#include "storm/solver/stateelimination/EliminatorBase.h"

#include "storm/utility/stateelimination.h"
#include "storm/utility/macros.h"
#include "storm/utility/constants.h"

#include "storm/exceptions/InvalidStateException.h"

namespace storm {
    namespace solver {
        namespace stateelimination {
            
            using namespace storm::utility::stateelimination;

            template<typename ValueType, ScalingMode Mode>
            EliminatorBase<ValueType, Mode>::EliminatorBase(storm::storage::FlexibleSparseMatrix<ValueType>& matrix, storm::storage::FlexibleSparseMatrix<ValueType>& transposedMatrix) : matrix(matrix), transposedMatrix(transposedMatrix) {
                // Intentionally left empty.
            }
            
            template<typename ValueType, ScalingMode Mode>
            void EliminatorBase<ValueType, Mode>::eliminate(uint64_t row, uint64_t column, bool clearRow) {
                // Start by finding the entry in the given column.
                bool hasEntryInColumn = false;
                ValueType columnValue = storm::utility::zero<ValueType>();
                FlexibleRowType& entriesInRow = matrix.getRow(row);
                for (auto entryIt = entriesInRow.begin(), entryIte = entriesInRow.end(); entryIt != entryIte; ++entryIt) {
                    if (entryIt->getColumn() >= column) {
                        if (entryIt->getColumn() == column) {
                            columnValue = entryIt->getValue();
                            hasEntryInColumn = true;
                            
                            // If we do not clear the row completely, we need to remove the entry in the requested column.
                            // All other elements are scaled with the entry anyway.
                            if (!clearRow) {
                                entriesInRow.erase(entryIt);
                            }
                        }
                        break;
                    }
                }
                
                // Scale all entries in this row.
                // Depending on the scaling mode, we scale the other entries of the row.
                STORM_LOG_TRACE((hasEntryInColumn ? "State has entry in column." : "State does not have entry in column."));
                if (Mode == ScalingMode::Divide) {
                    STORM_LOG_ASSERT(hasEntryInColumn, "The scaling mode 'divide' requires an element in the given column.");
                    STORM_LOG_ASSERT(storm::utility::isZero(columnValue), "The scaling mode 'divide' requires a non-zero element in the given column.");
                    columnValue = storm::utility::one<ValueType>() / columnValue;
                } else if (Mode == ScalingMode::DivideOneMinus) {
                    if (hasEntryInColumn) {
                        STORM_LOG_ASSERT(columnValue != storm::utility::one<ValueType>(), "The scaling mode 'divide-one-minus' requires a non-one value in the given column.");
                        columnValue = storm::utility::one<ValueType>() / (storm::utility::one<ValueType>() - columnValue);
                        columnValue = storm::utility::simplify(columnValue);
                    }
                }
                
                if (hasEntryInColumn) {
                    for (auto entryIt = entriesInRow.begin(), entryIte = entriesInRow.end(); entryIt != entryIte; ++entryIt) {
                        // Only scale the entries in a different column.
                        if (entryIt->getColumn() != column) {
                            entryIt->setValue(storm::utility::simplify((ValueType) (entryIt->getValue() * columnValue)));
                        }
                    }
                    updateValue(row, columnValue);
                }
                
                // Now substitute the row entries in all other rows that contain an element whose column is the current row.
                FlexibleRowType& elementsWithEntryInColumnEqualRow = transposedMatrix.getRow(column);
                
                // In case we have a constrained elimination, we need to keep track of the rows that keep their value
                // in the column equal to the current row.
                FlexibleRowType rowsKeepingEntryInColumnEqualRow;
                
                // For each entry in the row d, we need to build a list of other rows that will contain an element in the
                // column d.
                std::vector<FlexibleRowType> newBackwardEntries(entriesInRow.size());
                for (auto& backwardEntry : newBackwardEntries) {
                    backwardEntry.reserve(elementsWithEntryInColumnEqualRow.size());
                }
                
                // Now go through the rows with an entry in the column corresponding to the current row and substitute
                // the elements of this row unless the elimination is filtered.
                for (auto const& predecessorEntry : elementsWithEntryInColumnEqualRow) {
                    uint_fast64_t predecessor = predecessorEntry.getColumn();
                    STORM_LOG_TRACE("Found predecessor " << predecessor << ".");
                    
                    // Skip the row itself.
                    if (predecessor == row) {
                        assert(hasEntryInColumn);
                        continue;
                    }
                    
                    // Skip the state if the elimination is constrained, but the predecessor is not in the constraint.
                    if (isFilterPredecessor() && !filterPredecessor(predecessor)) {
                        rowsKeepingEntryInColumnEqualRow.emplace_back(predecessorEntry);
                        STORM_LOG_TRACE("Not eliminating predecessor " << predecessor << ", because it does not fit the filter.");
                        continue;
                    }
                    STORM_LOG_TRACE("Eliminating predecessor " << predecessor << ".");
                    
