#include <stdio.h> #include <cstdio> #include <string> #include <algorithm> #include <set> #include <vector> #include <iterator> #include <string.h> using namespace std; #define REP(i,n) for(int i=0;i<(n);++i) #define FOR(i,a,b) for(int i=(a);i<=(b);++i) #define FORD(i,a,b) for(int i=(a);i>=(b);--i) #define FOREACH(t, i,c) for(t::iterator i=(c).begin();i!=(c).end();++i) #define ZERO(a) memset(a,0,sizeof(a)) template<class T> inline int size(const T &c) { return c.size(); } #define LL unsigned long long #define MAXN 1000010 #define MOD 1000000007 #define DBG(X) //#define K3_DEBUG #ifndef _MSC_VER #define gets_s(a,b) gets(a) #endif LL powersOf2Mod[1000010]; class Clause; class CNFFormula; vector<Clause*> input_clauses; vector<CNFFormula*> spojne_formuly; LL liczba_wszystkich_literalow; LL computePowersOf2() { powersOf2Mod[0] = 1; for (int i = 1; i < MAXN; i++) { powersOf2Mod[i] = (powersOf2Mod[i - 1] * 2) % MOD; } return 0; } bool cmp_absolute(const int &a, const int &b) { return abs(a) < abs(b); } class Clause { public: int start; int len; int end; LL *bits; int bits_len64; bool invalid; Clause(vector<int> &raw_literals) { std::sort(raw_literals.begin(), raw_literals.end(), cmp_absolute); start = abs(raw_literals[0]); len = abs(raw_literals[raw_literals.size() - 1]) - start + 1; end = start + len - 1; bits_len64 = (len + 63) / 64; bits = new LL[bits_len64]; for (int i = 0; i < bits_len64; i++) { bits[i] = 0; } for (int i = 0; i < raw_literals.size(); i++) { int lit = raw_literals[i]; if (lit > 0) { set_var(i + start); if (!get_var(i + start) == 1) { DBG(printf("error!")); } } else { clear_var(i + start); } } invalid = false; } Clause(const Clause& c) { //printf("copy constructor"); start = c.start; len = c.len; end = c.end; bits_len64 = c.bits_len64; bits = new LL[bits_len64]; memcpy(bits, c.bits, c.bits_len64); invalid = c.invalid; } // Joined Clause Clause(Clause *a, Clause* b) { if (b->start > a->end) { DBG(printf("Wrong joined Clause()\n")); //throw "Wrong joined Clause()"; } start = a->start; end = b->end; len = end - start + 1; bits_len64 = (len + 63) / 64; bits = new LL[bits_len64]; memcpy(bits, a->bits, a->bits_len64); for (int i = a->bits_len64; i < bits_len64; i++) { bits[i] = 0; } for (int v = b->start; v <= b->end; v++) { if (b->get_var(v)) { set_var(v); } } invalid = false; } void print() const { printf("Clause: start=%d end=%d len=%d inv[%d]: ", start, end, len, invalid); for (int i = start; i <= end; i++) { printf("%d ", get_var(i)); } printf("\n"); } void selftest() { for (int i = 0; i < 64; i++) { printf("%d ", get_var(i)); set_var(i); printf("%d ", get_var(i)); clear_var(i); printf("%d\n", get_var(i)); } } inline int get_var(int idx) const { idx -= start; return ((bits[idx >> 6] >> (idx & 0x3F)) & 1ULL); } inline void set_var(int idx) { idx -= start; bits[idx >> 6] |= (1ULL << (idx & 0x3F)); } inline void clear_var(int idx) { idx -= start; bits[idx >> 6] &= ~(1ULL << (idx & 0x3F)); } inline void flip_var(int idx) { idx -= start; bits[idx >> 6] ^= (1ULL << (idx & 0x3F)); } // TODO: inline int get_var_range(int idx_s, int idx_e) { idx_s -= start; idx_e -= end; } bool operator<(Clause* other) { if (this->start == other->start) { return this->end < other->end; } return this->start < other->start; } bool operator<(Clause& other) { if (this->start == other.start) { return this->end < other.end; } return this->start < other.start; } bool operator==(Clause& other) { if (this->start != other.start) { return false; } if (this->len != other.len) { return false; } for (int i = 0; i < bits_len64; i++) { if (bits[i] != other.bits[i]) return false; } return true; } bool disjoint(const Clause* a, const Clause *b) { return (a->end < b->start) || (b->end < a->start); } bool inside(const Clause *b) { if (this->start >= b->start && this->end <= b->end) { for (int i = this->start; i <= this->end; i++) { if (get_var(i) != b->get_var(i)) { return false; } } return true; } return false; } bool operator^(const Clause& other) { return operator^(&other); } // Independent operator bool operator^(const Clause* other) { if (disjoint(this, other)) { return true; //throw "Do preprocessing to avoid disjoint clauses"; } // so they have common part; int s = max(this->start, other->start); int e = min(this->end, other->end); for (int i=s; i <= e; i++) { // TODO: use bitmask if (this->get_var(i) == !other->get_var(i)) { return true; } } return false; } int operator[](std::size_t idx) { return get_var(idx); } const int operator[](std::size_t idx) const { get_var(idx); } // non-copy-and-swap assignment Clause& operator=(const Clause& other) { //DBG(printf("non-copy-and-swap assignment\n")); // check for self-assignment if (&other == this) return *this; // reuse storage when possible if (bits_len64 < other.bits_len64) { bits_len64 = other.bits_len64; bits = new LL[other.bits_len64]; } start = other.start; end = other.end; len = other.len; invalid = other.invalid; memcpy(bits, other.bits, bits_len64); return *this; } static Clause* create(char* s, int parsed_len) { char * p = s; char* end = p + parsed_len; vector<int> literals; while (p < end) { int sign = 1; while (p < end) { if (*p == 'x' || *p == '~') { break; } p++; } if (p == end) { break; } if (*p == '~') { sign = -1; p++; } int xi; int offset = sscanf(p, "%*c%d", &xi); literals.push_back(xi * sign); p += offset; } return new Clause(literals); } }; bool operator<(const Clause& a, const Clause& other) { return a.start < other.start; } bool cmp_clause_ptr(const Clause* a, const Clause* b) { if (a->start == b->start) { return a->end < b->end; } return a->start < b->start; } bool cmp_clause_min_start(const Clause& a, const Clause& b) { if (a.start == b.start) { return a.end < b.end; } return a.start < b.start; } bool cmp_min_len(const Clause& a, const Clause& b) { if (a.len == b.len) { return a.start < b.start; } return a.len < b.len; } //struct APtrComp //{ // bool operator()(const A* lhs, const A* rhs) const { /* implement logic here */ } //}; vector<Clause> convert_to_independent(Clause &c1, Clause &c2) { vector<Clause> res; if (c1 ^ c2) { res.push_back(c1); res.push_back(c2); } else { // sa zalezne // sprawdz czy jedna nie zawiera sie w drugiej if (c1.inside(&c2)) { res.push_back(c1); #ifdef K3_DEBUG printf("C1 is inside C2\n"); c1.print(); c2.print(); #endif return res; } else if (c2.inside(&c1)) { #ifdef K3_DEBUG res.push_back(c2); printf("C2 is inside C1\n"); c2.print(); c1.print(); #endif return res; } vector<int> L; if (!(c1 < c2)) swap(c1, c2); // Zbior L to znaki pomiedzy c1.end+1 a c2.end Clause joined_c(&c1, &c2); res.push_back(c2); DBG(printf("Joining clauses:\n")); DBG(c1.print()); DBG(c2.print()); DBG(printf("Start...