#include <bits/stdc++.h> using namespace std; const int MXN=1e2+1; vector<int>pol[MXN]; constexpr int digits(int base) noexcept { return base <= 1 ? 0 : 1 + digits(base / 10); } constexpr int base = 1000'000'000; constexpr int base_digits = digits(base); constexpr int fft_base = 10'000; // fft_base^2 * n / fft_base_digits <= 10^15 for double constexpr int fft_base_digits = digits(fft_base); struct bigint { // value == 0 is represented by empty z vector<int> z; // digits // sign == 1 <==> value >= 0 // sign == -1 <==> value < 0 int sign; bigint(long long v = 0) { *this = v; } bigint &operator=(long long v) { sign = v < 0 ? -1 : 1; v *= sign; z.clear(); for (; v > 0; v = v / base) z.push_back((int)(v % base)); return *this; } bigint(const string &s) { read(s); } bigint &operator+=(const bigint &other) { if (sign == other.sign) { for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) { if (i == z.size()) z.push_back(0); z[i] += carry + (i < other.z.size() ? other.z[i] : 0); carry = z[i] >= base; if (carry) z[i] -= base; } } else if (other != 0 /* prevent infinite loop */) { *this -= -other; } return *this; } friend bigint operator+(bigint a, const bigint &b) { a += b; return a; } bigint &operator-=(const bigint &other) { if (sign == other.sign) { if ((sign == 1 && *this >= other) || (sign == -1 && *this <= other)) { for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) { z[i] -= carry + (i < other.z.size() ? other.z[i] : 0); carry = z[i] < 0; if (carry) z[i] += base; } trim(); } else { *this = other - *this; this->sign = -this->sign; } } else { *this += -other; } return *this; } friend bigint operator-(bigint a, const bigint &b) { a -= b; return a; } bigint &operator*=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = 0, carry = 0; i < z.size() || carry; ++i) { if (i == z.size()) z.push_back(0); long long cur = (long long)z[i] * v + carry; carry = (int)(cur / base); z[i] = (int)(cur % base); } trim(); return *this; } bigint operator*(int v) const { return bigint(*this) *= v; } friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) { int norm = base / (b1.z.back() + 1); bigint a = a1.abs() * norm; bigint b = b1.abs() * norm; bigint q, r; q.z.resize(a.z.size()); for (int i = (int)a.z.size() - 1; i >= 0; i--) { r *= base; r += a.z[i]; int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0; int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0; int d = (int)(((long long)s1 * base + s2) / b.z.back()); r -= b * d; while (r < 0) r += b, --d; q.z[i] = d; } q.sign = a1.sign * b1.sign; r.sign = a1.sign; q.trim(); r.trim(); return {q, r / norm}; } friend bigint sqrt(const bigint &a1) { bigint a = a1; while (a.z.empty() || a.z.size() % 2 == 1) a.z.push_back(0); int n = a.z.size(); int firstDigit = (int)::sqrt((double)a.z[n - 1] * base + a.z[n - 2]); int norm = base / (firstDigit + 1); a *= norm; a *= norm; while (a.z.empty() || a.z.size() % 2 == 1) a.z.push_back(0); bigint r = (long long)a.z[n - 1] * base + a.z[n - 2]; firstDigit = (int)::sqrt((double)a.z[n - 1] * base + a.z[n - 2]); int q = firstDigit; bigint res; for (int j = n / 2 - 1; j >= 0; j--) { for (;; --q) { bigint r1 = (r - (res * 2 * base + q) * q) * base * base + (j > 0 ? (long long)a.z[2 * j - 1] * base + a.z[2 * j - 2] : 0); if (r1 >= 0) { r = r1; break; } } res *= base; res += q; if (j > 0) { int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0; int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0; int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0; q = (int)(((long long)d1 * base * base + (long long)d2 * base + d3) / (firstDigit * 2)); } } res.trim(); return res / norm; } bigint operator/(const bigint &v) const { return divmod(*this, v).first; } bigint operator%(const bigint &v) const { return divmod(*this, v).second; } bigint &operator/=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = (int)z.size() - 1, rem = 0; i >= 0; --i) { long long cur = z[i] + rem * (long long)base; z[i] = (int)(cur / v); rem = (int)(cur % v); } trim(); return *this; } bigint operator/(int v) const { return bigint(*this) /= v; } int operator%(int v) const { if (v < 0) v = -v; int m = 0; for (int i = (int)z.size() - 1; i >= 0; --i) m = (int)((z[i] + m * (long long)base) % v); return m * sign; } bigint &operator*=(const bigint &v) { *this = *this * v; return *this; } bigint &operator/=(const bigint &v) { *this = *this / v; return *this; } bigint &operator%=(const bigint &v) { *this = *this % v; return *this; } bool operator<(const bigint &v) const { if (sign != v.sign) return sign < v.sign; if (z.size() != v.z.size()) return z.size() * sign < v.z.size() * v.sign; for (int i = (int)z.size() - 1; i >= 0; i--) if (z[i] != v.z[i]) return z[i] * sign < v.z[i] * sign; return false; } bool operator>(const bigint &v) const { return v < *this; } bool operator<=(const bigint &v) const { return !(v < *this); } bool operator>=(const bigint &v) const { return !(*this < v); } bool operator==(const bigint &v) const { return sign == v.sign && z == v.z; } bool operator!=(const bigint &v) const { return !(*this == v); } void trim() { while (!z.empty() && z.back() == 0) z.pop_back(); if (z.empty()) sign = 1; } bool isZero() const { return z.empty(); } friend bigint operator-(bigint v) { if (!v.z.empty()) v.sign = -v.sign; return v; } bigint abs() const { return sign == 1 ? *this : -*this; } long long longValue() const { long long res = 0; for (int i = (int)z.size() - 1; i >= 0; i--) res = res * base + z[i]; return res * sign; } friend bigint gcd(const bigint &a, const bigint &b) { return b.isZero() ? a : gcd(b, a % b); } friend bigint lcm(const bigint &a, const bigint &b) { return a / gcd(a, b) * b; } void read(const string &s) { sign = 1; z.clear(); int pos = 0; while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) { if (s[pos] == '-') sign = -sign; ++pos; } for (int i = (int)s.size() - 1; i >= pos; i -= base_digits) { int x = 0; for (int j = max(pos, i - base_digits + 1); j <= i; j++) x = x * 10 + s[j] - '0'; z.push_back(x); } trim(); } friend istream &operator>>(istream &stream, bigint &v) { string s; stream >> s; v.read(s); return stream; } friend ostream &operator<<(ostream &stream, const bigint &v) { if (v.sign == -1) stream << '-'; stream << (v.z.empty() ? 0 : v.z.back()); for (int i = (int)v.z.size() - 2; i >= 0; --i) stream << setw(base_digits) << setfill('0') << v.z[i]; return stream; } static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) { vector<long long> p(max(old_digits, new_digits) + 1); p[0] = 1; for (int i = 1; i < p.size(); i++) p[i] = p[i - 1] * 10; vector<int> res; long long cur = 0; int cur_digits = 0; for (int v : a) { cur += v * p[cur_digits]; cur_digits += old_digits; while (cur_digits >= new_digits) { res.push_back(int(cur % p[new_digits])); cur /= p[new_digits]; cur_digits -= new_digits; } } res.push_back((int)cur); while (!res.empty() && res.back() == 0) res.pop_back(); return res; } bigint operator*(const bigint &v) const { bigint res; res.sign = sign * v.sign; res.z.resize(z.size() + v.z.size()); for (int i = 0; i < z.size(); ++i) if (z[i]) for (int j = 0, carry = 0; j < v.z.size() || carry; ++j) { long long cur = res.z[i + j] + (long long)z[i] * (j < v.z.size() ? v.z[j] : 0) + carry; carry = (int)(cur / base); res.z[i + j] = (int)(cur % base); } res.trim(); return res; } }; bool check(bigint x, int n) { vector<bigint>a(n+1); a[1]=x; for (int i=1; i<=n; i++) { //~ cout<<" "<<i<<endl; int r=pol[i].size(); if (r==0) continue; if (a[i]%r!=0) return false; for (auto j : pol[i]) { a[j]+=a[i]/r; } } return true; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int n; cin>>n; bigint ans=1; for (int i=1; i<=n; i++) { int r; cin>>r; if (r) ans*=r; pol[i].resize(r); for (auto &j : pol[i]) cin>>j; } bigint cp=ans; for (int i=2; i<100; i++) { //~ cout<<i<<endl; if (cp%i==0) { while (cp%i==0) cp/=i; while (ans%i==0 && check(ans/i, n)) ans/=i; } } cout<<ans<<"\n"; }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 | #include <bits/stdc++.h> using namespace std; const int MXN=1e2+1; vector<int>pol[MXN]; constexpr int digits(int base) noexcept { return base <= 1 ? 