#include <iostream> #include <string> #include <queue> #include <cstdlib> #include <limits> #include <algorithm> #include <iterator> const int MAX_N = 1000009; const int MODULUS = 1000000007; struct clause { int start; int end; std::deque<bool> val; clause() : start(0), end(0) {} bool operator==(const clause& other) const { return start == other.start && val == other.val; } void add(int num, bool v) { if (start == 0) { start = num; end = num+1; val.push_back(v); } while (start > num) { val.push_front(false); --start; } while (num >= end) { val.push_back(false); ++end; } val[num-start] = v; } int size() const { return end - start; } }; int n; std::vector<clause> clauses; std::pair<long long, long long> exgcd(long long a, long long b) { long long p = 1, q = 0; long long r = 0, s = 1; while (b != 0) { long long c = a % b; long long quot = a/b; a = b; b = c; long long r_tmp = r; long long s_tmp = s; r = p - quot * r; s = q - quot * s; p = r_tmp; q = s_tmp; } return std::make_pair(p, q); } long long invert(long long a) { return exgcd(a, MODULUS).first; } struct mod_num { long long val; mod_num() : val(0) {} mod_num(long long v) { val = v; val %= MODULUS; val += MODULUS; val %= MODULUS; } mod_num& operator+=(const mod_num& o) { val += o.val; val %= MODULUS; } mod_num& operator-=(const mod_num& o) { val += MODULUS; val -= o.val; val %= MODULUS; return *this; } mod_num& operator*=(const mod_num& o) { val *= o.val; val %= MODULUS; return *this; } mod_num& operator/=(const mod_num& o) { return (*this) *= invert(o.val); } mod_num operator+(const mod_num& o) { mod_num rv(*this); rv += o; return rv; } mod_num operator-(const mod_num& o) { mod_num rv(*this); rv -= o; return rv; } mod_num operator*(const mod_num& o) { mod_num rv(*this); rv *= o; return rv; } mod_num operator/(const mod_num& o) { mod_num rv(*this); rv /= o; return rv; } friend std::ostream& operator<<(std::ostream& os, const mod_num& n) { return os << n.val; } }; mod_num modpow(mod_num b, int n) { mod_num r = 1; while (n) { if (n&1) { r *= b; } b *= b; n >>= 1; } return r; } std::ostream& operator<<(std::ostream& os, const clause& c) { if (c.val.empty()) { return os << "false"; } os << "("; if (!c.val[0]) { os << '~'; } os << "x" << c.start; for (int i = 1; i < c.val.size(); ++i) { os << " v "; if (!c.val[i]) { os << '~'; } os << "x" << c.start+i; } os << ")"; return os; } class parser { int pos; const std::string& input; int skipTo(char c) { while (input[pos] != c) ++pos; } void skipAfter(char c) { skipTo(c); ++pos; } clause parseClause() { clause rv; for (;;) { bool val = true; for (; input[pos] != 'x'; ++pos) { if (input[pos] == ')') { ++pos; return rv; } else if (input[pos] == '~') { val = false; } } ++pos; int num = atoi(input.c_str()+pos); rv.add(num, val); } } public: parser(const std::string& input) : pos(0), input(input) {} void parse() { clauses.push_back(clause()); while (pos < input.size()) { skipTo('('); clauses.emplace_back(parseClause()); } } }; bool check_overlap(const clause& a, const clause& b) { if (a.start > b.start) return check_overlap(b, a); int diff = b.start-a.start; int e = std::min(b.size(), a.size()-diff); for (int i = 0; i < e; ++i) { if (a.val[i+diff] != b.val[i]) return false; } return true; } bool check_in(const clause& a, const clause& b) { if (a.size() > b.size()) return check_in(b, a); int diff = a.start-b.start; for (int i = 0; i < a.size(); ++i) { if (a.val[i] != b.val[i+diff]) return false; } return true; } const int MAX_K = 2009; mod_num