\n")); for (int v = c1.end + 1; v <= c2.end; v++) { Clause c(joined_c); c.end = v; c.len = c.end - c.start + 1; c.flip_var(v); res.push_back(c); DBG(c.print()); } } DBG(printf("End of make independent\n")); return res; } /* Formula musi byc spojna!!! */ class CNFFormula { public: int number_of_variables; // number of variables xi int start; int end; vector<Clause> clauses; int formula_id; CNFFormula(int id) { formula_id = id; } void addClause(Clause clause) { if (clauses.empty()) { start = clause.start; end = clause.end; } if (clause.start < start) { throw "Wrong order while adding clauses to CNFFormula"; } clauses.push_back(clause); if (clause.end > end) { end = clause.end; } number_of_variables = end - start + 1; } void print() { printf("Formula %d:\n", formula_id); for (int i = 0; i < clauses.size(); i++) { clauses[i].print(); } } /* Number of solutions if clauses are mutually independent */ LL spojnyNBS() { LL res = powersOf2Mod[number_of_variables]; for (int i = 0; i < clauses.size(); i++) { res -= powersOf2Mod[number_of_variables - clauses[i].len]; res += MOD; res %= MOD; } return res; } LL niespojnyNBS() { if (clauses.size() == 0) { return powersOf2Mod[number_of_variables]; } int ci = 0; LL res = 1; std::sort(clauses.begin(), clauses.end(), cmp_clause_min_start); int uzyte_zmienne = 0; while (ci < clauses.size()) { Clause *c = &clauses[ci]; int i = ci + 1; int last_end = c->end; while (i < clauses.size() && clauses[i].start <= last_end) { c = &clauses[i]; i++; last_end = max(last_end, c->end); } DBG(printf("spojny [%d,%d]\n", clauses[ci].start, last_end)); int v_cnt = last_end - clauses[ci].start + 1; LL local_res = powersOf2Mod[v_cnt]; uzyte_zmienne += v_cnt; for (int j = ci; j < i; j++) { local_res -= powersOf2Mod[v_cnt - clauses[j].len]; local_res += MOD; local_res %= MOD; } res *= local_res; ci = i; } res *= powersOf2Mod[number_of_variables - uzyte_zmienne]; res %= MOD; return res; } }; vector<Clause> remove_insiders(vector<Clause>& clauses) { int len = clauses.size(); sort(clauses.begin(), clauses.end(), cmp_min_len); bool *invalid = new bool[len]; for (int i = 0; i < len; i++) { invalid[i] = false; } vector<Clause> res; for (int i = 0; i < len; i++) { if (invalid[i]|| clauses[i].invalid) { continue; } for (int j = i + 1; j < len; j++) { if (invalid[j] || clauses[j].invalid) { continue; } if (clauses[i].inside(&clauses[j])) { DBG(printf("Clause %d is inside clause %j. Removing:\n")); DBG(clauses[i].print()); DBG(clauses[j].print()); invalid[j] = true; } } if (!invalid[i] && !clauses[i].invalid) { res.push_back(clauses[i]); } } delete[] invalid; return res; } vector<Clause> transformToIndependent(vector<Clause> cs) { if (cs.size() == 1) { return cs; } if (cs.size() == 2) { return convert_to_independent(cs[0], cs[1]); } bool done = true; vector<pair<int, int> > dependent; cs = remove_insiders(cs); DBG(printf("After first removal of insiders:\n")); #ifdef K3_DEBUG for (int i = 0; i < cs.size(); i++) { cs[i].print(); } #endif for (int i = 0; i < cs.size(); i++) { for (int j = i + 1; j < cs.size(); j++) { if (!(cs[i] ^ cs[j])) { #ifdef K3_DEBUG printf("First pass: %d and %d are still DEPENDENT!\n", i, j); cs[i].print(); cs[j].print(); #endif done = false; dependent.push_back(make_pair(i, j)); } } } do { done = true; #ifdef K3_DEBUG DBG(printf("Loop start:\n")); for (int i = 0; i < cs.size(); i++) { cs[i].print(); } #endif vector<Clause> add_res; for (int i = 0; i < dependent.size(); i++) { int a = dependent[i].first; int b = dependent[i].second; if (cs[a].invalid || cs[b].invalid) { continue; } Clause ca = cs[a]; Clause cb = cs[b]; #ifdef K3_DEBUG printf("Making these two clauses independent:\n"); ca.print(); cb.print(); #endif