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#ifndef BIGINT_H_ #define BIGINT_H_ 20160312L
#include <vector> #include <climits> #include <iostream>
namespace csl { #define long long long class BigInt { public: typedef std::uint32_t uint; typedef std::uint64_t ulong; typedef std::vector< uint > container; typedef BigInt _Self;
public: static const int kcbitUint = 32; static const uint kuMaskHighBit = (uint)INT_MIN; static const int MultiplyThreshold = 32;
private: int _sign; container _bits;
public: BigInt() : _sign(0), _bits() { }
BigInt(int value) { if (value < 0) _sign = -1, _bits = container(1, -value); else if (value > 0) _sign = +1, _bits = container(1, value); else _sign = 0, _bits = container(); }
BigInt(uint value) : _sign(+1), _bits(1, value) { }
BigInt(long value) { if (INT_MIN <= value && value <= INT_MAX) *this = _Self(int(value)); else { ulong x = 0; if (value < 0) x = (ulong)-value, _sign = -1; else x = (ulong)value, _sign = +1; if (x <= UINT_MAX) _bits = container(1, x); else _bits = container(2), _bits[0] = x, _bits[1] = x >> kcbitUint; } }
BigInt(ulong value) { _sign = +1; if (value <= UINT_MAX) _bits = container(1, value); else _bits = container(2), _bits[0] = value, _bits[1] = value >> kcbitUint; }
BigInt(int n, const container& rgu) : _sign(n), _bits(rgu) { }
BigInt(const container& value, bool negative) { StripLeadingZero(_bits = value); _sign = !_bits.size() ? 0 : negative ? -1 : +1; }
BigInt(container&& value, bool negative) { StripLeadingZero(_bits = std::move(value)); _sign = !_bits.size() ? 0 : negative ? -1 : +1; }
BigInt(const std::string& s) { int n = s.size(), cur = 0; if (s[cur] == '0') _sign = 0, ++cur; else if (s[cur] == '-') _sign = -1, ++cur; else _sign = 1;
container base = container(1, 10); _bits = container(1, 0); while (cur < n) { uint d = s[cur++] - '0'; container lb = container(_bits.size() + base.size()); std::swap(lb, _bits); Multiply(lb.data(), lb.size(), base.data(), base.size(), data(), size()); container newBits = container(1, d); if (d) AddSelf(data(), size(), newBits.data(), newBits.size()); StripLeadingZero(_bits); } }
public: inline uint* data() { return _bits.data(); }
inline const uint* data() const { return _bits.data(); }
inline uint size() const { return _bits.size(); }
inline std::string to_string() const { return FormatBigInt(*this); }
inline _Self abs() const { return _Self(_sign < 0 ? -_sign : _sign, _bits); }
inline friend std::istream& operator >>(std::istream& is, _Self& value) { std::string s; return is >> s, value = _Self(s), is; }
inline friend std::ostream& operator <<(std::ostream& os, const _Self& value) { return os << value.to_string(); }
inline int compareTo(const _Self& other) const { if (_sign != other._sign) return _sign < other._sign ? -1 : +1; if (!_sign) return 0; int cmp = Compare(data(), size(), other.data(), other.size()); return _sign > 0 ? cmp : -cmp; }
inline bool equals(const _Self& other) const { if (_sign != other._sign) return false; if (_bits == other._bits) return true; return false; }
static void DnM(const _Self& left, const _Self& right, _Self& q, _Self& r) { if (!left._sign) q = r = left; else if (left.size() < right.size()) q = _Self(0), r = left; else { container cr = container(left._bits), cq = container(left.size() - right.size() + 1); Divide(cr.data(), cr.size(), right.data(), right.size(), cq.data(), cq.size()); r = _Self(std::move(cr), left._sign < 0); q = _Self(std::move(cq), (left._sign < 0) ^ (right._sign < 0)); } }
public: inline _Self operator +() const { return _Self(_sign, _bits); }
inline _Self operator -() const { return _Self(-_sign, _bits); }
inline bool operator !() const { return _sign == 0; }
inline friend bool operator <(const _Self& left, const _Self& right) { return left.compareTo(right) < 0; }
inline friend bool operator <=(const _Self& left, const _Self& right) { return left.compareTo(right) <= 0; }
inline friend bool operator >(const _Self& left, const _Self& right) { return left.compareTo(right) > 0; }
inline friend bool operator >=(const _Self& left, const _Self& right) { return left.compareTo(right) >= 0; }
inline friend bool operator ==(const _Self& left, const _Self& right) { return left.equals(right); }
inline friend bool operator !=(const _Self& left, const _Self& right) { return !left.equals(right); }
friend _Self operator +(_Self left, const _Self& right) { return left += right; }
friend _Self operator -(_Self left, const _Self& right) { return left -= right; }
friend _Self operator *(const _Self& left, const _Self& right) { if (!left._sign) return left; if (!right._sign) return right; container bits = container(left.size() + right.size()); if (left.size() < right.size()) Multiply(right.data(), right.size(), left.data(), left.size(), bits.data(), bits.size()); else Multiply(left.data(), left.size(), right.data(), right.size(), bits.data(), bits.size()); return _Self(std::move(bits), (left._sign < 0) ^ (right._sign < 0)); }
friend _Self operator /(const _Self& left, const _Self& right) { if (!left._sign) return left; if (left.size() < right.size()) return _Self(0); else { container local = container(left._bits), bits = container(left.size() - right.size() + 1); Divide(local.data(), local.size(), right.data(), right.size(), bits.data(), bits.size()); return _Self(std::move(bits), (left._sign < 0) ^ (right._sign < 0)); } }
friend _Self operator %(_Self left, const _Self& right) { return left %= right; }
friend _Self& operator +=(_Self& left, const _Self& right) { if (!right._sign) return left; if (!left._sign) return left = right; if (left._sign != right._sign) left = Subtract(left._bits, left._sign, right._bits, right._sign); else left = Add(left._bits, left._sign, right._bits, right._sign); return left; }
friend _Self& operator -=(_Self& left, const _Self& right) { if (!right._sign) return left; if (!left._sign) return left = -right; if (left._sign != right._sign) left = