#ifndef STORM_SOLVER_SYMBOLICMINMAXLINEAREQUATIONSOLVER_H_
#define STORM_SOLVER_SYMBOLICMINMAXLINEAREQUATIONSOLVER_H_

#include <memory>
#include <set>
#include <vector>
#include <boost/optional.hpp>

#include "storm/solver/SymbolicEquationSolver.h"
#include "storm/solver/OptimizationDirection.h"
#include "storm/solver/SymbolicLinearEquationSolver.h"
#include "storm/solver/MinMaxLinearEquationSolverRequirements.h"
#include "storm/solver/SolverStatus.h"

#include "storm/utility/NumberTraits.h"

#include "storm/storage/expressions/Variable.h"
#include "storm/storage/dd/DdType.h"
#include "SolverSelectionOptions.h"

namespace storm {
    
    class Environment;
    
    namespace dd {
        template<storm::dd::DdType Type, typename ValueType>
        class Add;
        
        template<storm::dd::DdType T>
        class Bdd;
    }
    
    namespace solver {
        /*!
         * An interface that represents an abstract symbolic linear equation solver. In addition to solving a system of
         * linear equations, the functionality to repeatedly multiply a matrix with a given vector is provided.
         */
        template<storm::dd::DdType DdType, typename ValueType>
        class SymbolicMinMaxLinearEquationSolver : public SymbolicEquationSolver<DdType, ValueType> {
        public:
            SymbolicMinMaxLinearEquationSolver();
            virtual ~SymbolicMinMaxLinearEquationSolver() = default;

            /*!
             * Constructs a symbolic min/max linear equation solver with the given meta variable sets and pairs.
             *
             * @param A The matrix defining the coefficients of the linear equation system.
             * @param diagonal An ADD characterizing the elements on the diagonal of the matrix.
             * @param allRows A BDD characterizing all rows of the equation system.
             * @param illegalMask A mask that characterizes all illegal choices (that are therefore not to be taken).
             * @param rowMetaVariables The meta variables used to encode the rows of the matrix.
             * @param columnMetaVariables The meta variables used to encode the columns of the matrix.
             * @param choiceVariables The variables encoding the choices of each row group.
             * @param rowColumnMetaVariablePairs The pairs of row meta variables and the corresponding column meta
             * variables.
             * @param settings The settings to use.
             */
            SymbolicMinMaxLinearEquationSolver(storm::dd::Add<DdType, ValueType> const& A, storm::dd::Bdd<DdType> const& allRows, storm::dd::Bdd<DdType> const& illegalMask, std::set<storm::expressions::Variable> const& rowMetaVariables, std::set<storm::expressions::Variable> const& columnMetaVariables, std::set<storm::expressions::Variable> const& choiceVariables, std::vector<std::pair<storm::expressions::Variable, storm::expressions::Variable>> const& rowColumnMetaVariablePairs, std::unique_ptr<SymbolicLinearEquationSolverFactory<DdType, ValueType>>&& linearEquationSolverFactory);
                        
            /*!
             * Solves the equation system A*x = b. The matrix A is required to be square and have a unique solution.
             * The solution of the set of linear equations will be written to the vector x. Note that the matrix A has
             * to be given upon construction time of the solver object.
             *
             * @param dir Determines the direction of the optimization.
             * @param x The initual guess for the solution vector. Its length must be equal to the number of row
             * groups of A.
             * @param b The right-hand side of the equation system. Its length must be equal to the number of row groups
             * of A.
             * @return The solution of the equation system.
             */
            virtual storm::dd::Add<DdType, ValueType> solveEquations(Environment const& env, storm::solver::OptimizationDirection const& dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            
            /*!
             * Performs repeated matrix-vector multiplication, using x[0] = x and x[i + 1] = A*x[i] + b. After
             * performing the necessary multiplications, the result is written to the input vector x. Note that the
             * matrix A has to be given upon construction time of the solver object.
             *
             * @param dir Determines the direction of the optimization.
             * @param x The initial vector with which to perform matrix-vector multiplication. Its length must be equal
             * to the number of row groups of A.
             * @param b If non-null, this vector is added after each multiplication. If given, its length must be equal
             * to the number of row groups of A.
             * @return The solution of the equation system.
             */
            virtual storm::dd::Add<DdType, ValueType> multiply(storm::solver::OptimizationDirection const& dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const* b = nullptr, uint_fast64_t n = 1) const;

            /*!
             * Sets an initial scheduler that is required by some solvers (see requirements).
             */
            void setInitialScheduler(storm::dd::Bdd<DdType> const& scheduler);
            
