#include "storm-pomdp/storage/BeliefManager.h"

#include "storm/adapters/RationalNumberAdapter.h"
#include "storm/utility/macros.h"
#include "storm/utility/constants.h"
#include "storm/models/sparse/Pomdp.h"

namespace storm {
    namespace storage {

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        uint64_t BeliefManager<PomdpType, BeliefValueType, StateType>::Triangulation::size() const {
            return weights.size();
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        BeliefManager<PomdpType, BeliefValueType, StateType>::FreudenthalDiff::FreudenthalDiff(StateType const &dimension, BeliefValueType &&diff) : dimension(dimension),
                                                                                                                                                     diff(std::move(diff)) {
            // Intentionally left empty
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        bool BeliefManager<PomdpType, BeliefValueType, StateType>::FreudenthalDiff::operator>(FreudenthalDiff const &other) const {
            if (diff != other.diff) {
                return diff > other.diff;
            } else {
                return dimension < other.dimension;
            }
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        std::size_t BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefHash::operator()(const BeliefType &belief) const {
            std::size_t seed = 0;
            // Assumes that beliefs are ordered
            for (auto const &entry : belief) {
                boost::hash_combine(seed, entry.first);
                boost::hash_combine(seed, entry.second);
            }
            return seed;
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefManager(PomdpType const &pomdp, BeliefValueType const &precision, TriangulationMode const &triangulationMode)
                : pomdp(pomdp), triangulationMode(triangulationMode) {
            cc = storm::utility::ConstantsComparator<ValueType>(precision, false);
            beliefToIdMap.resize(pomdp.getNrObservations());
            initialBeliefId = computeInitialBelief();
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        void BeliefManager<PomdpType, BeliefValueType, StateType>::setRewardModel(boost::optional<std::string> rewardModelName) {
            if (rewardModelName) {
                auto const &rewardModel = pomdp.getRewardModel(rewardModelName.get());
                pomdpActionRewardVector = rewardModel.getTotalRewardVector(pomdp.getTransitionMatrix());
            } else {
                setRewardModel(pomdp.getUniqueRewardModelName());
            }
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        void BeliefManager<PomdpType, BeliefValueType, StateType>::unsetRewardModel() {
            pomdpActionRewardVector.clear();
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefId BeliefManager<PomdpType, BeliefValueType, StateType>::noId() const {
            return std::numeric_limits<BeliefId>::max();
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        bool BeliefManager<PomdpType, BeliefValueType, StateType>::isEqual(BeliefId const &first, BeliefId const &second) const {
            return isEqual(getBelief(first), getBelief(second));
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        std::string BeliefManager<PomdpType, BeliefValueType, StateType>::toString(BeliefId const &beliefId) const {
            return toString(getBelief(beliefId));
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        std::string BeliefManager<PomdpType, BeliefValueType, StateType>::toString(Triangulation const &t) const {
            std::stringstream str;
            str << "(\n";
            for (uint64_t i = 0; i < t.size(); ++i) {
                str << "\t" << t.weights[i] << " * \t" << toString(getBelief(t.gridPoints[i])) << "\n";
            }
            str << ")\n";
            return str.str();
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::ValueType
        BeliefManager<PomdpType, BeliefValueType, StateType>::getWeightedSum(BeliefId const &beliefId, std::vector<ValueType> const &summands) {
            ValueType result = storm::utility::zero<ValueType>();
            for (auto const &entry : getBelief(beliefId)) {
                result += storm::utility::convertNumber<ValueType>(entry.second) * storm::utility::convertNumber<ValueType>(summands.at(entry.first));
            }
            return result;
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefId const &BeliefManager<PomdpType, BeliefValueType, StateType>::getInitialBelief() const {
            return initialBeliefId;
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::ValueType
        BeliefManager<PomdpType, BeliefValueType, StateType>::getBeliefActionReward(BeliefId const &beliefId, uint64_t const &localActionIndex) const {
            auto const &belief = getBelief(beliefId);
            STORM_LOG_ASSERT(!pomdpActionRewardVector.empty(), "Requested a reward although no reward model was specified.");
            auto result = storm::utility::zero<ValueType>();
            auto const &choiceIndices = pomdp.getTransitionMatrix().getRowGroupIndices();
            for (auto const &entry : belief) {
                uint64_t choiceIndex = choiceIndices[entry.first] + localActionIndex;
                STORM_LOG_ASSERT(choiceIndex < choiceIndices[entry.first + 1], "Invalid local action index.");
                STORM_LOG_ASSERT(choiceIndex < pomdpActionRewardVector.size(), "Invalid choice index.");
                result += entry.second * pomdpActionRewardVector[choiceIndex];
            }
            return result;
