#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <array>
#include <map>
#include <set>
#include <unordered_set>
#include <utility>
#include <cstring>
#include <functional>
#include <list>
#include <cctype>


#include "finite_function.hpp"

using namespace std;



const CellType CUR_BASE = 3;
const int ARGS_COUNT = 2;

template <size_t BASE>
class FixedIniter {
    public:
        // rules это отображение обязательных значений аргументов, к
        // значениями функции, которые не должны при них изменяться
        explicit FixedIniter(map<pair<size_t, size_t>, int> rules) : _rules(rules), _cur_values(BASE*BASE, 0) {
            for (auto it = rules.begin(); it != rules.end(); ++it) {
                size_t arg1 = it->first.first;
                size_t arg2 = it->first.second;
                int value = it->second;
                _cur_values.at(FiniteFunction<BASE>::get_index(arg1, arg2)) = value;

                _used_indexes.insert(FiniteFunction<BASE>::get_index(arg1, arg2));
            }
        }

        int operator() (int first, int second) const {
            return _cur_values[FiniteFunction<BASE>::get_index(first, second)];
        }

        // Возвращает true, пока может построить следующую функцию
        // если не может это сделать, то возвращает false
        bool set_next() {
            bool is_overflow = true;

            for (size_t i = 0; is_overflow; ++i) {
                if ( i >= _cur_values.size() )
                    return false;
                if ( _used_indexes.count(i) > 0 )
                    continue;
                _cur_values.at(i) += 1;
                bool is_overflow = (_cur_values.at(i) > static_cast<int>(BASE) - 1);
                if ( is_overflow )
                    _cur_values.at(i) = 0;
                else
                    return true;
            }
            throw "Wrong logic";
        }
    private:
        set<size_t> _used_indexes;
        map<pair<size_t, size_t>, int> _rules;
        vector<int> _cur_values;
};

template <class Iterable>
void write_function_class(ofstream &f_out, Iterable begin, Iterable end) {
    for (;begin != end; ++begin)
        f_out << *begin << "   ";
    f_out << endl;
}
/*
template <int BASE>
void get_permutations(vector<array<int, BASE>> &permutations) {
    permutations.clear();
    array<int, BASE> cur_perm;
    for (int i = 0; i < BASE; ++i)
        cur_perm[i] = i;
    do {
        permutations.push_back(cur_perm);
    } while ( next_permutation(cur_perm.begin(), cur_perm.end()) );
}
*/

template<class TripleArgsFiniteFunction>
bool is_one_arg_func(const TripleArgsFiniteFunction &h) {
    bool is_equaled_x = true;
    bool is_equaled_y = true;
    bool is_equaled_z = true;
    for (CellType x = 0; x < CUR_BASE; ++x)
        for (CellType y = 0; y < CUR_BASE; ++y) {
            for (CellType z = 0; z < CUR_BASE; ++z) {
                is_equaled_x = is_equaled_x && (h(x,y,z) == x);
                is_equaled_y = is_equaled_y && (h(x,y,z) == y);
                is_equaled_z = is_equaled_z && (h(x,y,z) == z);
            }
            if ( !is_equaled_x && !is_equaled_y && !is_equaled_z )
                return false;
        }
    return true;
}

template<class TripleArgsFiniteFunction>
bool is_projection(const TripleArgsFiniteFunction &h) {
    bool is_projection = true;
    for (CellType x = 0; x < CUR_BASE; ++x)
        for (CellType y = 0; y < CUR_BASE; ++y) {
            is_projection = (is_projection
                && h(x,x,y) == h(x,y,x)
                && h(x,y,x) == h(y,x,x)
                && h(y,x,x) == x);
        }
    return is_projection;
}

template<class TripleArgsFiniteFunction>
bool is_semiprojection(const TripleArgsFiniteFunction &h) {
    bool is_equaled_x = true;
    bool is_equaled_y = true;
    bool is_equaled_z = true;
    for (CellType x = 0; x < CUR_BASE; ++x)
        for (CellType y = 0; y < CUR_BASE; ++y)
            for (CellType z = 0; z < CUR_BASE; ++z) {
                // если все различны, то не рассматриваем
                if ( x != y && x != z && y != z )
                    continue;
                is_equaled_x = is_equaled_x && (h(x,y,z) == x);
                is_equaled_y = is_equaled_y && (h(x,y,z) == y);
                is_equaled_z = is_equaled_z && (h(x,y,z) == z);
            }
    return is_equaled_x || is_equaled_y || is_equaled_z;
}

bool is_passed_rosenberg(const FiniteFunction<CUR_BASE> &f) {
    auto h_1 = [f](const CellType x, const CellType y, CellType z) -> CellType {
        return f( f(x,y), f(x,z) );
    };
    if ( !is_one_arg_func(h_1) ) {
        if ( is_projection(h_1) || is_semiprojection(h_1) )
            return false;
    }