vector<Clause> r = convert_to_independent(cs[a], cs[b]); cs[a].invalid = true; cs[b].invalid = true; #ifdef K3_DEBUG printf("These two marked as invalid:\n"); cs[a].print(); cs[b].print(); #endif for (int i = 0; i < r.size(); i++) { add_res.push_back(r[i]); } #ifdef K3_DEBUG printf("Results:\n"); for (int i = 0; i < r.size(); i++) { r[i].print(); } printf("end of Results\n"); #endif } for (int i = 0; i < add_res.size(); i++) { cs.push_back(add_res[i]); } #ifdef K3_DEBUG printf("All clauses before removing insiders:\n"); for (int i = 0; i < cs.size(); i++) { cs[i].print(); } #endif cs = remove_insiders(cs); dependent.clear(); for (int i = 0; i < cs.size(); i++) { for (int j = i + 1; j < cs.size(); j++) { if (!(cs[i] ^ cs[j])) { #ifdef K3_DEBUG printf("%d and %d are still DEPENDENT!\n", i, j); cs[i].print(); cs[j].print(); done = false; #endif dependent.push_back(make_pair(i, j)); } } } } while (dependent.size() > 0); return cs; } void transformToIndependentClauses(CNFFormula& formula) { vector<Clause> res = transformToIndependent(formula.clauses); // TODO: spojne again? formula.clauses = res; #ifdef K3_DEBUG printf("Final clauses for formula %d\n", formula.formula_id); for (int i = 0; i < res.size(); i++) { res[i].print(); } #endif } // Algorythm: // Najpierw podziel na spojne skladowe // 1. Posortuj po koncach // jesli clause[i].end < clause[i+1].begin -> rozpocznij nowa skladowa (nowa formule) // policz zmiennych ktorych w ogole nie ma w rownaniu // dla kazdej skladowej policz niezalezne formuly // wynik = NBS(f1) * NBS(f2) * 2 ** (liczba zmiennych ktore nie wystepuja) int main() { computePowersOf2(); int n; scanf("%d", &n); liczba_wszystkich_literalow = n; const int MAX_BUF = 20000000; char *buf = new char[MAX_BUF]; gets_s(buf, MAX_BUF);// only newline gets_s(buf, MAX_BUF); char* p = buf; char* end = buf + strlen(buf); while (p < end) { char* begin = p; while (*p != ')') { p++; } // *p == ')' *p = 0; Clause *c = Clause::create(begin + 1, p - begin); DBG(c->print()); p++; while (p < end && *p != '(') p++; input_clauses.push_back(c); } std::sort(input_clauses.begin(), input_clauses.end(), cmp_clause_ptr); int formula_id = 0; CNFFormula *f = new CNFFormula(formula_id++); Clause *last_clause = input_clauses[0]; //last_clause->selftest(); int last_end = last_clause->end; f->addClause(*last_clause); for (int i = 1; i < input_clauses.size(); i++) { Clause *c = input_clauses[i]; if (last_clause->inside(c)) { continue; } if (c->start > last_end) { spojne_formuly.push_back(f); f = new CNFFormula(formula_id++); } f->addClause(*c); last_clause = c; last_end = max(last_end, last_clause->end); } spojne_formuly.push_back(f); int uzyte_zmienne = 0; for (int i = 0; i < spojne_formuly.size(); i++) { DBG(spojne_formuly[i]->print()); uzyte_zmienne += spojne_formuly[i]->number_of_variables; } LL res = 1; for (int i = 0; i < spojne_formuly.size(); i++) { DBG(printf("Transform to independent formula %d\n", i)); transformToIndependentClauses(*spojne_formuly[i]); res *= spojne_formuly[i]->niespojnyNBS(); res %= MOD; } res *= powersOf2Mod[liczba_wszystkich_literalow - uzyte_zmienne]; res %= MOD; printf("%llu\n", res); return 0; } /* Test spojne formuly: 21 (x1 v ~x2 v x3) ^ (x1 v x2) ^ (x3) ^ (~x4 v x5) ^ (x20 v x21) ^ (x10 v x11 v x12) ^ (x11 v x12) 4 (x1 v ~x2) ^ (x2 v x3 v x4) ^ (x1 v ~x3) ^ (~x3 v x4) 8 (x1 v x2 v x3 v x4 v x5) ^ (x5 v x6 v x7) ^ (x1 v x2 v x3 v x4 v x5 ^ ~x6) ^ (x1 v x2 v x3 v x4 v x5 ^ x6 ^ ~x7) ^ (x5 v ~x6 v x7 v x8) 3 2 3 8 3 2 5 2 3 7 3 */
