#include <cstdio> #include <vector> #include <iostream> #include <string> #include <set> #include <algorithm> //#define DEBUG_PARSE //#define DEBUG using namespace std; const int MAX = 1000100; const int MODULO = 1000000007; // TODO - porównywanie hashowaniem // TODO - zamienić long long na int struct Clause { int beg, end; long long good_vars; vector<bool> its; // iterals int included, pid; Clause(){} Clause(int beg, int end): beg(beg), end(end){} }; int n, m; long long W[MAX]; Clause __C[MAX]; Clause *C[MAX]; vector<Clause*> Q; inline long long MOD(long long x) { if(x >= MODULO) return x % MODULO; return x; } long long pow(int a) { if(a < 0) exit(1); long long ret = 1; long long b = 2; while(a) { if(a & 1) ret = MOD(ret * b); b = MOD(b * b); a >>= 1; } return ret; } bool cross(Clause *a, Clause *b) { if(b->beg < a->beg) swap(a,b); if(a->end < b->beg) return false; for(int ai = b->beg - a->beg, bi = 0; ai <= a->end - a->beg && bi <= b->end - b->beg; ai++, bi++) { if(a->its[ai] != b->its[bi]) return false; } return true; } bool inside(Clause *a, Clause *b) { if(b->beg < a->beg) swap(a,b); if(b->end <= a->end) return true; return false; } bool cmp(const Clause *a, const Clause *b) { return a->end > b->end; } void solve_clause(Clause *cl, int pid) { Clause __temp = Clause(cl->beg, cl->beg); auto ptr = upper_bound(Q.rbegin(), Q.rend(), &__temp, cmp); long long good1 = 1, good2 = 1; if(ptr != Q.rend()) good1 = (*ptr)->good_vars; if(Q.size()) good2 = Q.back()->good_vars; #ifdef DEBUG if(ptr != Q.rend()) printf("\tpid %d %d\n", (*ptr)->pid, Q.back()->pid); printf("\tgood %lld %lld\n", good1, good2); #endif int end1 = 0, end2 = 0; if(ptr != Q.rend()) end1 = (*ptr)->end; if(Q.size()) end2 = Q.back()->end; #ifdef DEBUG printf("\tend %d %d\n", end1, end2); #endif long long all = MOD(good2 * pow(cl->end - end2)); long long wrong = pow(cl->beg - 1 - end1); wrong = MOD(wrong * good1); #ifdef DEBUG printf("\tall/wrong %lld %lld\n", all, wrong); #endif vector<Clause*> tempV(Q.rbegin(), ptr); sort(tempV.begin(), tempV.end(), [](const Clause *a, const Clause *b) -> bool { return a->beg > b->beg; }); vector<Clause*> S; bool is_inside = false; for(auto it = Q.rbegin(); it != ptr; it++) { bool bol = true; for(auto jt = Q.rbegin(); jt != it; jt++) { if(cross(*it, *jt) && (*jt)->included == pid) { bol = false; break; } } if(bol) { if((*it)->end < cl->beg || cross(*it, cl)) { S.push_back(*it); (*it)->included = pid; } } } for(auto x: S) { //if(x->beg > cl->beg) continue; if(x->beg < cl->beg) { #ifdef DEBUG printf("odejmuje wrong %d %lld\n", x->pid, W[x->pid]); #endif wrong = MOD(wrong - W[x->pid]); } else { #ifdef DEBUG printf("odejmuje wrong %d %lld\n", x->pid, good1 *pow(min(x->beg, cl->beg) - 1 - end1)); #endif wrong = MOD(wrong - MOD(good1 * pow(min(x->beg, cl->beg) - 1 - end1))); } } W[cl->pid] = wrong; cl->good_vars = MOD(all - wrong); #ifdef DEBUG printf("Answer: %lld %lld\n", cl->good_vars, wrong); #endif Q.push_back(cl); } void solve() { for(int i = 0; i < m; i++) { #ifdef DEBUG printf("Solve Clause %d\n", i); #endif solve_clause(C[i], i + 1); } } string input; void parse_input(); int main() { getline(cin, input); n = stoi(input); getline(cin, input); string::iterator end = remove(input.begin(), input.end(), '('); end = remove(input.begin(), end, ')'); end = remove(input.begin(), end, 'x'); end = remove(input.begin(), end, ' '); input = input.substr(0, end - input.begin()); parse_input(); for(int i = 0; i < m; i++) { for(int j = i + 1; j < m; j++) { if(cross(C[i], C[j]) && inside(C[i], C[j])) { if(C[i]->beg < C[j]->beg || C[i]->end > C[j]->end) { swap(C[i], C[m - 1]); m--; i--; break; } else { swap(C[j], C[m-1]); m--; j--; } } } } sort(C, C + m, [](const Clause *a, const Clause *b) -> bool { if(a->end == b->end) return a->beg < b->beg; return a->end < b->end; }); for(int i = 0; i < m; i++) C[i]->pid = i; #ifdef DEBUG for(int i = 0; i < m; i++) { cout << C[i]->beg << " " << C[i]->end << " "; for(auto x: C[i]->its) cout << x; cout << "\n"; } for(int i = 0; i < m; i++) { for(int j = i + 1; j < m; j++) { cout << "cross " << i << "x" << j << ": " << cross(C[i], C[j]) << " " << cross(C[j], C[i]) << "\n"; } } #endif solve(); printf("%lld\n", MOD(Q.back()->good_vars * pow(n - Q.back()->end))); } void parse_literal(set<pair<int, bool>> &S, string lit) { #ifdef DEBUG_PARSE cout << "\tLiteral: " << lit << "\n"; #endif if(lit[0] == '~') { lit.erase(0, 1); S.insert(make_pair(stoi(lit), 0)); } else S.insert(make_pair(stoi(lit), 1)); } void parse_clause(int b, int e) { set<pair<int,bool>> S; string cl = input.substr(b, e - b); #ifdef DEBUG_PARSE cout << "Clause: " << cl << "\n"; #endif int pos = 0, nxt; while((nxt = cl.find('v', pos)) != string::npos) { parse_literal(S, cl.substr(pos, nxt - pos)); pos = nxt + 1; } parse_literal(S, cl.substr(pos)); #ifdef DEBUG_PARSE for(auto x: S) cout << x.first << "," << x.second << " "; cout << "\n"; #endif __C[m].beg = S.begin()->first; __C[m].end = S.rbegin()->first; for(auto &x: S) __C[m].its.push_back(x.second); C[m] = &__C[m]; m++; } void parse_input() { int pos = 0, nxt; #ifdef DEBUG_PARSE cout << input << "\n"; #endif while((nxt = input.find('^', pos)) != string::npos) { parse_clause(pos, nxt); pos = nxt + 1; } parse_clause(pos, input.size() - pos); }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 | #include <cstdio> #include <vector> #include <iostream> #include <string> #include <set> #include <algorithm> //#define DEBUG_PARSE //#define DEBUG using namespace std; const int MAX = 1000100; const int MODULO = 1000000007; // TODO - porównywanie hashowaniem // TODO - zamienić long long na int struct Clause { int beg, end; long long good_vars; vector<bool> its; // iterals int included, pid; Clause(){} Clause(int beg, int end): beg(beg), end(end){} }; int n, m; long long W[MAX]; Clause __C[MAX]; Clause *C[MAX]; vector<Clause*> Q; inline long long MOD(long long x) { if(x >= MODULO) return x % MODULO; return x; } long long pow(int a) { if(a < 0) exit(1); long long ret = 1; long long b = 2; while(a) { if(a & 1) ret = MOD(ret * b); b = MOD(b * b); a >>= 1; } return ret; } bool cross(Clause *a, Clause *b) { if(b->beg < a->beg) swap(a,b); if(a->end < b->beg) return false; for(int ai = b->beg - a->beg, bi = 0; ai <= a->end - a->beg && bi <= b->end - b->beg; ai++, bi++) { if(a->its[ai] != b->its[bi]) return false; } return true; } bool inside(Clause *a, Clause *b) { if(b->beg < a->beg) swap(a,b); if(b->end <= a->end) return true; return false; } bool cmp(const Clause *a, const Clause *b) { return a->end > b->end; } void solve_clause(Clause *cl, int pid) { Clause __temp = Clause(cl->beg, cl->beg); auto ptr = upper_bound(Q.rbegin(), Q.rend(), &__temp, cmp); long long good1 = 1, good2 = 1; if(ptr != Q.rend()) good1 = (*ptr)->good_vars; if(Q.size()) good2 = Q.back()->good_vars; #ifdef DEBUG if(ptr != Q.rend()) printf("\tpid %d %d\n", (*ptr)->pid, Q.back()->pid); printf("\tgood %lld %lld\n", good1, good2); #endif int end1 = 0, end2 = 0; if(ptr != Q.rend()) end1 = (*ptr)->end; if(Q.size()) end2 = Q.back()->end; #ifdef DEBUG