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        uint32_t BeliefManager<PomdpType, BeliefValueType, StateType>::getBeliefObservation(BeliefId beliefId) {
            return getBeliefObservation(getBelief(beliefId));
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        uint64_t BeliefManager<PomdpType, BeliefValueType, StateType>::getBeliefNumberOfChoices(BeliefId beliefId) {
            auto const &belief = getBelief(beliefId);
            return pomdp.getNumberOfChoices(belief.begin()->first);
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::Triangulation
        BeliefManager<PomdpType, BeliefValueType, StateType>::triangulateBelief(BeliefId beliefId, BeliefValueType resolution) {
            return triangulateBelief(getBelief(beliefId), resolution);
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        template<typename DistributionType>
        void BeliefManager<PomdpType, BeliefValueType, StateType>::addToDistribution(DistributionType &distr, StateType const &state, BeliefValueType const &value) {
            auto insertionRes = distr.emplace(state, value);
            if (!insertionRes.second) {
                insertionRes.first->second += value;
            }
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        void BeliefManager<PomdpType, BeliefValueType, StateType>::joinSupport(BeliefId const &beliefId, BeliefSupportType &support) {
            auto const &belief = getBelief(beliefId);
            for (auto const &entry : belief) {
                support.insert(entry.first);
            }
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefId BeliefManager<PomdpType, BeliefValueType, StateType>::getNumberOfBeliefIds() const {
            return beliefs.size();
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        std::vector<std::pair<typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefId, typename BeliefManager<PomdpType, BeliefValueType, StateType>::ValueType>>
        BeliefManager<PomdpType, BeliefValueType, StateType>::expandAndTriangulate(BeliefId const &beliefId, uint64_t actionIndex,
                                                                                   std::vector<BeliefValueType> const &observationResolutions) {
            return expandInternal(beliefId, actionIndex, observationResolutions);
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        std::vector<std::pair<typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefId, typename BeliefManager<PomdpType, BeliefValueType, StateType>::ValueType>>
        BeliefManager<PomdpType, BeliefValueType, StateType>::expand(BeliefId const &beliefId, uint64_t actionIndex) {
            return expandInternal(beliefId, actionIndex);
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefType const &BeliefManager<PomdpType, BeliefValueType, StateType>::getBelief(BeliefId const &id) const {
            STORM_LOG_ASSERT(id != noId(), "Tried to get a non-existend belief.");
            STORM_LOG_ASSERT(id < getNumberOfBeliefIds(), "Belief index " << id << " is out of range.");
            return beliefs[id];
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefId BeliefManager<PomdpType, BeliefValueType, StateType>::getId(BeliefType const &belief) const {
            uint32_t obs = getBeliefObservation(belief);
            STORM_LOG_ASSERT(obs < beliefToIdMap.size(), "Belief has unknown observation.");
            auto idIt = beliefToIdMap[obs].find(belief);
            STORM_LOG_ASSERT(idIt != beliefToIdMap[obs].end(), "Unknown Belief.");
            return idIt->second;
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        std::string BeliefManager<PomdpType, BeliefValueType, StateType>::toString(BeliefType const &belief) const {
            std::stringstream str;
            str << "{ ";
            bool first = true;
            for (auto const &entry : belief) {
                if (first) {
                    first = false;
                } else {
                    str << ", ";
                }
                str << entry.first << ": " << entry.second;
            }
            str << " }";
            return str.str();
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        bool BeliefManager<PomdpType, BeliefValueType, StateType>::isEqual(BeliefType const &first, BeliefType const &second) const {
            if (first.size() != second.size()) {
                return false;
            }
            auto secondIt = second.begin();
            for (auto const &firstEntry : first) {
                if (firstEntry.first != secondIt->first) {
                    return false;
                }
                if (!cc.isEqual(firstEntry.second, secondIt->second)) {
                    return false;
                }
                ++secondIt;
            }
            return true;
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        bool BeliefManager<PomdpType, BeliefValueType, StateType>::assertBelief(BeliefType const &belief) const {
            BeliefValueType sum = storm::utility::zero<ValueType>();
            boost::optional<uint32_t> observation;
            for (auto const &entry : belief) {
                if (entry.first >= pomdp.getNumberOfStates()) {
                    STORM_LOG_ERROR("Belief does refer to non-existing pomdp state " << entry.first << ".");
                    return false;
                }
                uint64_t entryObservation = pomdp.getObservation(entry.first);
                if (observation) {
                    if (observation.get() != entryObservation) {
                        STORM_LOG_ERROR("Beliefsupport contains different observations.");
                        return false;
                    }
                } else {
                    observation = entryObservation;
