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#include <iostream>
#include <vector>
#include <assert.h>
#include <unordered_map>
#include <string>
#include <algorithm>
using namespace std;
typedef vector<int> transitions;
typedef vector<int> word;
struct Automaton {
int states;
vector<int> accept;
vector<transitions> delta;
int initial;
Automaton(int in, int n, const vector<transitions> &d, const vector<int> &acc) {
assert(in < n);
assert(d.size() == n);
accept = acc;
delta.resize(n);
for (int i = 0; i < d.size(); i++) {
delta[i] = transitions(d[i]);
}
in = initial;
states = n;
}
int apply(const word &w, int beg) {
int crawl = beg;
for (auto c: w) {
crawl = delta[crawl][c];
}
return crawl;
}
bool check(const word &s) {
int q = apply(s, initial);
for (auto i: accept) {
if (q == i)
return true;
}
return false;
}
void dump() {
cout << "States: " << states << "; accepting: ";
for (auto i: accept) cout << i << " ";
cout << "\n";
cout << "Transition table:\n";
for (int i = 0; i < states; i++) {
cout << i << ":";
for (int j = 0; j < delta[i].size(); j++) {
cout << "\t--" << (char)(j + 'a') << "--> " << delta[i][j] << "\n";
}
}
}
};
void fill_accepts(int mask, int states, vector<int> &acc) {
acc.clear();
for (int i = 0; i < states; i++) {
if (mask & (1<<i))
acc.push_back(1);
else
acc.push_back(0);
}
}
bool nextperm(int states, transitions &t, int alph_sz) {
for (int s = 0; s < alph_sz; s++) {
t[s]++;
if (t[s] == states) {
t[s] = 0;
}
else {
return true;
}
}
return false;
}
void reset_transition(transitions &t, int alph_sz) {
for (int s = 0; s < alph_sz; s++) {
t[s] = 0;
}
}
bool next_word(word &w, int alph_sz) {
for (int i = 0; i < w.size(); i++) {
w[i]++;
if (w[i] == alph_sz) {
w[i] = 0;
} else return true;
}
return false;
}
vector<word> generate_words(int max_len, int alph_sz) {
vector<word> result;
for (int len = 0; len <= max_len; len++) {
word w;
for (int i = 0; i < len; i++) w.push_back(0);
do {
result.push_back(w);
} while (next_word(w, alph_sz));
}
return result;
}
void get_transitions(Automaton &aut, word &w, vector<int> &res) {
res.clear();
for (int i = 0; i < aut.states; i++) {
res.push_back(aut.apply(w, i));
}
}
int my_power(int a, int b) {
if (b == 0) return 1;
return a * my_power(a, b-1);
}
bool check_automaton(vector<word> &words, Automaton &aut) {
vector<vector<int>> funcs;
for (auto w: words) {
vector<int> trans;
get_transitions(aut, w, trans);
funcs.push_back(trans);
}
sort(funcs.begin(), funcs.end());
auto it = unique(funcs.begin(), funcs.end());
funcs.erase(it, funcs.end());
cout << funcs.size() << "\n";
if (funcs.size() == my_power(aut.states, aut.states)) {
cout << "mamy to!!\n";
aut.dump();
return true;
}
return false;
}
vector<Automaton> generate_automatons(int states, int alph_sz, vector<word> &words) {
vector<Automaton> result;
vector<transitions> delta;
vector<int> accepts;
for (int i = 0; i < states; i++) {
delta.push_back(transitions());
for (int s = 0; s < alph_sz; s++) {
delta[i].push_back(0);
}
}
/* loop over accepting states */
// for (int i = 0; i < (1<<states); i++) {
// if (i == 0) continue;
fill_accepts(1, states, accepts);
/* loop over possible transitions */
bool last = false;
while (!last) {
Automaton a(0, states, delta, accepts);
if (check_automaton(words, a)) {
return result;
}
// result.push_back(a);
last = true;
for (int i = 0; i < states; i++) {
if (nextperm(states, delta[i], alph_sz)) {
last = false;
break;
}
else {
reset_transition(delta[i], alph_sz);
}
}
}
// }
return result;
}
Automaton automaton_from_input() {
int states, alph_sz;
cin >> states >> alph_sz;
vector<int> accept;
vector<transitions> delta;
int initial;
fill_accepts(1, states, accept);
initial = 0;
for (int i = 0; i < states; i++) {
cout << i << ":";
delta.push_back(transitions());
for (int j = 0; j < alph_sz; j++) {
int x;
cout << "\t--" << (char)(j + 'a') << "--> ? ";
cin >> x;
delta[i].push_back(x);
}
}
return Automaton(0, states, delta, accept);
}
int main(int argc, char *argv[]) {
if (argc != 4) {
fprintf(stderr, "Usage: %s states alph_sz word_sz\n", argv[0]);
return -1;
}
int states = atoi(argv[1]);
int alph_sz = atoi(argv[2]);
int word_sz = atoi(argv[3]);
// vector<Automaton> automatons = generate_automatons(states, alph_sz);
// for (auto a: automatons) {
// a.dump();
// cout << "\n";
// }
fprintf(stderr, "Generating words...\n");
vector<word> words = generate_words(word_sz, alph_sz);
// for (auto w: words) {
// for (auto c: w) {
// cout << (char)(c + 'a');
// }
// cout << "\n";
// }
// fprintf(stderr, "Generating %d automatons...\n", my_power(alph_sz, alph_sz * states));
// generate_automatons(states, alph_sz, words);
Automaton aut = automaton_from_input();
check_automaton(words, aut);
}
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