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#define REP(i,n) for(int i=0;i<(n);++i) #define FOR(i,a,b) for(int i=(a);i<=(b);++i) #define FORD(i,a,b) for(int i=(a);i>=(b);--i) #define FOREACH(t, i,c) for(t::iterator i=(c).begin();i!=(c).end();++i) #define ZERO(a) memset(a,0,sizeof(a)) template<class T> inline int size(const T &c) { return c.size(); } #define LL unsigned long long #define MAXN 1000010 #define MOD 1000000007 #define DBG(X) //#define K3_DEBUG #ifndef _MSC_VER #define gets_s(a,b) gets(a) #endif LL powersOf2Mod[1000010]; class Clause; class CNFFormula; vector<Clause*> input_clauses; vector<CNFFormula*> spojne_formuly; LL liczba_wszystkich_literalow; LL computePowersOf2() { powersOf2Mod[0] = 1; for (int i = 1; i < MAXN; i++) { powersOf2Mod[i] = (powersOf2Mod[i - 1] * 2) % MOD; } return 0; } bool cmp_absolute(const int &a, const int &b) { return abs(a) < abs(b); } class Clause { public: int start; int len; int end; LL *bits; int bits_len64; bool invalid; Clause(vector<int> &raw_literals) { std::sort(raw_literals.begin(), raw_literals.end(), cmp_absolute); start = abs(raw_literals[0]); len = abs(raw_literals[raw_literals.size() - 1]) - start + 1; end = start + len - 1; bits_len64 = (len + 63) / 64; bits = new LL[bits_len64]; for (int i = 0; i < bits_len64; i++) { bits[i] = 0; } for (int i = 0; i < raw_literals.size(); i++) { int lit = raw_literals[i]; if (lit > 0) { set_var(i + start); if (!get_var(i + start) == 1) { DBG(printf("error!")); } } else { clear_var(i + start); } } invalid = false; } Clause(const Clause& c) { //printf("copy constructor"); start = c.start; len = c.len; end = c.end; bits_len64 = c.bits_len64; bits = new LL[bits_len64]; memcpy(bits, c.bits, c.bits_len64); invalid = c.invalid; } // Joined Clause Clause(Clause *a, Clause* b) { if (b->start > a->end) { DBG(printf("Wrong joined Clause()\n")); //throw "Wrong joined Clause()"; } start = a->start; end = b->end; len = end - start + 1; bits_len64 = (len + 63) / 64; bits = new LL[bits_len64]; memcpy(bits, a->bits, a->bits_len64); for (int i = a->bits_len64; i < bits_len64; i++) { bits[i] = 0; } for (int v = b->start; v <= b->end; v++) { if (b->get_var(v)) { set_var(v); } } invalid = false; } void print() const { printf("Clause: start=%d end=%d len=%d inv[%d]: ", start, end, len, invalid); for (int i = start; i <= end; i++) { printf("%d ", get_var(i)); } printf("\n"); } void selftest() { for (int i = 0; i < 64; i++) { printf("%d ", get_var(i)); set_var(i); printf("%d ", get_var(i)); clear_var(i); printf("%d\n", get_var(i)); } } inline int get_var(int idx) const { idx -= start; return ((bits[idx >> 6] >> (idx & 0x3F)) & 1ULL); } inline void set_var(int idx) { idx -= start; bits[idx >> 6] |= (1ULL << (idx & 0x3F)); } inline void clear_var(int idx) { idx -= start; bits[idx >> 6] &= ~(1ULL << (idx & 0x3F)); } inline void flip_var(int idx) { idx -= start; bits[idx >> 6] ^= (1ULL << (idx & 0x3F)); } // TODO: inline int get_var_range(int idx_s, int idx_e) { idx_s -= start; idx_e -= end; } bool operator<(Clause* other) { if (this->start == other->start) { return this->end < other->end; } return this->start < other->start; } bool operator<(Clause& other) { if (this->start == other.start) { return this->end < other.end; } return this->start < other.start; } bool operator==(Clause& other) { if (this->start != other.start) { return false; } if (this->len != other.len) { return