printf("\tend %d %d\n", end1, end2); #endif long long all = MOD(good2 * pow(cl->end - end2)); long long wrong = pow(cl->beg - 1 - end1); wrong = MOD(wrong * good1); #ifdef DEBUG printf("\tall/wrong %lld %lld\n", all, wrong); #endif vector<Clause*> tempV(Q.rbegin(), ptr); sort(tempV.begin(), tempV.end(), [](const Clause *a, const Clause *b) -> bool { return a->beg > b->beg; }); vector<Clause*> S; bool is_inside = false; for(auto it = Q.rbegin(); it != ptr; it++) { bool bol = true; for(auto jt = Q.rbegin(); jt != it; jt++) { if(cross(*it, *jt) && (*jt)->included == pid) { bol = false; break; } } if(bol) { if((*it)->end < cl->beg || cross(*it, cl)) { S.push_back(*it); (*it)->included = pid; } } } for(auto x: S) { //if(x->beg > cl->beg) continue; if(x->beg < cl->beg) { #ifdef DEBUG printf("odejmuje wrong %d %lld\n", x->pid, W[x->pid]); #endif wrong = MOD(wrong - W[x->pid]); } else { #ifdef DEBUG printf("odejmuje wrong %d %lld\n", x->pid, good1 *pow(min(x->beg, cl->beg) - 1 - end1)); #endif wrong = MOD(wrong - MOD(good1 * pow(min(x->beg, cl->beg) - 1 - end1))); } } W[cl->pid] = wrong; cl->good_vars = MOD(all - wrong); #ifdef DEBUG printf("Answer: %lld %lld\n", cl->good_vars, wrong); #endif Q.push_back(cl); } void solve() { for(int i = 0; i < m; i++) { #ifdef DEBUG printf("Solve Clause %d\n", i); #endif solve_clause(C[i], i + 1); } } string input; void parse_input(); int main() { getline(cin, input); n = stoi(input); getline(cin, input); string::iterator end = remove(input.begin(), input.end(), '('); end = remove(input.begin(), end, ')'); end = remove(input.begin(), end, 'x'); end = remove(input.begin(), end, ' '); input = input.substr(0, end - input.begin()); parse_input(); for(int i = 0; i < m; i++) { for(int j = i + 1; j < m; j++) { if(cross(C[i], C[j]) && inside(C[i], C[j])) { if(C[i]->beg < C[j]->beg || C[i]->end > C[j]->end) { swap(C[i], C[m - 1]); m--; i--; break; } else { swap(C[j], C[m-1]); m--; j--; } } } } sort(C, C + m, [](const Clause *a, const Clause *b) -> bool { if(a->end == b->end) return a->beg < b->beg; return a->end < b->end; }); for(int i = 0; i < m; i++) C[i]->pid = i; #ifdef DEBUG for(int i = 0; i < m; i++) { cout << C[i]->beg << " " << C[i]->end << " "; for(auto x: C[i]->its) cout << x; cout << "\n"; } for(int i = 0; i < m; i++) { for(int j = i + 1; j < m; j++) { cout << "cross " << i << "x" << j << ": " << cross(C[i], C[j]) << " " << cross(C[j], C[i]) << "\n"; } } #endif solve(); printf("%lld\n", MOD(Q.back()->good_vars * pow(n - Q.back()->end))); } void parse_literal(set<pair<int, bool>> &S, string lit) { #ifdef DEBUG_PARSE cout << "\tLiteral: " << lit << "\n"; #endif if(lit[0] == '~') { lit.erase(0, 1); S.insert(make_pair(stoi(lit), 0)); } else S.insert(make_pair(stoi(lit), 1)); } void parse_clause(int b, int e) { set<pair<int,bool>> S; string cl = input.substr(b, e - b); #ifdef DEBUG_PARSE cout << "Clause: " << cl << "\n"; #endif int pos = 0, nxt; while((nxt = cl.find('v', pos)) != string::npos) { parse_literal(S, cl.substr(pos, nxt - pos)); pos = nxt + 1; } parse_literal(S, cl.substr(pos)); #ifdef DEBUG_PARSE for(auto x: S) cout << x.first << "," << x.second << " "; cout << "\n"; #endif __C[m].beg = S.begin()->first; __C[m].end = S.rbegin()->first; for(auto &x: S) __C[m].its.push_back(x.second); C[m] = &__C[m]; m++; } void parse_input() { int pos = 0, nxt; #ifdef DEBUG_PARSE cout << input << "\n"; #endif while((nxt = input.find('^', pos)) != string::npos) { parse_clause(pos, nxt); pos = nxt + 1; } parse_clause(pos, input.size() - pos); } |