agents

-module(backtracking_engine).
-behaviour(gen_statem).

-export([start_link/0, start_link/1]).
-export([solve/2, add_constraint/2, remove_constraint/2, reset/1, get_solution/1]).
-export([init/1, callback_mode/0, terminate/3, code_change/4]).
-export([idle/3, problem_analysis/3, variable_selection/3, value_assignment/3, 
         constraint_checking/3, backtracking/3, solution_found/3, 
         optimization/3, learning/3, failed/3]).

-record(backtrack_data, {
    problem_id :: term(),
    variables = [] :: [term()],
    domains = #{} :: #{term() => [term()]},
    constraints = [] :: [term()],
    assignments = #{} :: #{term() => term()},
    search_stack = [] :: [#{term() => term()}],
    solution_count = 0 :: non_neg_integer(),
    best_solution = undefined :: undefined | #{term() => term()},
    optimization_function = undefined :: undefined | fun(),
    learning_data = #{} :: #{term() => term()},
    heuristics = #{} :: #{term() => term()},
    statistics = #{} :: #{atom() => term()},
    max_solutions = 1 :: pos_integer(),
    timeout = infinity :: timeout(),
    start_time :: erlang:timestamp()
}).

start_link() ->
    gen_statem:start_link(?MODULE, [], []).

start_link(Options) ->
    gen_statem:start_link(?MODULE, Options, []).

solve(Pid, Problem) ->
    gen_statem:call(Pid, {solve, Problem}).

add_constraint(Pid, Constraint) ->
    gen_statem:call(Pid, {add_constraint, Constraint}).

remove_constraint(Pid, Constraint) ->
    gen_statem:call(Pid, {remove_constraint, Constraint}).

reset(Pid) ->
    gen_statem:call(Pid, reset).

get_solution(Pid) ->
    gen_statem:call(Pid, get_solution).

init(Options) ->
    Data = #backtrack_data{
        start_time = erlang:timestamp(),
        max_solutions = proplists:get_value(max_solutions, Options, 1),
        timeout = proplists:get_value(timeout, Options, infinity),
        optimization_function = proplists:get_value(optimization_function, Options, undefined),
        heuristics = #{
            variable_selection => most_constrained_variable,
            value_selection => least_constraining_value,
            constraint_propagation => arc_consistency,
            learning => conflict_directed_backjumping
        },
        statistics = #{
            nodes_visited => 0,
            backtracks => 0,
            constraint_checks => 0,
            learning_events => 0
        }
    },
    {ok, idle, Data}.

callback_mode() -> [state_functions, state_enter].

idle(enter, _OldState, Data) ->
    {keep_state, Data};
idle({call, From}, {solve, Problem}, Data) ->
    NewData = initialize_problem(Problem, Data),
    {next_state, problem_analysis, NewData, [{reply, From, ok}]};
idle({call, From}, reset, Data) ->
    ResetData = Data#backtrack_data{
        variables = [],
        domains = #{},
        constraints = [],
        assignments = #{},
        search_stack = [],
        solution_count = 0,
        best_solution = undefined,
        learning_data = #{},
        start_time = erlang:timestamp(),
        statistics = #{
            nodes_visited => 0,
            backtracks => 0,
            constraint_checks => 0,
            learning_events => 0
        }
    },
    {keep_state, ResetData, [{reply, From, ok}]};
idle({call, From}, get_solution, Data) ->
    {keep_state, Data, [{reply, From, {ok, Data#backtrack_data.best_solution}}]};
idle(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

problem_analysis(enter, _OldState, Data) ->
    AnalysisData = analyze_problem_structure(Data),
    case validate_problem(AnalysisData) of
        valid ->
            {next_state, variable_selection, AnalysisData};
        {invalid, Reason} ->
            {next_state, failed, AnalysisData#backtrack_data{statistics = 
                maps:put(failure_reason, Reason, AnalysisData#backtrack_data.statistics)}}
    end;
problem_analysis(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

variable_selection(enter, _OldState, Data) ->
    case select_next_variable(Data) of
        {ok, Variable} ->
            UpdatedData = Data#backtrack_data{
                statistics = maps:update_with(nodes_visited, fun(X) -> X + 1 end, 1, 
                    Data#backtrack_data.statistics)
            },
            {next_state, value_assignment, UpdatedData, [{state_timeout, 0, {variable_selected, Variable}}]};
        no_variables ->
            {next_state, solution_found, Data}
    end;
variable_selection(state_timeout, {variable_selected, Variable}, Data) ->
    {next_state, value_assignment, Data, [{state_timeout, 0, {assign_variable, Variable}}]};
variable_selection(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

value_assignment(enter, _OldState, Data) ->
    {keep_state, Data};
value_assignment(state_timeout, {assign_variable, Variable}, Data) ->
    case select_value_for_variable(Variable, Data) of
        {ok, Value} ->
            NewAssignments = maps:put(Variable, Value, Data#backtrack_data.assignments),
            NewData = Data#backtrack_data{assignments = NewAssignments},
            {next_state, constraint_checking, NewData, 
                [{state_timeout, 0, {check_constraints, Variable, Value}}]};
        no_values ->
            {next_state, backtracking, Data}
    end;
value_assignment(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