            /*!
             * Retrieves the initial scheduler (if there is any).
             */
            storm::dd::Bdd<DdType> const& getInitialScheduler() const;
            
            /*!
             * Retrieves whether an initial scheduler was set.
             */
            bool hasInitialScheduler() const;
            
            /*!
             * Retrieves the requirements of the solver.
             */
            virtual MinMaxLinearEquationSolverRequirements getRequirements(Environment const& env, boost::optional<storm::solver::OptimizationDirection> const& direction = boost::none) const;
            
                        /*!
             * Sets whether the solution to the min max equation system is known to be unique.
             */
            void setHasUniqueSolution(bool value = true);
            
            /*!
             * Retrieves whether the solution to the min max equation system is assumed to be unique
             */
            bool hasUniqueSolution() const;
            
            /*!
             * Notifies the solver that the requirements for solving equations have been checked. If this has not been
             * done before solving equations, the solver might issue a warning, perform the checks itself or even fail.
             */
            void setRequirementsChecked(bool value = true);
            
            /*!
             * Retrieves whether the solver is aware that the requirements were checked.
             */
            bool isRequirementsCheckedSet() const;

            /*!
             * Determines whether the given vector x satisfies x = min/max Ax + b.
             */
            bool isSolution(OptimizationDirection dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;

        private:
            
            MinMaxMethod getMethod(Environment const& env, bool isExactMode) const;
            
            storm::dd::Add<DdType, ValueType> solveEquationsWithScheduler(Environment const& env, storm::dd::Bdd<DdType> const& scheduler, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            storm::dd::Add<DdType, ValueType> solveEquationsWithScheduler(Environment const& env, SymbolicLinearEquationSolver<DdType, ValueType>& solver, storm::dd::Bdd<DdType> const& scheduler, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b, storm::dd::Add<DdType, ValueType> const& diagonal) const;
            
            storm::dd::Add<DdType, ValueType> solveEquationsValueIteration(Environment const& env, storm::solver::OptimizationDirection const& dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            storm::dd::Add<DdType, ValueType> solveEquationsPolicyIteration(Environment const& env, storm::solver::OptimizationDirection const& dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            storm::dd::Add<DdType, ValueType> solveEquationsRationalSearch(Environment const& env, storm::solver::OptimizationDirection const& dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            
            template<typename RationalType, typename ImpreciseType>
            static storm::dd::Add<DdType, RationalType> sharpen(OptimizationDirection dir, uint64_t precision, SymbolicMinMaxLinearEquationSolver<DdType, RationalType> const& rationalSolver, storm::dd::Add<DdType, ImpreciseType> const& x, storm::dd::Add<DdType, RationalType> const& rationalB, bool& isSolution);
            
            template<typename RationalType, typename ImpreciseType>
            storm::dd::Add<DdType, RationalType> solveEquationsRationalSearchHelper(Environment const& env, OptimizationDirection dir, SymbolicMinMaxLinearEquationSolver<DdType, RationalType> const& rationalSolver, SymbolicMinMaxLinearEquationSolver<DdType, ImpreciseType> const& impreciseSolver, storm::dd::Add<DdType, RationalType> const& rationalB, storm::dd::Add<DdType, ImpreciseType> const& x, storm::dd::Add<DdType, ImpreciseType> const& b) const;
            template<typename ImpreciseType>
            typename std::enable_if<std::is_same<ValueType, ImpreciseType>::value && storm::NumberTraits<ValueType>::IsExact, storm::dd::Add<DdType, ValueType>>::type solveEquationsRationalSearchHelper(Environment const& env, storm::solver::OptimizationDirection const& dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            template<typename ImpreciseType>
            typename std::enable_if<std::is_same<ValueType, ImpreciseType>::value && !storm::NumberTraits<ValueType>::IsExact, storm::dd::Add<DdType, ValueType>>::type solveEquationsRationalSearchHelper(Environment const& env, storm::solver::OptimizationDirection const& dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            template<typename ImpreciseType>
            typename std::enable_if<!std::is_same<ValueType, ImpreciseType>::value, storm::dd::Add<DdType, ValueType>>::type solveEquationsRationalSearchHelper(Environment const& env, storm::solver::OptimizationDirection const& dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            
            template<storm::dd::DdType DdTypePrime, typename ValueTypePrime>
            friend class SymbolicMinMaxLinearEquationSolver;
            
            struct ValueIterationResult {
                ValueIterationResult(SolverStatus status, uint64_t iterations, storm::dd::Add<DdType, ValueType> const& values) : status(status), iterations(iterations), values(values) {
                    // Intentionally left empty.
                }
                
