576 lines
21 KiB
C++
576 lines
21 KiB
C++
#include <iostream>
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#include <fstream>
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#include <vector>
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#include <algorithm>
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#include <array>
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#include <map>
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#include <set>
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#include <unordered_set>
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#include <utility>
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#include <cstring>
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#include <functional>
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#include <list>
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#include <cctype>
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using namespace std;
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typedef int8_t CellType;
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const CellType CUR_BASE = 3;
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const int ARGS_COUNT = 2;
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// Пока положим, что только два аргумента, чтобы упростить реализацию
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template <CellType BASE>
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class FiniteFunction {
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public:
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FiniteFunction() {}
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// Устанавливает результат функции, использую другую функцию как
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// инициализатор
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template <class Callable>
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FiniteFunction(Callable initer) : _num(0) {
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for (CellType first = 0; first < BASE; ++first)
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for (CellType second = 0; second < BASE; ++second) {
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auto inited_result = initer(first, second);
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set_result(first, second, inited_result);
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}
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update_num();
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}
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explicit FiniteFunction(string text_repr) {
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size_t cur_ind = 0;
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for (auto ch: text_repr) {
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if ( !isdigit(ch) )
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continue;
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_results.at(cur_ind) = stoi(string(1, ch));
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++cur_ind;
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}
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update_num();
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}
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~FiniteFunction() {}
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// Устанавливает результат функции по двум аргументам
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void set_result(CellType first, CellType second, CellType result) {
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_results[get_index(first, second)] = result;
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}
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int operator() (CellType first, CellType second) const {
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return _results[get_index(first, second)];
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}
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bool operator < (const FiniteFunction &f) const {
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return _num < f._num;
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}
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bool operator == (const FiniteFunction &f) const {
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return _num == f._num;
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}
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FiniteFunction reversed() const {
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// f(x,y) -> f(y,x)
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FiniteFunction res;
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for (CellType first = 0; first < BASE; ++first)
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for (CellType second = 0; second < BASE; ++second) {
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res.set_result(first, second, (*this)(second, first));
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}
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res.update_num();
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return res;
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}
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FiniteFunction equaled() const {
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// f(x,y) -> f(x,x)
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FiniteFunction res;
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for (CellType first = 0; first < BASE; ++first)
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for (CellType second = 0; second < BASE; ++second) {
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res.set_result(first, second, (*this)(first, first));
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}
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res.update_num();
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return res;
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}
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FiniteFunction apply_to_first_partial(const FiniteFunction &g) const {
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// -> this(g(x,y), x)
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FiniteFunction res;
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for (CellType first = 0; first < BASE; ++first)
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for (CellType second = 0; second < BASE; ++second) {
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res.set_result(first, second, (*this)(g(first, second), first));
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}
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res.update_num();
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return res;
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}
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tuple<FiniteFunction, FiniteFunction> apply_to_first(const FiniteFunction &g) const {
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// -> this(g(x,y), x), this(g(x,y), y)
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FiniteFunction res_1, res_2;
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for (CellType first = 0; first < BASE; ++first)
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for (CellType second = 0; second < BASE; ++second) {
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res_1.set_result(first, second, (*this)(g(first, second), first));
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res_2.set_result(first, second, (*this)(g(first, second), second));
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}
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res_1.update_num();
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res_2.update_num();
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return make_tuple(res_1, res_2);
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}
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FiniteFunction apply_two(const FiniteFunction &g, const FiniteFunction &h) const {
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FiniteFunction res;
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for (CellType first = 0; first < BASE; ++first)
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for (CellType second = 0; second < BASE; ++second) {
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res.set_result(
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first,
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second,
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(*this)(g(first, second), h(first, second))