                }
                // Don't use cc for these checks, because computations with zero are usually fine
                if (storm::utility::isZero(entry.second)) {
                    // We assume that beliefs only consider their support.
                    STORM_LOG_ERROR("Zero belief probability.");
                    return false;
                }
                if (entry.second < storm::utility::zero<BeliefValueType>()) {
                    STORM_LOG_ERROR("Negative belief probability.");
                    return false;
                }
                if (cc.isLess(storm::utility::one<BeliefValueType>(), entry.second)) {
                    STORM_LOG_ERROR("Belief probability greater than one.");
                    return false;
                }
                sum += entry.second;
            }
            if (!cc.isOne(sum)) {
                STORM_LOG_ERROR("Belief does not sum up to one. (" << sum << " instead).");
                return false;
            }
            return true;
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        bool BeliefManager<PomdpType, BeliefValueType, StateType>::assertTriangulation(BeliefType const &belief, Triangulation const &triangulation) const {
            if (triangulation.weights.size() != triangulation.gridPoints.size()) {
                STORM_LOG_ERROR("Number of weights and points in triangulation does not match.");
                return false;
            }
            if (triangulation.size() == 0) {
                STORM_LOG_ERROR("Empty triangulation.");
                return false;
            }
            BeliefType triangulatedBelief;
            BeliefValueType weightSum = storm::utility::zero<BeliefValueType>();
            for (uint64_t i = 0; i < triangulation.weights.size(); ++i) {
                if (cc.isZero(triangulation.weights[i])) {
                    STORM_LOG_ERROR("Zero weight in triangulation.");
                    return false;
                }
                if (cc.isLess(triangulation.weights[i], storm::utility::zero<BeliefValueType>())) {
                    STORM_LOG_ERROR("Negative weight in triangulation.");
                    return false;
                }
                if (cc.isLess(storm::utility::one<BeliefValueType>(), triangulation.weights[i])) {
                    STORM_LOG_ERROR("Weight greater than one in triangulation.");
                }
                weightSum += triangulation.weights[i];
                BeliefType const &gridPoint = getBelief(triangulation.gridPoints[i]);
                for (auto const &pointEntry : gridPoint) {
                    BeliefValueType &triangulatedValue = triangulatedBelief.emplace(pointEntry.first, storm::utility::zero<ValueType>()).first->second;
                    triangulatedValue += triangulation.weights[i] * pointEntry.second;
                }
            }
            if (!cc.isOne(weightSum)) {
                STORM_LOG_ERROR("Triangulation weights do not sum up to one.");
                return false;
            }
            if (!assertBelief(triangulatedBelief)) {
                STORM_LOG_ERROR("Triangulated belief is not a belief.");
            }
            if (!isEqual(belief, triangulatedBelief)) {
                STORM_LOG_ERROR("Belief:\n\t" << toString(belief) << "\ndoes not match triangulated belief:\n\t" << toString(triangulatedBelief) << ".");
                return false;
            }
            return true;
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        uint32_t BeliefManager<PomdpType, BeliefValueType, StateType>::getBeliefObservation(BeliefType belief) const {
            STORM_LOG_ASSERT(assertBelief(belief), "Invalid belief.");
            return pomdp.getObservation(belief.begin()->first);
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        void
        BeliefManager<PomdpType, BeliefValueType, StateType>::triangulateBeliefFreudenthal(BeliefType const &belief, BeliefValueType const &resolution, Triangulation &result) {
            STORM_LOG_ASSERT(resolution != 0, "Invalid resolution: 0");
            STORM_LOG_ASSERT(storm::utility::isInteger(resolution), "Expected an integer resolution");
            StateType numEntries = belief.size();
            // This is the Freudenthal Triangulation as described in Lovejoy (a whole lotta math)
            // Probabilities will be triangulated to values in 0/N, 1/N, 2/N, ..., N/N
            // Variable names are mostly based on the paper
            // However, we speed this up a little by exploiting that belief states usually have sparse support (i.e. numEntries is much smaller than pomdp.getNumberOfStates()).
            // Initialize diffs and the first row of the 'qs' matrix (aka v)
            std::set<FreudenthalDiff, std::greater<FreudenthalDiff>> sorted_diffs; // d (and p?) in the paper
            std::vector<BeliefValueType> qsRow; // Row of the 'qs' matrix from the paper (initially corresponds to v
            qsRow.reserve(numEntries);
            std::vector<StateType> toOriginalIndicesMap; // Maps 'local' indices to the original pomdp state indices
            toOriginalIndicesMap.reserve(numEntries);
            BeliefValueType x = resolution;
            for (auto const &entry : belief) {
                qsRow.push_back(storm::utility::floor(x)); // v
                sorted_diffs.emplace(toOriginalIndicesMap.size(), x - qsRow.back()); // x-v
                toOriginalIndicesMap.push_back(entry.first);
                x -= entry.second * resolution;
            }
            // Insert a dummy 0 column in the qs matrix so the loops below are a bit simpler
            qsRow.push_back(storm::utility::zero<BeliefValueType>());