false; } for (int i = 0; i < bits_len64; i++) { if (bits[i] != other.bits[i]) return false; } return true; } bool disjoint(const Clause* a, const Clause *b) { return (a->end < b->start) || (b->end < a->start); } bool inside(const Clause *b) { if (this->start >= b->start && this->end <= b->end) { for (int i = this->start; i <= this->end; i++) { if (get_var(i) != b->get_var(i)) { return false; } } return true; } return false; } bool operator^(const Clause& other) { return operator^(&other); } // Independent operator bool operator^(const Clause* other) { if (disjoint(this, other)) { return true; //throw "Do preprocessing to avoid disjoint clauses"; } // so they have common part; int s = max(this->start, other->start); int e = min(this->end, other->end); for (int i=s; i <= e; i++) { // TODO: use bitmask if (this->get_var(i) == !other->get_var(i)) { return true; } } return false; } int operator[](std::size_t idx) { return get_var(idx); } const int operator[](std::size_t idx) const { get_var(idx); } // non-copy-and-swap assignment Clause& operator=(const Clause& other) { //DBG(printf("non-copy-and-swap assignment\n")); // check for self-assignment if (&other == this) return *this; // reuse storage when possible if (bits_len64 < other.bits_len64) { bits_len64 = other.bits_len64; bits = new LL[other.bits_len64]; } start = other.start; end = other.end; len = other.len; invalid = other.invalid; memcpy(bits, other.bits, bits_len64); return *this; } static Clause* create(char* s, int parsed_len) { char * p = s; char* end = p + parsed_len; vector<int> literals; while (p < end) { int sign = 1; while (p < end) { if (*p == 'x' || *p == '~') { break; } p++; } if (p == end) { break; } if (*p == '~') { sign = -1; p++; } int xi; int offset = sscanf(p, "%*c%d", &xi); literals.push_back(xi * sign); p += offset; } return new Clause(literals); } }; bool operator<(const Clause& a, const Clause& other) { return a.start < other.start; } bool cmp_clause_ptr(const Clause* a, const Clause* b) { if (a->start == b->start) { return a->end < b->end; } return a->start < b->start; } bool cmp_clause_min_start(const Clause& a, const Clause& b) { if (a.start == b.start) { return a.end < b.end; } return a.start < b.start; } bool cmp_min_len(const Clause& a, const Clause& b) { if (a.len == b.len) { return a.start < b.start; } return a.len < b.len; } //struct APtrComp //{ // bool operator()(const A* lhs, const A* rhs) const { /* implement logic here */ } //}; vector<Clause> convert_to_independent(Clause &c1, Clause &c2) { vector<Clause> res; if (c1 ^ c2) { res.push_back(c1); res.push_back(c2); } else { // sa zalezne // sprawdz czy jedna nie zawiera sie w drugiej if (c1.inside(&c2)) { res.push_back(c1); #ifdef K3_DEBUG printf("C1 is inside C2\n"); c1.print(); c2.print(); #endif return res; } else if (c2.inside(&c1)) { #ifdef K3_DEBUG res.push_back(c2); printf("C2 is inside C1\n"); c2.print(); c1.print(); #endif return res; } vector<int> L; if (!(c1 < c2)) swap(c1, c2); // Zbior L to znaki pomiedzy c1.end+1 a c2.end Clause joined_c(&c1, &c2); res.push_back(c2); DBG(printf("Joining clauses:\n")); DBG(c1.print()); DBG(c2.print()); DBG(printf("Start...