                    // First, find the probability with which the predecessor can move to the current state, because
                    // the forward probabilities of the state to be eliminated need to be scaled with this factor.
                    FlexibleRowType& predecessorForwardTransitions = matrix.getRow(predecessor);
                    FlexibleRowIterator multiplyElement = std::find_if(predecessorForwardTransitions.begin(), predecessorForwardTransitions.end(), [&](storm::storage::MatrixEntry<typename storm::storage::FlexibleSparseMatrix<ValueType>::index_type, typename storm::storage::FlexibleSparseMatrix<ValueType>::value_type> const& a) { return a.getColumn() == column; });
                    
                    // Make sure we have found the probability and set it to zero.
                    STORM_LOG_THROW(multiplyElement != predecessorForwardTransitions.end(), storm::exceptions::InvalidStateException, "No probability for successor found.");
                    ValueType multiplyFactor = multiplyElement->getValue();
                    multiplyElement->setValue(storm::utility::zero<ValueType>());
                    
                    // At this point, we need to update the (forward) transitions of the predecessor.
                    FlexibleRowIterator first1 = predecessorForwardTransitions.begin();
                    FlexibleRowIterator last1 = predecessorForwardTransitions.end();
                    FlexibleRowIterator first2 = entriesInRow.begin();
                    FlexibleRowIterator last2 = entriesInRow.end();
                    
                    FlexibleRowType newSuccessors;
                    newSuccessors.reserve((last1 - first1) + (last2 - first2));
                    std::insert_iterator<FlexibleRowType> result(newSuccessors, newSuccessors.end());
                    
                    uint_fast64_t successorOffsetInNewBackwardTransitions = 0;
                    // Now we merge the two successor lists. (Code taken from std::set_union and modified to suit our needs).
                    for (; first1 != last1; ++result) {
                        // Skip the transitions to the state that is currently being eliminated.
                        if (first1->getColumn() == column || (first2 != last2 && first2->getColumn() == column)) {
                            if (first1->getColumn() == column) {
                                ++first1;
                            }
                            if (first2 != last2 && first2->getColumn() == column) {
                                ++first2;
                            }
                            continue;
                        }
                        
                        if (first2 == last2) {
                            std::copy_if(first1, last1, result, [&] (storm::storage::MatrixEntry<typename storm::storage::FlexibleSparseMatrix<ValueType>::index_type, typename storm::storage::FlexibleSparseMatrix<ValueType>::value_type> const& a) { return a.getColumn() != column; } );
                            break;
                        }
                        if (first2->getColumn() < first1->getColumn()) {
                            auto successorEntry = storm::utility::simplify(std::move(*first2 * multiplyFactor));
                            *result = successorEntry;
                            newBackwardEntries[successorOffsetInNewBackwardTransitions].emplace_back(predecessor, successorEntry.getValue());
                            ++first2;
                            ++successorOffsetInNewBackwardTransitions;
                        } else if (first1->getColumn() < first2->getColumn()) {
                            *result = *first1;
                            ++first1;
                        } else {
                            ValueType sprod = multiplyFactor * first2->getValue();
                            ValueType sum = first1->getValue() + storm::utility::simplify(sprod);
                            auto probability = storm::utility::simplify(sum);
                            *result = storm::storage::MatrixEntry<typename storm::storage::FlexibleSparseMatrix<ValueType>::index_type, typename storm::storage::FlexibleSparseMatrix<ValueType>::value_type>(first1->getColumn(), probability);
                            newBackwardEntries[successorOffsetInNewBackwardTransitions].emplace_back(predecessor, probability);
                            ++first1;
                            ++first2;
                            ++successorOffsetInNewBackwardTransitions;
                        }
                    }
                    for (; first2 != last2; ++first2) {
                        if (first2->getColumn() != column) {
                            auto stateProbability = storm::utility::simplify(std::move(*first2 * multiplyFactor));
                            *result = stateProbability;
                            newBackwardEntries[successorOffsetInNewBackwardTransitions].emplace_back(predecessor, stateProbability.getValue());
                            ++successorOffsetInNewBackwardTransitions;
                        }
                    }
                    
                    // Now move the new transitions in place.
                    predecessorForwardTransitions = std::move(newSuccessors);
                    STORM_LOG_TRACE("Fixed new next-state probabilities of predecessor state " << predecessor << ".");
                    
                    updatePredecessor(predecessor, multiplyFactor, row);
                    
                    STORM_LOG_TRACE("Updating priority of predecessor.");
                    updatePriority(predecessor);
                }
                
                // Finally, we need to add the predecessor to the set of predecessors of every successor.
                uint_fast64_t successorOffsetInNewBackwardTransitions = 0;
                for (auto const& successorEntry : entriesInRow) {
                    if (successorEntry.getColumn() == column) {
                        continue;
                    }
                    
                    FlexibleRowType& successorBackwardTransitions = transposedMatrix.getRow(successorEntry.getColumn());
                    