tab[MAX_K][MAX_K][2]; bool comp[MAX_K]; int main() { std::ios_base::sync_with_stdio(false); std::cin >> n; std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n'); { std::string input; getline(std::cin, input); parser p(input); p.parse(); } std::sort(++clauses.begin(), clauses.end(), [](const clause& a, const clause& b) { return a.end < b.end || (a.end == b.end && a.start > b.start); }); mod_num result = modpow(2, n); int i = 1; for (int z = 1; z < clauses.size(); ++z) { const clause& c = clauses[z]; tab[i][1][0] = modpow(2, n-c.size()); tab[i][1][1] = tab[i-1][1][1]+tab[i-1][1][0]; int q; bool uniq = true; for (q = i-1; q > 0; --q) { const clause& c2 = clauses[q]; if (c2.end <= c.start) { break; } if (c2.start >= c.start && check_in(c2, c)) { uniq = false; break; } comp[q] = check_overlap(c, c2); } if (!uniq) { continue; } //std::cout << c << std::endl; //std::cout << i << " q(" << q << ") "; //std::cout << tab[i][1][0]; for (int j = 2; j <= i; ++j) { tab[i][j][1] = tab[i-1][j][1]+tab[i-1][j][0]; } for (int j = 2; j <= i; ++j) { for (int k = q+1; k < i; ++k) { if (comp[k]) { tab[i][j][0] += tab[k][j-1][0]/modpow(2, c.size()-(clauses[k].end-c.start)); } } tab[i][j][0] += tab[q+1][j-1][1]/modpow(2, c.size()); //std::cout << " " << tab[i][j][0]; //std::cout << "=" << tab[q+1][j-1][1] << "/" << modpow(2, c.size()); } if (i < z) { clauses[i] = clauses[z]; } ++i; //std::cout << std::endl; } int m = i-1; /* for (int i = 1; i <= m; ++i) { std::cout << " " << tab[m][i][0]+tab[m][i][1]; } std::cout << std::endl; */ for (int i = 1; i <= m; i += 2) { result -= tab[m][i][0]+tab[m][i][1]; } for (int i = 2; i <= m; i += 2) { result += tab[m][i][0]+tab[m][i][1]; } std::cout << result << std::endl; }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 | #include <iostream> #include <string> #include <queue> #include <cstdlib> #include <limits> #include <algorithm> #include <iterator> const int MAX_N = 1000009; const int MODULUS = 1000000007; struct clause { int start; int end; std::deque<bool> val; clause() : start(0), end(0) {} bool operator==(const clause& other) const { return start == other.start && val == other.val; } void add(int num, bool v) { if (start == 0) { start = num; end = num+1; val.push_back(v); } while (start > num) { val.push_front(false); --start; } while (num >= end) { val.push_back(false); ++end; } val[num-start] = v; } int size() const { return end - start; } }; int n; std::vector<clause> clauses; std::pair<long long, long long> exgcd(long long a, long long b) { long long p = 1, q = 0; long long r = 0, s = 1; while (b != 0) { long long c = a % b; long long quot = a/b; a = b; b = c; long long r_tmp = r; long long s_tmp = s; r = p - quot * r; s = q - quot * s; p = r_tmp; q = s_tmp; } return std::make_pair(p, q); } long long invert(long long a) { return exgcd(a, MODULUS).first; } struct mod_num { long long val; mod_num() : val(0) {} mod_num(long long v) { val = v; val %= MODULUS; val += MODULUS; val %= MODULUS; } mod_num& operator+=(const mod_num& o) { val += o.val; val %= MODULUS; } mod_num& operator-=(const mod_num& o) { val += MODULUS; val -= o.val; val %= MODULUS; return *this; } mod_num& operator*=(const mod_num& o) { val *= o.val; val %= MODULUS; return *this; } mod_num& operator/=(const mod_num& o) { return (*this) *= invert(o.val); } mod_num operator+(const mod_num& o) { mod_num rv(*this); rv += o; return rv; } mod_num operator-(const mod_num& o) { mod_num rv(*this); rv -= o; return rv; } mod_num operator*(const