    }

}

DFA DFA::minimize() const

{

    QVector<bool> inequivalentStates(count() * count());

    inequivalentStates.fill(false);

    for (int i = 0; i < count(); ++i)

        for (int j = 0; j < i; ++j) {

            if (i != j && at(i).symbol != at(j).symbol)

                inequivalentStates[i * count() + j] = true;

        }

    bool done;

    do {

        done = true;

        for (int i = 0; i < count(); ++i)

            for (int j = 0; j < count(); ++j) {

                if (i == j)

                    continue;

                if (inequivalentStates[i * count() + j])

                    continue;

                if (at(i).transitions.keys() != at(j).transitions.keys()) {

                    inequivalentStates[i * count() + j] = true;

                    done = false;

                    continue;

                }

                foreach (InputType a, at(i).transitions.keys()) {

                    int r = at(i).transitions.value(a, -1);

                    if (r == -1)

                        continue;

                    int s = at(j).transitions.value(a, -1);

                    if (s == -1)

                        continue;

                    if (inequivalentStates[r * count() + s]

                        || r == s) {

                        inequivalentStates[i * count() + j] = true;

                        done = false;

                        break;

                    }

                }

            }

    } while (!done);

    QHash<int, int> statesToEliminate;

    for (int i = 0; i < count(); ++i)

        for (int j = 0; j < i; ++j)

            if (!inequivalentStates[i * count() + j]) {

                statesToEliminate.insertMulti(i, j);

            }

    /*

    qDebug() << "states to eliminiate:" << statesToEliminate.count();;

    qDebug() << "merging" << statesToEliminate;

    debug();

    */

    return *this;

}