constraint_checking(enter, _OldState, Data) ->
    {keep_state, Data};
constraint_checking(state_timeout, {check_constraints, Variable, Value}, Data) ->
    UpdatedStats = maps:update_with(constraint_checks, fun(X) -> X + 1 end, 1, 
        Data#backtrack_data.statistics),
    UpdatedData = Data#backtrack_data{statistics = UpdatedStats},
    
    case check_all_constraints(Variable, Value, UpdatedData) of
        consistent ->
            propagate_constraints(Variable, Value, UpdatedData),
            {next_state, variable_selection, UpdatedData};
        inconsistent ->
            learn_from_conflict(Variable, Value, UpdatedData),
            {next_state, backtracking, UpdatedData};
        {inconsistent, ConflictInfo} ->
            LearnedData = advanced_conflict_learning(ConflictInfo, UpdatedData),
            {next_state, backtracking, LearnedData}
    end;
constraint_checking(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

backtracking(enter, _OldState, Data) ->
    UpdatedStats = maps:update_with(backtracks, fun(X) -> X + 1 end, 1, 
        Data#backtrack_data.statistics),
    BacktrackData = Data#backtrack_data{statistics = UpdatedStats},
    
    case perform_intelligent_backtrack(BacktrackData) of
        {ok, RestoredData} ->
            {next_state, variable_selection, RestoredData};
        {backjump, JumpData} ->
            {next_state, variable_selection, JumpData};
        no_more_choices ->
            {next_state, failed, BacktrackData}
    end;
backtracking(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

solution_found(enter, _OldState, Data) ->
    SolutionData = record_solution(Data),
    case SolutionData#backtrack_data.solution_count >= SolutionData#backtrack_data.max_solutions of
        true ->
            case SolutionData#backtrack_data.optimization_function of
                undefined ->
                    {next_state, learning, SolutionData};
                _OptFunc ->
                    {next_state, optimization, SolutionData}
            end;
        false ->
            {next_state, backtracking, SolutionData}
    end;
solution_found(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

optimization(enter, _OldState, Data) ->
    OptimizedData = optimize_solution(Data),
    {next_state, learning, OptimizedData};
optimization(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

learning(enter, _OldState, Data) ->
    LearnedData = perform_learning_phase(Data),
    {next_state, idle, LearnedData};
learning({call, From}, get_solution, Data) ->
    {keep_state, Data, [{reply, From, {ok, Data#backtrack_data.best_solution}}]};
learning(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

failed(enter, _OldState, Data) ->
    {keep_state, Data};
failed({call, From}, get_solution, Data) ->
    {keep_state, Data, [{reply, From, {error, no_solution}}]};
failed({call, From}, reset, Data) ->
    {next_state, idle, reset_data(Data), [{reply, From, ok}]};
failed(EventType, Event, Data) ->
    handle_common_events(EventType, Event, Data).

terminate(_Reason, _State, _Data) ->
    ok.

code_change(_Vsn, State, Data, _Extra) ->
    {ok, State, Data}.

initialize_problem({Variables, Domains, Constraints}, Data) ->
    Data#backtrack_data{
        variables = Variables,
        domains = Domains,
        constraints = Constraints,
        assignments = #{},
        search_stack = [#{}],
        solution_count = 0,
        best_solution = undefined,
        start_time = erlang:timestamp()
    }.

analyze_problem_structure(Data) ->
    Variables = Data#backtrack_data.variables,
    Constraints = Data#backtrack_data.constraints,
    
    ConstraintGraph = build_constraint_graph(Variables, Constraints),
    VariableOrdering = compute_variable_ordering(Variables, ConstraintGraph),
    DomainSizes = compute_domain_statistics(Data#backtrack_data.domains),
    
    UpdatedHeuristics = maps:merge(Data#backtrack_data.heuristics, #{
        constraint_graph => ConstraintGraph,
        variable_ordering => VariableOrdering,
        domain_statistics => DomainSizes
    }),
    
    Data#backtrack_data{heuristics = UpdatedHeuristics}.

validate_problem(Data) ->
    case {Data#backtrack_data.variables, Data#backtrack_data.domains} of
        {[], _} -> {invalid, no_variables};
        {_, Domains} when map_size(Domains) =:= 0 -> {invalid, no_domains};
        _ -> 
            case check_domain_consistency(Data) of
                true -> valid;
                false -> {invalid, inconsistent_domains}
            end
    end.

select_next_variable(Data) ->
    UnassignedVars = [V || V <- Data#backtrack_data.variables, 
                          not maps:is_key(V, Data#backtrack_data.assignments)],
    case UnassignedVars of
        [] -> no_variables;
        Vars -> 
            Strategy = maps:get(variable_selection, Data#backtrack_data.heuristics, 
                              most_constrained_variable),
            {ok, apply_variable_selection_heuristic(Strategy, Vars, Data)}
    end.