mod_num& o) { mod_num rv(*this); rv *= o; return rv; } mod_num operator/(const mod_num& o) { mod_num rv(*this); rv /= o; return rv; } friend std::ostream& operator<<(std::ostream& os, const mod_num& n) { return os << n.val; } }; mod_num modpow(mod_num b, int n) { mod_num r = 1; while (n) { if (n&1) { r *= b; } b *= b; n >>= 1; } return r; } std::ostream& operator<<(std::ostream& os, const clause& c) { if (c.val.empty()) { return os << "false"; } os << "("; if (!c.val[0]) { os << '~'; } os << "x" << c.start; for (int i = 1; i < c.val.size(); ++i) { os << " v "; if (!c.val[i]) { os << '~'; } os << "x" << c.start+i; } os << ")"; return os; } class parser { int pos; const std::string& input; int skipTo(char c) { while (input[pos] != c) ++pos; } void skipAfter(char c) { skipTo(c); ++pos; } clause parseClause() { clause rv; for (;;) { bool val = true; for (; input[pos] != 'x'; ++pos) { if (input[pos] == ')') { ++pos; return rv; } else if (input[pos] == '~') { val = false; } } ++pos; int num = atoi(input.c_str()+pos); rv.add(num, val); } } public: parser(const std::string& input) : pos(0), input(input) {} void parse() { clauses.push_back(clause()); while (pos < input.size()) { skipTo('('); clauses.emplace_back(parseClause()); } } }; bool check_overlap(const clause& a, const clause& b) { if (a.start > b.start) return check_overlap(b, a); int diff = b.start-a.start; int e = std::min(b.size(), a.size()-diff); for (int i = 0; i < e; ++i) { if (a.val[i+diff] != b.val[i]) return false; } return true; } bool check_in(const clause& a, const clause& b) { if (a.size() > b.size()) return check_in(b, a); int diff = a.start-b.start; for (int i = 0; i < a.size(); ++i) { if (a.val[i] != b.val[i+diff]) return false; } return true; } const int MAX_K = 2009; mod_num tab[MAX_K][MAX_K][2]; bool comp[MAX_K]; int main() { std::ios_base::sync_with_stdio(false); std::cin >> n; std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n'); { std::string input; getline(std::cin, input); parser p(input); p.parse(); } std::sort(++clauses.begin(), clauses.end(), [](const clause& a, const clause& b) { return a.end < b.end || (a.end == b.end && a.start > b.start); }); mod_num result = modpow(2, n); int i = 1; for (int z = 1; z < clauses.size(); ++z) { const clause& c = clauses[z]; tab[i][1][0] = modpow(2, n-c.size()); tab[i][1][1] = tab[i-1][1][1]+tab[i-1][1][0]; int q; bool uniq = true; for (q = i-1; q > 0; --q) { const clause& c2 = clauses[q]; if (c2.end <= c.start) { break; } if (c2.start >= c.start && check_in(c2, c)) { uniq = false; break; } comp[q] = check_overlap(c, c2); } if (!uniq) { continue; } //std::cout << c << std::endl; //std::cout << i << " q(" << q << ") "; //std::cout << tab[i][1][0]; for (int j = 2; j <= i; ++j) { tab[i][j][1] = tab[i-1][j][1]+tab[i-1][j][0]; } for (int j = 2; j <= i; ++j) { for (int k = q+1; k < i; ++k) { if (comp[k]) { tab[i][j][0] += tab[k][j-1][0]/modpow(2, c.size()-(clauses[k].end-c.start)); } } tab[i][j][0] += tab[q+1][j-1][1]/modpow(2, c.size()); //std::cout << " " << tab[i][j][0]; //std::cout << "=" << tab[q+1][j-1][1] << "/" << modpow(2, c.size()); } if (i < z) { clauses[i] = clauses[z]; } ++i; //std::cout << std::endl; } int m = i-1; /* for (int i = 1; i <= m; ++i) { std::cout << " " << tab[m][i][0]+tab[m][i][1]; } std::cout << std::endl; */ for (int i = 1; i <= m; i += 2) { result -= tab[m][i][0]+tab[m][i][1]; } for (int i = 2; i <= m; i += 2) { result += tab[m][i][0]+tab[m][i][1]; } std::cout << result << std::endl; } |