\n")); for (int v = c1.end + 1; v <= c2.end; v++) { Clause c(joined_c); c.end = v; c.len = c.end - c.start + 1; c.flip_var(v); res.push_back(c); DBG(c.print()); } } DBG(printf("End of make independent\n")); return res; } /* Formula musi byc spojna!!! */ class CNFFormula { public: int number_of_variables; // number of variables xi int start; int end; vector<Clause> clauses; int formula_id; CNFFormula(int id) { formula_id = id; } void addClause(Clause clause) { if (clauses.empty()) { start = clause.start; end = clause.end; } if (clause.start < start) { throw "Wrong order while adding clauses to CNFFormula"; } clauses.push_back(clause); if (clause.end > end) { end = clause.end; } number_of_variables = end - start + 1; } void print() { printf("Formula %d:\n", formula_id); for (int i = 0; i < clauses.size(); i++) { clauses[i].print(); } } /* Number of solutions if clauses are mutually independent */ LL spojnyNBS() { LL res = powersOf2Mod[number_of_variables]; for (int i = 0; i < clauses.size(); i++) { res -= powersOf2Mod[number_of_variables - clauses[i].len]; res += MOD; res %= MOD; } return res; } LL niespojnyNBS() { if (clauses.size() == 0) { return powersOf2Mod[number_of_variables]; } int ci = 0; LL res = 1; std::sort(clauses.begin(), clauses.end(), cmp_clause_min_start); int uzyte_zmienne = 0; while (ci < clauses.size()) { Clause *c = &clauses[ci]; int i = ci + 1; int last_end = c->end; while (i < clauses.size() && clauses[i].start <= last_end) { c = &clauses[i]; i++; last_end = max(last_end, c->end); } DBG(printf("spojny [%d,%d]\n", clauses[ci].start, last_end)); int v_cnt = last_end - clauses[ci].start + 1; LL local_res = powersOf2Mod[v_cnt]; uzyte_zmienne += v_cnt; for (int j = ci; j < i; j++) { local_res -= powersOf2Mod[v_cnt - clauses[j].len]; local_res += MOD; local_res %= MOD; } res *= local_res; ci = i; } res *= powersOf2Mod[number_of_variables - uzyte_zmienne]; res %= MOD; return res; } }; vector<Clause> remove_insiders(vector<Clause>& clauses) { int len = clauses.size(); sort(clauses.begin(), clauses.end(), cmp_min_len); bool *invalid = new bool[len]; for (int i = 0; i < len; i++) { invalid[i] = false; } vector<Clause> res; for (int i = 0; i < len; i++) { if (invalid[i]|| clauses[i].invalid) { continue; } for (int j = i + 1; j < len; j++) { if (invalid[j] || clauses[j].invalid) { continue; } if (clauses[i].inside(&clauses[j])) { DBG(printf("Clause %d is inside clause %j. Removing:\n")); DBG(clauses[i].print()); DBG(clauses[j].print()); invalid[j] = true; } } if (!invalid[i] && !clauses[i].invalid) { res.push_back(clauses[i]); } } delete[] invalid; return res; } vector<Clause> transformToIndependent(vector<Clause> cs) { if (cs.size() == 1) { return cs; } if (cs.size() == 2) { return convert_to_independent(cs[0], cs[1]); } bool done = true; vector<pair<int, int> > dependent; cs = remove_insiders(cs); DBG(printf("After first removal of insiders:\n")); #ifdef K3_DEBUG for (int i = 0; i < cs.size(); i++) { cs[i].print(); } #endif for (int i = 0; i < cs.size(); i++) { for (int j = i + 1; j < cs.size(); j++) { if (!(cs[i] ^ cs[j])) { #ifdef K3_DEBUG printf("First pass: %d and %d are still DEPENDENT!\n", i, j); cs[i].print(); cs[j].print(); #endif done = false; dependent.push_back(make_pair(i, j)); } } } do { done = true; #ifdef K3_DEBUG DBG(printf("Loop start:\n")); for (int i = 0; i < cs.size(); i++) { cs[i].print(); } #endif vector<Clause> add_res; for (int i = 0; i < dependent.size(); i++) { int a = dependent[i].first; int b = dependent[i].second; if (cs[a].invalid || cs[b].invalid) { continue; } Clause ca = cs[a]; Clause cb = cs[b]; #ifdef K3_DEBUG printf("Making these two clauses independent:\n"); ca.print(); cb.print(); #endif vector<Clause> r = convert_to_independent(cs[a], cs[b]); cs[a].invalid = true; cs[b].invalid = true; #ifdef K3_DEBUG printf("These two marked as invalid:\n"); cs[a].print(); cs[b].print(); #endif for (int i = 0; i < r.size(); i++) { add_res.push_back(r[i]); } #ifdef K3_DEBUG printf("Results:\n"); for (int i = 0; i < r.size(); i++) { r[i].print(); } printf("end of Results\n"); #endif } for (int i = 0; i < add_res.size(); i++) { cs.push_back(add_res[i]); } #ifdef K3_DEBUG printf("All clauses before removing insiders:\n"); for (int i = 0; i < cs.size(); i++) { cs[i].print(); } #endif cs = remove_insiders(cs); dependent.clear(); for (int i = 0; i < cs.size(); i++) { for (int j = i + 1; j < cs.size(); j++) { if (!(cs[i] ^ cs[j])) { #ifdef K3_DEBUG printf("%d and %d are still DEPENDENT!\n", i, j); cs[i].print(); cs[j].print(); done = false; #endif dependent.push_back(make_pair(i, j)); } } } } while (dependent.size() > 0); return cs; } void transformToIndependentClauses(CNFFormula& formula) { vector<Clause> res = transformToIndependent(formula.clauses); // TODO: spojne again? formula.clauses = res; #ifdef K3_DEBUG printf("Final clauses for formula %d\n", formula.formula_id); for (int i = 0; i < res.size(); i++) { res[i].print(); } #endif } // Algorythm: // Najpierw podziel na spojne skladowe // 1. Posortuj po koncach // jesli clause[i].end < clause[i+1].begin -> rozpocznij nowa skladowa (nowa formule) // policz zmiennych ktorych w ogole nie ma w rownaniu // dla kazdej skladowej policz niezalezne formuly // wynik = NBS(f1) * NBS(f2) * 2 ** (liczba zmiennych ktore nie wystepuja) int main() { computePowersOf2(); int n; scanf("%d", &n); liczba_wszystkich_literalow = n; const int MAX_BUF = 20000000; char *buf = new char[MAX_BUF]; gets_s(buf, MAX_BUF);// only newline gets_s(buf, MAX_BUF); char* p = buf; char* end = buf + strlen(buf); while (p < end) { char* begin = p; while (*p != ')') { p++; } // *p == ')' *p = 0; Clause *c = Clause::create(begin + 1, p - begin); DBG(c->print()); p++; while (p < end && *p != '(') p++; input_clauses.push_back(c); } std::sort(input_clauses.begin(), input_clauses.end(), cmp_clause_ptr); int formula_id = 0; CNFFormula *f = new CNFFormula(formula_id++); Clause *last_clause = input_clauses[0]; //last_clause->selftest(); int last_end = last_clause->end; f->addClause(*last_clause); for (int i = 1; i < input_clauses.size(); i++) { Clause *c = input_clauses[i]; if (last_clause->inside(c)) { continue; } if (c->start > last_end) { spojne_formuly.push_back(f); f = new CNFFormula(formula_id++); } f->addClause(*c); last_clause = c; last_end = max(last_end, last_clause->end); } spojne_formuly.push_back(f); int uzyte_zmienne = 0; for (int i = 0; i < spojne_formuly.size(); i++) { DBG(spojne_formuly[i]->print()); uzyte_zmienne += spojne_formuly[i]->number_of_variables; } LL res = 1; for (int i = 0; i < spojne_formuly.size(); i++) { DBG(printf("Transform to independent formula %d\n", i)); transformToIndependentClauses(*spojne_formuly[i]); res *= spojne_formuly[i]->niespojnyNBS(); res %= MOD; } res *= powersOf2Mod[liczba_wszystkich_literalow - uzyte_zmienne]; res %= MOD; printf("%llu\n", res); return 0; } /* Test spojne formuly: 21 (x1 v ~x2 v x3) ^ (x1 v x2) ^ (x3) ^ (~x4 v x5) ^ (x20 v x21) ^ (x10 v x11 v x12) ^ (x11 v x12) 4 (x1 v ~x2) ^ (x2 v x3 v x4) ^ (x1 v ~x3) ^ (~x3 v x4) 8 (x1 v x2 v x3 v x4 v x5) ^ (x5 v x6 v x7) ^ (x1 v x2 v x3 v x4 v x5 ^ ~x6) ^ (x1 v x2 v x3 v x4 v x5 ^ x6 ^ ~x7) ^ (x5 v ~x6 v x7 v x8) 3 2 3 8 3 2 5 2 3 7 3 */ |