select_value_for_variable(Variable, Data) ->
    Domain = maps:get(Variable, Data#backtrack_data.domains, []),
    AvailableValues = filter_available_values(Variable, Domain, Data),
    case AvailableValues of
        [] -> no_values;
        Values ->
            Strategy = maps:get(value_selection, Data#backtrack_data.heuristics, 
                              least_constraining_value),
            {ok, apply_value_selection_heuristic(Strategy, Variable, Values, Data)}
    end.

check_all_constraints(Variable, Value, Data) ->
    Constraints = Data#backtrack_data.constraints,
    Assignments = Data#backtrack_data.assignments,
    check_constraints_recursive(Constraints, Variable, Value, Assignments).

perform_intelligent_backtrack(Data) ->
    case Data#backtrack_data.search_stack of
        [_Current] -> no_more_choices;
        [_Current | Rest] ->
            case maps:get(learning, Data#backtrack_data.heuristics, basic_backtrack) of
                conflict_directed_backjumping ->
                    perform_backjump(Data);
                basic_backtrack ->
                    perform_basic_backtrack(Rest, Data)
            end
    end.

record_solution(Data) ->
    CurrentSolution = Data#backtrack_data.assignments,
    UpdatedCount = Data#backtrack_data.solution_count + 1,
    
    BestSolution = case Data#backtrack_data.optimization_function of
        undefined -> CurrentSolution;
        _OptFunc when Data#backtrack_data.best_solution =:= undefined -> CurrentSolution;
        OptFunc -> 
            case OptFunc(CurrentSolution, Data#backtrack_data.best_solution) of
                better -> CurrentSolution;
                _ -> Data#backtrack_data.best_solution
            end
    end,
    
    Data#backtrack_data{
        solution_count = UpdatedCount,
        best_solution = BestSolution
    }.

optimize_solution(Data) ->
    case Data#backtrack_data.optimization_function of
        undefined -> Data;
        OptFunc ->
            OptimizedSolution = apply_optimization_techniques(Data#backtrack_data.best_solution, OptFunc),
            Data#backtrack_data{best_solution = OptimizedSolution}
    end.

perform_learning_phase(Data) ->
    LearningStats = maps:update_with(learning_events, fun(X) -> X + 1 end, 1, 
        Data#backtrack_data.statistics),
    
    UpdatedHeuristics = learn_from_search_experience(Data),
    
    Data#backtrack_data{
        statistics = LearningStats,
        heuristics = maps:merge(Data#backtrack_data.heuristics, UpdatedHeuristics)
    }.

handle_common_events({call, From}, {add_constraint, Constraint}, Data) ->
    NewConstraints = [Constraint | Data#backtrack_data.constraints],
    {keep_state, Data#backtrack_data{constraints = NewConstraints}, [{reply, From, ok}]};
handle_common_events({call, From}, {remove_constraint, Constraint}, Data) ->
    NewConstraints = lists:delete(Constraint, Data#backtrack_data.constraints),
    {keep_state, Data#backtrack_data{constraints = NewConstraints}, [{reply, From, ok}]};
handle_common_events(_EventType, _Event, _Data) ->
    {keep_state_and_data, [postpone]}.

build_constraint_graph(_Variables, _Constraints) ->
    #{}.

compute_variable_ordering(Variables, _Graph) ->
    Variables.

compute_domain_statistics(Domains) ->
    maps:map(fun(_Var, Domain) -> length(Domain) end, Domains).

check_domain_consistency(_Data) ->
    true.

apply_variable_selection_heuristic(_Strategy, [Var|_], _Data) ->
    Var.

filter_available_values(_Variable, Domain, _Data) ->
    Domain.

apply_value_selection_heuristic(_Strategy, _Variable, [Value|_], _Data) ->
    Value.

check_constraints_recursive([], _Variable, _Value, _Assignments) ->
    consistent;
check_constraints_recursive([_Constraint|Rest], Variable, Value, Assignments) ->
    check_constraints_recursive(Rest, Variable, Value, Assignments).

propagate_constraints(_Variable, _Value, _Data) ->
    ok.

learn_from_conflict(_Variable, _Value, _Data) ->
    ok.

advanced_conflict_learning(_ConflictInfo, Data) ->
    Data.

perform_backjump(Data) ->
    {ok, Data}.

perform_basic_backtrack([PrevState|_], Data) ->
    {ok, Data#backtrack_data{assignments = PrevState}}.

apply_optimization_techniques(Solution, _OptFunc) ->
    Solution.

learn_from_search_experience(_Data) ->
    #{}.

reset_data(Data) ->
    Data#backtrack_data{
        variables = [],
        domains = #{},
        constraints = [],
        assignments = #{},
        search_stack = [],
        solution_count = 0,
        best_solution = undefined
    }.