                SolverStatus status;
                uint64_t iterations;
                storm::dd::Add<DdType, ValueType> values;
            };
            
            ValueIterationResult performValueIteration(storm::solver::OptimizationDirection const& dir, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b, ValueType const& precision, bool relativeTerminationCriterion, uint64_t maximalIterations) const;
            
        protected:
            // The matrix defining the coefficients of the linear equation system.
            storm::dd::Add<DdType, ValueType> A;
            
            // A BDD characterizing the illegal choices.
            storm::dd::Bdd<DdType> illegalMask;
            
            // An ADD characterizing the illegal choices.
            storm::dd::Add<DdType, ValueType> illegalMaskAdd;
            
            // The row variables.
            std::set<storm::expressions::Variable> rowMetaVariables;
            
            // The column variables.
            std::set<storm::expressions::Variable> columnMetaVariables;
            
            // The choice variables.
            std::set<storm::expressions::Variable> choiceVariables;
            
            // The pairs of meta variables used for renaming.
            std::vector<std::pair<storm::expressions::Variable, storm::expressions::Variable>> rowColumnMetaVariablePairs;
            
            // A factory for creating linear equation solvers when needed.
            std::unique_ptr<SymbolicLinearEquationSolverFactory<DdType, ValueType>> linearEquationSolverFactory;
            
            // Whether the solver can assume that the min-max equation system has a unique solution
            bool uniqueSolution;
            
            // A flag indicating whether the requirements were checked.
            bool requirementsChecked;
            
            // A scheduler that specifies with which schedulers to start.
            boost::optional<storm::dd::Bdd<DdType>> initialScheduler;
            
        private:
            /*!
             * Forwards the known bounds of this solver to the given linear equation solver.
             */
            void forwardBounds(storm::solver::SymbolicLinearEquationSolver<DdType, ValueType>& solver) const;
        };
        
        template<storm::dd::DdType DdType, typename ValueType>
        class SymbolicMinMaxLinearEquationSolverFactory {
        public:
            virtual ~SymbolicMinMaxLinearEquationSolverFactory() = default;

            virtual std::unique_ptr<storm::solver::SymbolicMinMaxLinearEquationSolver<DdType, ValueType>> create(storm::dd::Add<DdType, ValueType> const& A, storm::dd::Bdd<DdType> const& allRows, storm::dd::Bdd<DdType> const& illegalMask, std::set<storm::expressions::Variable> const& rowMetaVariables, std::set<storm::expressions::Variable> const& columnMetaVariables, std::set<storm::expressions::Variable> const& choiceVariables, std::vector<std::pair<storm::expressions::Variable, storm::expressions::Variable>> const& rowColumnMetaVariablePairs) const = 0;
            
            /*!
             * Retrieves the requirements of the solver that would be created when calling create() right now. The
             * requirements are guaranteed to be ordered according to their appearance in the SolverRequirement type.
             */
            MinMaxLinearEquationSolverRequirements getRequirements(Environment const& env, bool hasUniqueSolution = false, boost::optional<storm::solver::OptimizationDirection> const& direction = boost::none) const;
            
        private:
            virtual std::unique_ptr<storm::solver::SymbolicMinMaxLinearEquationSolver<DdType, ValueType>> create() const = 0;
        };
        
        template<storm::dd::DdType DdType, typename ValueType>
        class GeneralSymbolicMinMaxLinearEquationSolverFactory : public SymbolicMinMaxLinearEquationSolverFactory<DdType, ValueType> {
        public:
            virtual std::unique_ptr<storm::solver::SymbolicMinMaxLinearEquationSolver<DdType, ValueType>> create(storm::dd::Add<DdType, ValueType> const& A, storm::dd::Bdd<DdType> const& allRows, storm::dd::Bdd<DdType> const& illegalMask, std::set<storm::expressions::Variable> const& rowMetaVariables, std::set<storm::expressions::Variable> const& columnMetaVariables, std::set<storm::expressions::Variable> const& choiceVariables, std::vector<std::pair<storm::expressions::Variable, storm::expressions::Variable>> const& rowColumnMetaVariablePairs) const override;
            
        private:
            virtual std::unique_ptr<storm::solver::SymbolicMinMaxLinearEquationSolver<DdType, ValueType>> create() const override;
            
        };
        
    } // namespace solver
} // namespace storm

#endif /* STORM_SOLVER_SYMBOLICMINMAXLINEAREQUATIONSOLVER_H_ */