    auto h_2 = [f](const CellType x, const CellType y, CellType z) -> CellType {
        return f( f(x, y), f(z, x) );
    };
    if ( !is_one_arg_func(h_2) ) {
        if ( is_projection(h_2) || is_semiprojection(h_2) )
            return false;
    }

    auto h_3 = [f](const CellType x, const CellType y, CellType z) -> CellType {
        return f( f(x,y), f(y,z) );
    };
    if ( !is_one_arg_func(h_3) ) {
        if ( is_projection(h_3) || is_semiprojection(h_3) )
            return false;
    }

    auto h_4 = [f](const CellType x, const CellType y, CellType z) -> CellType {
        return f( f(x,y), f(z,y) );
    };
    if ( !is_one_arg_func(h_4) ) {
        if ( is_projection(h_4) || is_semiprojection(h_4) )
            return false;
    }
    return true;
}

template <CellType BASE>
vector<FiniteFunction<BASE>> get_funcs() {
    size_t count = 0;

    map<pair<size_t, size_t>, int> rules;
    for (int i = 0; i < BASE; ++i)
        rules[make_pair<size_t, size_t>(i,i)] = i;
    FixedIniter<BASE> initer(rules);

    //vector<array<int, BASE>> permutations;
    //get_permutations<BASE>(permutations);

    vector<FiniteFunction<BASE>> funcs;
    set< FiniteFunction<BASE> > permutated_funcs;
    do {
        ++count;
        auto cur_func = FiniteFunction<BASE>(initer);
        //if ( permutated_funcs.find(cur_func) != permutated_funcs.end() )
        //    continue;
        // если закомментить, то 17 классов, вместо 20
        //for (auto&& permutation: permutations)
       //     permutated_funcs.insert(cur_func.apply_permutation(permutation));
        funcs.push_back(cur_func);
    } while (initer.set_next());
    cout << "Total " << count << " functions" << endl;

    funcs.erase(
        remove_if(
            funcs.begin(),
            funcs.end(),
            [](const FiniteFunction<BASE> & f) {
                return !is_passed_rosenberg(f);
            }
        ),
        funcs.end()
    );

    cout << "After Rosenberg " << funcs.size() << " functions" << endl;
    //if ( permutated_funcs.size() != count )
     //   throw "Permutation's logic error!";
    return funcs;
}


template <CellType BASE>
set<FiniteFunction<BASE>> generate_function_class(FiniteFunction<BASE> base_function) {
    auto FiniteFunctionHasher = [](const FiniteFunction<BASE> &f) -> uint32_t {
        return f.get_hash();
    };
    unordered_set<
        FiniteFunction<CUR_BASE>,
        decltype(FiniteFunctionHasher)
    > func_class(1024, FiniteFunctionHasher);
    func_class.insert(base_function);
    //cout << "start with " << base_function << " ";

    size_t last_size = 0;  // размер в прошлой итерации
    while (true) {
        unordered_set<
            FiniteFunction<CUR_BASE>,
            decltype(FiniteFunctionHasher)
        >  new_funcs(1024, FiniteFunctionHasher);

        for (const auto& f_main: func_class) {
            new_funcs.insert(f_main.reversed());
            //new_funcs.insert(f_main.equaled());
            for (const auto& f_applied: func_class) {
                //FiniteFunction<BASE> f_left_1, f_left_2;
                //tie(f_left_1, f_left_2) = f_main.apply_to_first(f_applied);
                FiniteFunction<BASE> f_left;
                f_left = f_main.apply_to_first_partial(f_applied);
                new_funcs.insert(f_left);
            }
        }
        if ( new_funcs.size() == last_size ) {
            break;
        }

        func_class.insert(new_funcs.begin(), new_funcs.end());
        last_size = new_funcs.size();
    }
    return set<FiniteFunction<BASE>>(func_class.begin(), func_class.end());
}

int main() {
    auto FiniteFunctionHasher = [](const FiniteFunction<CUR_BASE> &f) -> uint32_t {
        return f.get_hash();
    };

    auto funcs = get_funcs<CUR_BASE>();
    cout << "Removing permutations " << funcs.size() << " functions" << endl;
    /*vector<array<int, 3>> permutations;
    get_permutations<3>(permutations);
    string function_to_str("000 112 212");
    cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[1]) << endl;
    cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[2]) << endl;
    cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[3]) << endl;
    cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[4]) << endl;
    cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[5]) << endl;
    */
    //cout << "022_210_002 -> " << FiniteFunction<3>(string("022 210 002")) << endl;

    //set<FiniteFunction<3>> allowed_functions(funcs.begin(), funcs.end());
    list< set<FiniteFunction<CUR_BASE>> > function_classes;
    unordered_set<
        FiniteFunction<CUR_BASE>,
        decltype(FiniteFunctionHasher)
    > allowed_functions(funcs.begin(), funcs.end(), 128, FiniteFunctionHasher);