                    // Delete the current state as a predecessor of the successor state only if we are going to remove the
                    // current state's forward transitions.
                    if (clearRow) {
                        FlexibleRowIterator elimIt = std::find_if(successorBackwardTransitions.begin(), successorBackwardTransitions.end(), [&](storm::storage::MatrixEntry<typename storm::storage::FlexibleSparseMatrix<ValueType>::index_type, typename storm::storage::FlexibleSparseMatrix<ValueType>::value_type> const& a) { return a.getColumn() == row; });
                        STORM_LOG_ASSERT(elimIt != successorBackwardTransitions.end(), "Expected a proper backward transition from " << successorEntry.getColumn() << " to " << column << ", but found none.");
                        successorBackwardTransitions.erase(elimIt);
                    }
                    
                    FlexibleRowIterator first1 = successorBackwardTransitions.begin();
                    FlexibleRowIterator last1 = successorBackwardTransitions.end();
                    FlexibleRowIterator first2 = newBackwardEntries[successorOffsetInNewBackwardTransitions].begin();
                    FlexibleRowIterator last2 = newBackwardEntries[successorOffsetInNewBackwardTransitions].end();
                    
                    FlexibleRowType newPredecessors;
                    newPredecessors.reserve((last1 - first1) + (last2 - first2));
                    std::insert_iterator<FlexibleRowType> result(newPredecessors, newPredecessors.end());
                    
                    for (; first1 != last1; ++result) {
                        if (first2 == last2) {
                            std::copy(first1, last1, result);
                            break;
                        }
                        if (first2->getColumn() < first1->getColumn()) {
                            if (first2->getColumn() != row) {
                                *result = *first2;
                            }
                            ++first2;
                        } else if (first1->getColumn() == first2->getColumn()) {
                            if (estimateComplexity(first1->getValue()) > estimateComplexity(first2->getValue())) {
                                *result = *first1;
                            } else {
                                *result = *first2;
                            }
                            ++first1;
                            ++first2;
                        } else {
                            *result = *first1;
                            ++first1;
                        }
                    }
                    if (isFilterPredecessor()) {
                        std::copy_if(first2, last2, result, [&] (storm::storage::MatrixEntry<typename storm::storage::FlexibleSparseMatrix<ValueType>::index_type, typename storm::storage::FlexibleSparseMatrix<ValueType>::value_type> const& a) { return a.getColumn() != row && filterPredecessor(a.getColumn()); });
                    } else {
                        std::copy_if(first2, last2, result, [&] (storm::storage::MatrixEntry<typename storm::storage::FlexibleSparseMatrix<ValueType>::index_type, typename storm::storage::FlexibleSparseMatrix<ValueType>::value_type> const& a) { return a.getColumn() != row; });
                    }
                    // Now move the new predecessors in place.
                    successorBackwardTransitions = std::move(newPredecessors);
                    ++successorOffsetInNewBackwardTransitions;
                }
                STORM_LOG_TRACE("Fixed predecessor lists of successor states.");
                
                // Clear the row if requested.
                if (clearRow) {
                    entriesInRow.clear();
                    entriesInRow.shrink_to_fit();
                }
                
                // If the substitution was filtered, we need to store the new rows that have an entry in column equal to this row.
                if (isFilterPredecessor()) {
                    elementsWithEntryInColumnEqualRow = std::move(rowsKeepingEntryInColumnEqualRow);
                } else {
                    elementsWithEntryInColumnEqualRow.clear();
                    elementsWithEntryInColumnEqualRow.shrink_to_fit();
                }
            }
            
            template<typename ValueType, ScalingMode Mode>
            void EliminatorBase<ValueType, Mode>::updateValue(storm::storage::sparse::state_type const&, ValueType const&) {
                // Intentionally left empty.
            }
            
            template<typename ValueType, ScalingMode Mode>
            void EliminatorBase<ValueType, Mode>::updatePredecessor(storm::storage::sparse::state_type const&, ValueType const&, storm::storage::sparse::state_type const&) {
                // Intentionally left empty.
            }
            
            template<typename ValueType, ScalingMode Mode>
            void EliminatorBase<ValueType, Mode>::updatePriority(storm::storage::sparse::state_type const&) {
                // Intentionally left empty.
            }
            
            template<typename ValueType, ScalingMode Mode>
            bool EliminatorBase<ValueType, Mode>::filterPredecessor(storm::storage::sparse::state_type const&) {
                STORM_LOG_ASSERT(false, "Must not filter predecessors.");
                return false;
            }
            
            template<typename ValueType, ScalingMode Mode>
            bool EliminatorBase<ValueType, Mode>::isFilterPredecessor() const {
                return false;
            }
            
            template class EliminatorBase<double, ScalingMode::Divide>;
            template class EliminatorBase<double, ScalingMode::DivideOneMinus>;

#ifdef STORM_HAVE_CARL
            template class EliminatorBase<storm::RationalNumber, ScalingMode::Divide>;
            template class EliminatorBase<storm::RationalFunction, ScalingMode::Divide>;

            template class EliminatorBase<storm::RationalNumber, ScalingMode::DivideOneMinus>;
            template class EliminatorBase<storm::RationalFunction, ScalingMode::DivideOneMinus>;
#endif
        }
    }
}