0 : 1 + digits(base / 10); } constexpr int base = 1000'000'000; constexpr int base_digits = digits(base); constexpr int fft_base = 10'000; // fft_base^2 * n / fft_base_digits <= 10^15 for double constexpr int fft_base_digits = digits(fft_base); struct bigint { // value == 0 is represented by empty z vector<int> z; // digits // sign == 1 <==> value >= 0 // sign == -1 <==> value < 0 int sign; bigint(long long v = 0) { *this = v; } bigint &operator=(long long v) { sign = v < 0 ? -1 : 1; v *= sign; z.clear(); for (; v > 0; v = v / base) z.push_back((int)(v % base)); return *this; } bigint(const string &s) { read(s); } bigint &operator+=(const bigint &other) { if (sign == other.sign) { for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) { if (i == z.size()) z.push_back(0); z[i] += carry + (i < other.z.size() ? other.z[i] : 0); carry = z[i] >= base; if (carry) z[i] -= base; } } else if (other != 0 /* prevent infinite loop */) { *this -= -other; } return *this; } friend bigint operator+(bigint a, const bigint &b) { a += b; return a; } bigint &operator-=(const bigint &other) { if (sign == other.sign) { if ((sign == 1 && *this >= other) || (sign == -1 && *this <= other)) { for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) { z[i] -= carry + (i < other.z.size() ? other.z[i] : 0); carry = z[i] < 0; if (carry) z[i] += base; } trim(); } else { *this = other - *this; this->sign = -this->sign; } } else { *this += -other; } return *this; } friend bigint operator-(bigint a, const bigint &b) { a -= b; return a; } bigint &operator*=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = 0, carry = 0; i < z.size() || carry; ++i) { if (i == z.size()) z.push_back(0); long long cur = (long long)z[i] * v + carry; carry = (int)(cur / base); z[i] = (int)(cur % base); } trim(); return *this; } bigint operator*(int v) const { return bigint(*this) *= v; } friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) { int norm = base / (b1.z.back() + 1); bigint a = a1.abs() * norm; bigint b = b1.abs() * norm; bigint q, r; q.z.resize(a.z.size()); for (int i = (int)a.z.size() - 1; i >= 0; i--) { r *= base; r += a.z[i]; int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0; int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0; int d = (int)(((long long)s1 * base + s2) / b.z.back()); r -= b * d; while (r < 0) r += b, --d; q.z[i] = d; } q.sign = a1.sign * b1.sign; r.sign = a1.sign; q.trim(); r.trim(); return {q, r / norm}; } friend bigint sqrt(const bigint &a1) { bigint a = a1; while (a.z.empty() || a.z.size() % 2 == 1) a.z.push_back(0); int n = a.z.size(); int firstDigit = (int)::sqrt((double)a.z[n - 1] * base + a.z[n - 2]); int norm = base / (firstDigit + 1); a *= norm; a *= norm; while (a.z.empty() || a.z.size() % 2 == 1) a.z.push_back(0); bigint r = (long long)a.z[n - 1] * base + a.z[n - 2]; firstDigit = (int)::sqrt((double)a.z[n - 1] * base + a.z[n - 2]); int q = firstDigit; bigint res; for (int j = n / 2 - 1; j >= 0; j--) { for (;; --q) { bigint r1 = (r - (res * 2 * base + q) * q) * base * base + (j > 0 ? (long long)a.z[2 * j - 1] * base + a.z[2 * j - 2] : 0); if (r1 >= 0) { r = r1; break; } } res *= base; res += q; if (j > 0) { int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0; int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0; int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0; q = (int)(((long long)d1 * base * base + (long long)d2 * base + d3) / (firstDigit * 2)); } } res.trim(); return res / norm; } bigint operator/(const bigint &v) const { return divmod(*this, v).first; } bigint operator%(const bigint &v) const { return divmod(*this, v).second; } bigint &operator/=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = (int)z.size() - 1, rem = 0; i >= 0; --i) { long long cur = z[i] + rem * (long