            result.weights.reserve(numEntries);
            result.gridPoints.reserve(numEntries);
            auto currentSortedDiff = sorted_diffs.begin();
            auto previousSortedDiff = sorted_diffs.end();
            --previousSortedDiff;
            for (StateType i = 0; i < numEntries; ++i) {
                // Compute the weight for the grid points
                BeliefValueType weight = previousSortedDiff->diff - currentSortedDiff->diff;
                if (i == 0) {
                    // The first weight is a bit different
                    weight += storm::utility::one<ValueType>();
                } else {
                    // 'compute' the next row of the qs matrix
                    qsRow[previousSortedDiff->dimension] += storm::utility::one<BeliefValueType>();
                }
                if (!cc.isZero(weight)) {
                    result.weights.push_back(weight);
                    // Compute the grid point
                    BeliefType gridPoint;
                    for (StateType j = 0; j < numEntries; ++j) {
                        BeliefValueType gridPointEntry = qsRow[j] - qsRow[j + 1];
                        if (!cc.isZero(gridPointEntry)) {
                            gridPoint[toOriginalIndicesMap[j]] = gridPointEntry / resolution;
                        }
                    }
                    result.gridPoints.push_back(getOrAddBeliefId(gridPoint));
                }
                previousSortedDiff = currentSortedDiff++;
            }
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        void BeliefManager<PomdpType, BeliefValueType, StateType>::triangulateBeliefDynamic(BeliefType const &belief, BeliefValueType const &resolution, Triangulation &result) {
            // Find the best resolution for this belief, i.e., N such that the largest distance between one of the belief values to a value in {i/N | 0 ≤ i ≤ N} is minimal
            STORM_LOG_ASSERT(storm::utility::isInteger(resolution), "Expected an integer resolution");
            BeliefValueType finalResolution = resolution;
            uint64_t finalResolutionMisses = belief.size() + 1;
            // We don't need to check resolutions that are smaller than the maximal resolution divided by 2 (as we already checked multiples of these)
            for (BeliefValueType currResolution = resolution; currResolution > resolution / 2; --currResolution) {
                uint64_t currResMisses = 0;
                bool continueWithNextResolution = false;
                for (auto const &belEntry : belief) {
                    BeliefValueType product = belEntry.second * currResolution;
                    if (!cc.isZero(product - storm::utility::round(product))) {
                        ++currResMisses;
                        if (currResMisses >= finalResolutionMisses) {
                            // This resolution is not better than a previous resolution
                            continueWithNextResolution = true;
                            break;
                        }
                    }
                }
                if (!continueWithNextResolution) {
                    STORM_LOG_ASSERT(currResMisses < finalResolutionMisses, "Distance for this resolution should not be larger than a previously checked one.");
                    finalResolution = currResolution;
                    finalResolutionMisses = currResMisses;
                    if (currResMisses == 0) {
                        break;
                    }
                }
            }