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);
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}
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res.update_num();
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return res;
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}
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FiniteFunction apply_permutation(array<int, BASE> perm) const {
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FiniteFunction res;
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for (CellType first = 0; first < BASE; ++first)
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for (CellType second = 0; second < BASE; ++second) {
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res.set_result(
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first,
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second,
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find(
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perm.begin(),
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perm.end(),
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(*this)(perm[first], perm[second])
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) - perm.begin()
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);
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}
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res.update_num();
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return res;
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}
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uint32_t get_hash() const {
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return _num;
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}
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static size_t get_index(CellType first, CellType second) {
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return first * BASE + second;
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}
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template <CellType _BASE>
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friend ostream& operator << (ostream& os, const FiniteFunction<_BASE> &f);
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private:
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void update_num() {
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_num = 0;
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for (auto&& val: _results) {
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_num *= BASE;
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_num += val;
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}
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}
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uint32_t _num;
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array<CellType, BASE*BASE> _results;
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};
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template <CellType BASE>
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ostream& operator << (ostream& os, const FiniteFunction<BASE> &f){
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for (int first = 0; first < BASE; ++first) {
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for (int second = 0; second < BASE; ++second) {
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os << f(first, second);
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}
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if ( first != BASE-1 )
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os << " ";
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}
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return os;
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}
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template <size_t BASE>
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class FixedIniter {
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public:
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// rules это отображение обязательных значений аргументов, к
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// значениями функции, которые не должны при них изменяться
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explicit FixedIniter(map<pair<size_t, size_t>, int> rules) : _rules(rules), _cur_values(BASE*BASE, 0) {
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for (auto it = rules.begin(); it != rules.end(); ++it) {
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size_t arg1 = it->first.first;
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size_t arg2 = it->first.second;
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int value = it->second;
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_cur_values.at(FiniteFunction<BASE>::get_index(arg1, arg2)) = value;
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_used_indexes.insert(FiniteFunction<BASE>::get_index(arg1, arg2));
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}
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}
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int operator() (int first, int second) const {
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return _cur_values[FiniteFunction<BASE>::get_index(first, second)];
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}
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// Возвращает true, пока может построить следующую функцию
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// если не может это сделать, то возвращает false
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bool set_next() {
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bool is_overflow = true;
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for (size_t i = 0; is_overflow; ++i) {
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if ( i >= _cur_values.size() )
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return false;
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if ( _used_indexes.count(i) > 0 )
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continue;
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_cur_values.at(i) += 1;
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bool is_overflow = (_cur_values.at(i) > static_cast<int>(BASE) - 1);
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if ( is_overflow )
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_cur_values.at(i) = 0;
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else
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return true;
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}
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throw "Wrong logic";
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}
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private:
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set<size_t> _used_indexes;
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map<pair<size_t, size_t>, int> _rules;
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vector<int> _cur_values;
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};
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template <class Iterable>
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void write_function_class(ofstream &f_out, Iterable begin, Iterable end) {
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for (;begin != end; ++begin)
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f_out << *begin << " ";
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f_out << endl;
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}
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/*
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template <int BASE>
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void get_permutations(vector<array<int, BASE>> &permutations) {
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permutations.clear();
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array<int, BASE> cur_perm;
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for (int i = 0; i < BASE; ++i)
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cur_perm[i] = i;
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do {
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permutations.push_back(cur_perm);
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} while ( next_permutation(cur_perm.begin(), cur_perm.end()) );
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}
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*/
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template<class TripleArgsFiniteFunction>
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bool is_one_arg_func(const TripleArgsFiniteFunction &h) {