long)base; z[i] = (int)(cur / v); rem = (int)(cur % v); } trim(); return *this; } bigint operator/(int v) const { return bigint(*this) /= v; } int operator%(int v) const { if (v < 0) v = -v; int m = 0; for (int i = (int)z.size() - 1; i >= 0; --i) m = (int)((z[i] + m * (long long)base) % v); return m * sign; } bigint &operator*=(const bigint &v) { *this = *this * v; return *this; } bigint &operator/=(const bigint &v) { *this = *this / v; return *this; } bigint &operator%=(const bigint &v) { *this = *this % v; return *this; } bool operator<(const bigint &v) const { if (sign != v.sign) return sign < v.sign; if (z.size() != v.z.size()) return z.size() * sign < v.z.size() * v.sign; for (int i = (int)z.size() - 1; i >= 0; i--) if (z[i] != v.z[i]) return z[i] * sign < v.z[i] * sign; return false; } bool operator>(const bigint &v) const { return v < *this; } bool operator<=(const bigint &v) const { return !(v < *this); } bool operator>=(const bigint &v) const { return !(*this < v); } bool operator==(const bigint &v) const { return sign == v.sign && z == v.z; } bool operator!=(const bigint &v) const { return !(*this == v); } void trim() { while (!z.empty() && z.back() == 0) z.pop_back(); if (z.empty()) sign = 1; } bool isZero() const { return z.empty(); } friend bigint operator-(bigint v) { if (!v.z.empty()) v.sign = -v.sign; return v; } bigint abs() const { return sign == 1 ? *this : -*this; } long long longValue() const { long long res = 0; for (int i = (int)z.size() - 1; i >= 0; i--) res = res * base + z[i]; return res * sign; } friend bigint gcd(const bigint &a, const bigint &b) { return b.isZero() ? a : gcd(b, a % b); } friend bigint lcm(const bigint &a, const bigint &b) { return a / gcd(a, b) * b; } void read(const string &s) { sign = 1; z.clear(); int pos = 0; while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) { if (s[pos] == '-') sign = -sign; ++pos; } for (int i = (int)s.size() - 1; i >= pos; i -= base_digits) { int x = 0; for (int j = max(pos, i - base_digits + 1); j <= i; j++) x = x * 10 + s[j] - '0'; z.push_back(x); } trim(); } friend istream &operator>>(istream &stream, bigint &v) { string s; stream >> s; v.read(s); return stream; } friend ostream &operator<<(ostream &stream, const bigint &v) { if (v.sign == -1) stream << '-'; stream << (v.z.empty() ? 0 : v.z.back()); for (int i = (int)v.z.size() - 2; i >= 0; --i) stream << setw(base_digits) << setfill('0') << v.z[i]; return stream; } static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) { vector<long long> p(max(old_digits, new_digits) + 1); p[0] = 1; for (int i = 1; i < p.size(); i++) p[i] = p[i - 1] * 10; vector<int> res; long long cur = 0; int cur_digits = 0; for (int v : a) { cur += v * p[cur_digits]; cur_digits += old_digits; while (cur_digits >= new_digits) { res.push_back(int(cur % p[new_digits])); cur /= p[new_digits]; cur_digits -= new_digits; } } res.push_back((int)cur); while (!res.empty() && res.back() == 0) res.pop_back(); return res; } bigint operator*(const bigint &v) const { bigint res; res.sign = sign * v.sign; res.z.resize(z.size() + v.z.size()); for (int i = 0; i < z.size(); ++i) if (z[i]) for (int j = 0, carry = 0; j < v.z.size() || carry; ++j) { long long cur = res.z[i + j] + (long long)z[i] * (j < v.z.size() ? v.z[j] : 0) + carry; carry = (int)(cur / base); res.z[i + j] = (int)(cur % base); } res.trim(); return res; } }; bool check(bigint x, int n) { vector<bigint>a(n+1); a[1]=x; for (int i=1; i<=n; i++) { //~ cout<<" "<<i<<endl; int r=pol[i].size(); if (r==0) continue; if (a[i]%r!=0) return false; for (auto j : pol[i]) { a[j]+=a[i]/r; } } return true; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int n; cin>>n; bigint ans=1; for (int i=1; i<=n; i++) { int r; cin>>r; if (r) ans*=r; pol[i].resize(r); for (auto &j : pol[i]) cin>>j; } bigint cp=ans; for (int i=2; i<100; i++) { //~ cout<<i<<endl; if (cp%i==0) { while (cp%i==0) cp/=i; while (ans%i==0 && check(ans/i, n)) ans/=i; } } cout<<ans<<"\n"; } |