#include #include #include #include #include #include #include #include using namespace std; // base and base_digits must be consistent const int base = 1000000000; const int base_digits = 9; struct bigint { vector z; int sign; bigint() : sign(1) { } bigint(long long v) { *this = v; } bigint(const string &s) { read(s); } void operator=(const bigint &v) { sign = v.sign; z = v.z; } void operator=(long long v) { sign = 1; if (v < 0) sign = -1, v = -v; z.clear(); for (; v > 0; v = v / base) z.push_back(v % base); } bigint operator+(const bigint &v) const { if (sign == v.sign) { bigint res = v; for (int i = 0, carry = 0; i < (int) max(z.size(), v.z.size()) || carry; ++i) { if (i == (int) res.z.size()) res.z.push_back(0); res.z[i] += carry + (i < (int) z.size() ? z[i] : 0); carry = res.z[i] >= base; if (carry) res.z[i] -= base; } return res; } return *this - (-v); } bigint operator-(const bigint &v) const { if (sign == v.sign) { if (abs() >= v.abs()) { bigint res = *this; for (int i = 0, carry = 0; i < (int) v.z.size() || carry; ++i) { res.z[i] -= carry + (i < (int) v.z.size() ? v.z[i] : 0); carry = res.z[i] < 0; if (carry) res.z[i] += base; } res.trim(); return res; } return -(v - *this); } return *this + (-v); } void operator*=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = 0, carry = 0; i < (int) z.size() || carry; ++i) { if (i == (int) z.size()) z.push_back(0); long long cur = z[i] * (long long) v + carry; carry = (int) (cur / base); z[i] = (int) (cur % base); //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base)); } trim(); } bigint operator*(int v) const { bigint res = *this; res *= v; return res; } friend pair 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 = 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 = ((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 make_pair(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 = ((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; } void 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(); } bigint operator/(int v) const { bigint res = *this; res /= v; return res; } int operator%(int v) const { if (v < 0) v = -v; int m = 0; for (int i = z.size() - 1; i >= 0; --i) m = (z[i] + m * (long long) base) % v; return m * sign; } void operator+=(const bigint &v) { *this = *this + v; } void operator-=(const bigint &v) { *this = *this - v; } void operator*=(const bigint &v) { *this = *this * v; } void operator/=(const bigint &v) { *this = *this / v; } 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 = 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 !(*this < v) && !(v < *this); } bool operator!=(const bigint &v) const { return *this < v || v < *this; } void trim() { while (!z.empty() && z.back() == 0) z.pop_back(); if (z.empty()) sign = 1; } bool isZero() const { return z.empty() || (z.size() == 1 && !z[0]); } bigint operator-() const { bigint res = *this; res.sign = -sign; return res; } bigint abs() const { bigint res = *this; res.sign *= res.sign; return res; } long long longValue() const { long long res = 0; for (int i = 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 < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) { if (s[pos] == '-') sign = -sign; ++pos; } for (int i = 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 convert_base(const vector &a, int old_digits, int new_digits) { vector p(max(old_digits, new_digits) + 1); p[0] = 1; for (int i = 1; i < (int) p.size(); i++) p[i] = p[i - 1] * 10; vector res; long long cur = 0; int cur_digits = 0; for (int i = 0; i < (int) a.size(); i++) { cur += a[i] * 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; } typedef vector vll; static vll karatsubaMultiply(const vll &a, const vll &b) { int n = a.size(); vll res(n + n); if (n <= 32) { for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) res[i + j] += a[i] * b[j]; return res; } int k = n >> 1; vll a1(a.begin(), a.begin() + k); vll a2(a.begin() + k, a.end()); vll b1(b.begin(), b.begin() + k); vll b2(b.begin() + k, b.end()); vll a1b1 = karatsubaMultiply(a1, b1); vll a2b2 = karatsubaMultiply(a2, b2); for (int i = 0; i < k; i++) a2[i] += a1[i]; for (int i = 0; i < k; i++) b2[i] += b1[i]; vll r = karatsubaMultiply(a2, b2); for (int i = 0; i < (int) a1b1.size(); i++) r[i] -= a1b1[i]; for (int i = 0; i < (int) a2b2.size(); i++) r[i] -= a2b2[i]; for (int i = 0; i < (int) r.size(); i++) res[i + k] += r[i]; for (int i = 0; i < (int) a1b1.size(); i++) res[i] += a1b1[i]; for (int i = 0; i < (int) a2b2.size(); i++) res[i + n] += a2b2[i]; return res; } bigint operator*(const bigint &v) const { vector a6 = convert_base(this->z, base_digits, 6); vector b6 = convert_base(v.z, base_digits, 6); vll a(a6.begin(), a6.end()); vll b(b6.begin(), b6.end()); while (a.size() < b.size()) a.push_back(0); while (b.size() < a.size()) b.push_back(0); while (a.size() & (a.size() - 1)) a.push_back(0), b.push_back(0); vll c = karatsubaMultiply(a, b); bigint res; res.sign = sign * v.sign; for (int i = 0, carry = 0; i < (int) c.size(); i++) { long long cur = c[i] + carry; res.z.push_back((int) (cur % 1000000)); carry = (int) (cur / 1000000); } res.z = convert_base(res.z, 6, base_digits); res.trim(); return res; } }; bigint random_bigint(int n) { string s; for (int i = 0; i < n; i++) { s += rand() % 10 + '0'; } return bigint(s); } // random tests int main() { for(int i = 0; i < 1000; i++) { cout << i << endl; int n = rand() % 100 + 1; bigint a = random_bigint(n); bigint res = sqrt(a); bigint xx = res * res; bigint yy = (res + 1) * (res + 1); if (xx > a || yy <= a) { cout << a << " " << res << endl; break; } int m = rand() % n + 1; bigint b = random_bigint(m) + 1; res = a / b; xx = res * b; yy = b * (res + 1); if (xx > a || yy <= a) { cout << a << " " << b << " " << res << endl; break; } } bigint a = random_bigint(10000); bigint b = random_bigint(2000); clock_t start = clock(); bigint c = a / b; fprintf(stdout, "time=%.3lfsec\n", 0.001 * (clock() - start)); bigint x = 5; x = 6; cout << x << endl; }