            STORM_LOG_TRACE("Picking resolution " << finalResolution << " for belief " << toString(belief));

            // do standard freudenthal with the found resolution
            triangulateBeliefFreudenthal(belief, finalResolution, result);
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::Triangulation
        BeliefManager<PomdpType, BeliefValueType, StateType>::triangulateBelief(BeliefType const &belief, BeliefValueType const &resolution) {
            STORM_LOG_ASSERT(assertBelief(belief), "Input belief for triangulation is not valid.");
            Triangulation result;
            // Quickly triangulate Dirac beliefs
            if (belief.size() == 1u) {
                result.weights.push_back(storm::utility::one<BeliefValueType>());
                result.gridPoints.push_back(getOrAddBeliefId(belief));
            } else {
                auto ceiledResolution = storm::utility::ceil<BeliefValueType>(resolution);
                switch (triangulationMode) {
                    case TriangulationMode::Static:
                        triangulateBeliefFreudenthal(belief, ceiledResolution, result);
                        break;
                    case TriangulationMode::Dynamic:
                        triangulateBeliefDynamic(belief, ceiledResolution, result);
                        break;
                    default:
                        STORM_LOG_ASSERT(false, "Invalid triangulation mode.");
                }
            }
            STORM_LOG_ASSERT(assertTriangulation(belief, result), "Incorrect triangulation: " << toString(result));
            return result;
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        std::vector<std::pair<typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefId, typename BeliefManager<PomdpType, BeliefValueType, StateType>::ValueType>>
        BeliefManager<PomdpType, BeliefValueType, StateType>::expandInternal(BeliefId const &beliefId, uint64_t actionIndex,
                                                                             boost::optional<std::vector<BeliefValueType>> const &observationTriangulationResolutions) {
            std::vector<std::pair<BeliefId, ValueType>> destinations;

            BeliefType belief = getBelief(beliefId);

            // Find the probability we go to each observation
            BeliefType successorObs; // This is actually not a belief but has the same type
            for (auto const &pointEntry : belief) {
                uint64_t state = pointEntry.first;
                for (auto const &pomdpTransition : pomdp.getTransitionMatrix().getRow(state, actionIndex)) {
                    if (!storm::utility::isZero(pomdpTransition.getValue())) {
                        auto obs = pomdp.getObservation(pomdpTransition.getColumn());
                        addToDistribution(successorObs, obs, pointEntry.second * pomdpTransition.getValue());
                    }
                }
            }

            // Now for each successor observation we find and potentially triangulate the successor belief
            for (auto const &successor : successorObs) {
                BeliefType successorBelief;
                for (auto const &pointEntry : belief) {
                    uint64_t state = pointEntry.first;
                    for (auto const &pomdpTransition : pomdp.getTransitionMatrix().getRow(state, actionIndex)) {
                        if (pomdp.getObservation(pomdpTransition.getColumn()) == successor.first) {
                            ValueType prob = pointEntry.second * pomdpTransition.getValue() / successor.second;
                            addToDistribution(successorBelief, pomdpTransition.getColumn(), prob);
                        }
                    }
                }
                STORM_LOG_ASSERT(assertBelief(successorBelief), "Invalid successor belief.");

                // Insert the destination. We know that destinations have to be disjoined since they have different observations
                if (observationTriangulationResolutions) {
                    Triangulation triangulation = triangulateBelief(successorBelief, observationTriangulationResolutions.get()[successor.first]);
                    for (size_t j = 0; j < triangulation.size(); ++j) {
                        // Here we additionally assume that triangulation.gridPoints does not contain the same point multiple times
                        destinations.emplace_back(triangulation.gridPoints[j], triangulation.weights[j] * successor.second);
                    }
                } else {
                    destinations.emplace_back(getOrAddBeliefId(successorBelief), successor.second);
                }
            }

            return destinations;

        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefId BeliefManager<PomdpType, BeliefValueType, StateType>::computeInitialBelief() {
            STORM_LOG_ASSERT(pomdp.getInitialStates().getNumberOfSetBits() < 2,
                             "POMDP contains more than one initial state");
            STORM_LOG_ASSERT(pomdp.getInitialStates().getNumberOfSetBits() == 1,
                             "POMDP does not contain an initial state");
            BeliefType belief;
            belief[*pomdp.getInitialStates().begin()] = storm::utility::one<ValueType>();

            STORM_LOG_ASSERT(assertBelief(belief), "Invalid initial belief.");
            return getOrAddBeliefId(belief);
        }

        template<typename PomdpType, typename BeliefValueType, typename StateType>
        typename BeliefManager<PomdpType, BeliefValueType, StateType>::BeliefId BeliefManager<PomdpType, BeliefValueType, StateType>::getOrAddBeliefId(BeliefType const &belief) {
            uint32_t obs = getBeliefObservation(belief);
            STORM_LOG_ASSERT(obs < beliefToIdMap.size(), "Belief has unknown observation.");
            auto insertioRes = beliefToIdMap[obs].emplace(belief, beliefs.size());
            if (insertioRes.second) {
                // There actually was an insertion, so add the new belief
                beliefs.push_back(belief);
            }
            // Return the id
            return insertioRes.first->second;
        }

        template class BeliefManager<storm::models::sparse::Pomdp<double>>;

        template class BeliefManager<storm::models::sparse::Pomdp<storm::RationalNumber>>;
    }
}