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bool is_equaled_x = true;
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bool is_equaled_y = true;
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bool is_equaled_z = true;
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for (CellType x = 0; x < CUR_BASE; ++x)
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for (CellType y = 0; y < CUR_BASE; ++y) {
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for (CellType z = 0; z < CUR_BASE; ++z) {
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is_equaled_x = is_equaled_x && (h(x,y,z) == x);
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is_equaled_y = is_equaled_y && (h(x,y,z) == y);
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is_equaled_z = is_equaled_z && (h(x,y,z) == z);
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}
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if ( !is_equaled_x && !is_equaled_y && !is_equaled_z )
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return false;
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}
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return true;
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}
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template<class TripleArgsFiniteFunction>
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bool is_projection(const TripleArgsFiniteFunction &h) {
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bool is_projection = true;
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for (CellType x = 0; x < CUR_BASE; ++x)
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for (CellType y = 0; y < CUR_BASE; ++y) {
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is_projection = (is_projection
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&& h(x,x,y) == h(x,y,x)
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&& h(x,y,x) == h(y,x,x)
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&& h(y,x,x) == x);
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}
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return is_projection;
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}
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template<class TripleArgsFiniteFunction>
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bool is_semiprojection(const TripleArgsFiniteFunction &h) {
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bool is_equaled_x = true;
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bool is_equaled_y = true;
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bool is_equaled_z = true;
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for (CellType x = 0; x < CUR_BASE; ++x)
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for (CellType y = 0; y < CUR_BASE; ++y)
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for (CellType z = 0; z < CUR_BASE; ++z) {
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// если все различны, то не рассматриваем
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if ( x != y && x != z && y != z )
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continue;
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is_equaled_x = is_equaled_x && (h(x,y,z) == x);
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is_equaled_y = is_equaled_y && (h(x,y,z) == y);
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is_equaled_z = is_equaled_z && (h(x,y,z) == z);
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}
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return is_equaled_x || is_equaled_y || is_equaled_z;
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}
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bool is_passed_rosenberg(const FiniteFunction<CUR_BASE> &f) {
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auto h_1 = [f](const CellType x, const CellType y, CellType z) -> CellType {
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return f( f(x,y), f(x,z) );
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};
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if ( !is_one_arg_func(h_1) ) {
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if ( is_projection(h_1) || is_semiprojection(h_1) )
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return false;
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}
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auto h_2 = [f](const CellType x, const CellType y, CellType z) -> CellType {
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return f( f(x, y), f(z, x) );
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};
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if ( !is_one_arg_func(h_2) ) {
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if ( is_projection(h_2) || is_semiprojection(h_2) )
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return false;
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}
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auto h_3 = [f](const CellType x, const CellType y, CellType z) -> CellType {
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return f( f(x,y), f(y,z) );
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};
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if ( !is_one_arg_func(h_3) ) {
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if ( is_projection(h_3) || is_semiprojection(h_3) )
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return false;
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}
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auto h_4 = [f](const CellType x, const CellType y, CellType z) -> CellType {
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return f( f(x,y), f(z,y) );
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};
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if ( !is_one_arg_func(h_4) ) {
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if ( is_projection(h_4) || is_semiprojection(h_4) )
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return false;
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}
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return true;
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}
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template <CellType BASE>
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vector<FiniteFunction<BASE>> get_funcs() {
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size_t count = 0;
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map<pair<size_t, size_t>, int> rules;
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for (int i = 0; i < BASE; ++i)
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rules[make_pair<size_t, size_t>(i,i)] = i;
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FixedIniter<BASE> initer(rules);
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//vector<array<int, BASE>> permutations;
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//get_permutations<BASE>(permutations);
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vector<FiniteFunction<BASE>> funcs;
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set< FiniteFunction<BASE> > permutated_funcs;
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do {
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++count;
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auto cur_func = FiniteFunction<BASE>(initer);
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//if ( permutated_funcs.find(cur_func) != permutated_funcs.end() )
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// continue;
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// если закомментить, то 17 классов, вместо 20
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//for (auto&& permutation: permutations)
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// permutated_funcs.insert(cur_func.apply_permutation(permutation));
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funcs.push_back(cur_func);
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} while (initer.set_next());
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cout << "Total " << count << " functions" << endl;
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funcs.erase(
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remove_if(
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funcs.begin(),
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funcs.end(),
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[](const FiniteFunction<BASE> & f) {
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return !is_passed_rosenberg(f);
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}
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),