    FiniteFunction<CUR_BASE> identical_x(string("000 111 222"));
    FiniteFunction<CUR_BASE> identical_y(string("012 012 012"));

    allowed_functions.erase(identical_x);
    allowed_functions.erase(identical_y);

    cout << "Total " << allowed_functions.size() << " functions" << endl;
    std::ofstream f_all_out("all_classes.txt");
    while ( allowed_functions.size() > 0 ) {
        //if (allowed_functions.size() % 10 == 0)
        //cout << 100 - allowed_functions.size() * 100. / funcs.size() << "%" << endl;
        auto base_function = *allowed_functions.begin();

        allowed_functions.erase(base_function);
        set< FiniteFunction<CUR_BASE> > func_class = generate_function_class(base_function);
        func_class.erase(identical_x);
        func_class.erase(identical_y);
        //f_all_out << base_function << " -> ";
        //write_function_class(f_all_out, func_class.begin(), func_class.end());

        bool is_need_append = true;
        vector<decltype(function_classes)::iterator> functions_to_remove;
        for (auto it = function_classes.begin(); it != function_classes.end(); ++it) {
            if ( func_class.size() < it->size() ) {
                if (includes(
                        it->begin(),
                        it->end(),
                        func_class.begin(),
                        func_class.end()
                    )
                ) {
                    // новый класс функций часть уже существующего
                    functions_to_remove.push_back(it);
                }
            } else {
                if (includes(
                        func_class.begin(),
                        func_class.end(),
                        it->begin(),
                        it->end()
                    )
                ) {
                    // новый класс функций надмножество существующего
                    is_need_append = false;
                    break;
                }
            }
        }
        if ( is_need_append )
            function_classes.push_back(func_class);
        for (auto&& to_remove: functions_to_remove)
            function_classes.erase(to_remove);
    }
    cout << function_classes.size() << " functions!" << endl;
    // перегоняем список с классами в массив с классами
    vector< set<FiniteFunction<CUR_BASE>> > vector_classes(
        function_classes.begin(),
        function_classes.end()
    );
    /*// фильтруем перестановки
    vector<array<int, CUR_BASE>> permutations;
    get_permutations<CUR_BASE>(permutations);
    map<size_t, vector<vector<set<FiniteFunction<CUR_BASE>>>::iterator> > classes_per_size;
    for (auto it = vector_classes.begin(); it != vector_classes.end(); ++it) {
        classes_per_size[it->size()].push_back(it);
    }

    set<vector<set<FiniteFunction<CUR_BASE>>>::iterator> classes_to_remove;


    for (auto&& class_fixed_size: classes_per_size) {
        typedef pair<FiniteFunction<CUR_BASE>,vector<set<FiniteFunction<CUR_BASE>>>::iterator> sorting_arr_type;
        cout << class_fixed_size.first << " -> " <<
            class_fixed_size.second.size() << endl;

        vector< sorting_arr_type > all_class_elements;
        for (auto &&cur_class_it: class_fixed_size.second) {
            for (auto&& cur_fn: (*cur_class_it)) {
                if ( (cur_fn == identical_x) || (cur_fn == identical_y) )
                    continue;
                for (auto&& permutation: permutations)
                    all_class_elements.push_back(make_pair(
                        cur_fn.apply_permutation(permutation),
                        cur_class_it
                    ));
            }
        }
        cout << all_class_elements.size() << endl;
        // сортируем массив
        sort(all_class_elements.begin(),all_class_elements.end());
        for (auto&& el: all_class_elements)
            cout << el.first << "|";
        // выбираем, кого удалить
        for (size_t i = 0; i < all_class_elements.size(); ++i) {
            decltype(classes_to_remove) cur_vals_to_remove;
            size_t j;
            for (
                j = i;
                (j < all_class_elements.size()) &&
                (all_class_elements.at(i).first == all_class_elements.at(j).first);
                ++j
            ) {
                cout << all_class_elements.at(i).first << "<->" <<
                all_class_elements.at(j).first <<  " " <<
                (all_class_elements.at(i).second == all_class_elements.at(j).second )
                <<endl;
                cur_vals_to_remove.insert(all_class_elements.at(j).second);
            }

            for (
                    auto it = next(cur_vals_to_remove.begin());
                    it != cur_vals_to_remove.end();
                    ++it
            ) {
                classes_to_remove.insert(*it);
            }

            cout << "size " << cur_vals_to_remove.size() << endl;
            i = j;
        }


    }
    cout << "classes_to_remove.size() = " <<classes_to_remove.size() << endl;
    // удаляем
    {
        decltype(vector_classes) new_vector_classes;
        for (auto it = vector_classes.begin(); it != vector_classes.end(); ++it)
            if ( classes_to_remove.find(it) == classes_to_remove.end() )
                new_vector_classes.push_back(*it);
        swap(new_vector_classes, vector_classes);
    }*/
    std::ofstream f_out("classes.txt");
    for (const auto& func_class: vector_classes) {
        write_function_class(f_out, func_class.begin(), func_class.end());
    }
    f_out.close();
    return 0;
}