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funcs.end()
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);
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cout << "After Rosenberg " << funcs.size() << " functions" << endl;
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//if ( permutated_funcs.size() != count )
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// throw "Permutation's logic error!";
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return funcs;
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}
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template <CellType BASE>
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set<FiniteFunction<BASE>> generate_function_class(FiniteFunction<BASE> base_function) {
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auto FiniteFunctionHasher = [](const FiniteFunction<BASE> &f) -> uint32_t {
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return f.get_hash();
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};
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unordered_set<
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FiniteFunction<CUR_BASE>,
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decltype(FiniteFunctionHasher)
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> func_class(1024, FiniteFunctionHasher);
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func_class.insert(base_function);
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//cout << "start with " << base_function << " ";
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size_t last_size = 0; // размер в прошлой итерации
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while (true) {
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unordered_set<
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FiniteFunction<CUR_BASE>,
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decltype(FiniteFunctionHasher)
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> new_funcs(1024, FiniteFunctionHasher);
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for (const auto& f_main: func_class) {
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new_funcs.insert(f_main.reversed());
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//new_funcs.insert(f_main.equaled());
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for (const auto& f_applied: func_class) {
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//FiniteFunction<BASE> f_left_1, f_left_2;
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//tie(f_left_1, f_left_2) = f_main.apply_to_first(f_applied);
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FiniteFunction<BASE> f_left;
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f_left = f_main.apply_to_first_partial(f_applied);
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new_funcs.insert(f_left);
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}
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}
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if ( new_funcs.size() == last_size ) {
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break;
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}
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func_class.insert(new_funcs.begin(), new_funcs.end());
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last_size = new_funcs.size();
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}
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return set<FiniteFunction<BASE>>(func_class.begin(), func_class.end());
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}
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int main() {
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auto FiniteFunctionHasher = [](const FiniteFunction<CUR_BASE> &f) -> uint32_t {
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return f.get_hash();
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};
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auto funcs = get_funcs<CUR_BASE>();
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cout << "Removing permutations " << funcs.size() << " functions" << endl;
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/*vector<array<int, 3>> permutations;
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get_permutations<3>(permutations);
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string function_to_str("000 112 212");
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cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[1]) << endl;
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cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[2]) << endl;
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cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[3]) << endl;
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cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[4]) << endl;
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cout << FiniteFunction<3>(function_to_str).apply_permutation(permutations[5]) << endl;
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*/
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//cout << "022_210_002 -> " << FiniteFunction<3>(string("022 210 002")) << endl;
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//set<FiniteFunction<3>> allowed_functions(funcs.begin(), funcs.end());
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list< set<FiniteFunction<CUR_BASE>> > function_classes;
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unordered_set<
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FiniteFunction<CUR_BASE>,
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decltype(FiniteFunctionHasher)
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> allowed_functions(funcs.begin(), funcs.end(), 128, FiniteFunctionHasher);
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FiniteFunction<CUR_BASE> identical_x(string("000 111 222"));
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FiniteFunction<CUR_BASE> identical_y(string("012 012 012"));
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allowed_functions.erase(identical_x);
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allowed_functions.erase(identical_y);
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cout << "Total " << allowed_functions.size() << " functions" << endl;
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std::ofstream f_all_out("all_classes.txt");
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while ( allowed_functions.size() > 0 ) {
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//if (allowed_functions.size() % 10 == 0)
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//cout << 100 - allowed_functions.size() * 100. / funcs.size() << "%" << endl;
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auto base_function = *allowed_functions.begin();
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allowed_functions.erase(base_function);
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set< FiniteFunction<CUR_BASE> > func_class = generate_function_class(base_function);
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func_class.erase(identical_x);
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func_class.erase(identical_y);
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//f_all_out << base_function << " -> ";
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//write_function_class(f_all_out, func_class.begin(), func_class.end());
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bool is_need_append = true;
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vector<decltype(function_classes)::iterator> functions_to_remove;
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for (auto it = function_classes.begin(); it != function_classes.end(); ++it) {
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if ( func_class.size() < it->size() ) {
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if (includes(
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it->begin(),
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it->end(),
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func_class.begin(),
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func_class.end()
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)
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) {
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// новый класс функций часть уже существующего
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functions_to_remove.push_back(it);
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}
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} 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;
|
||
}
|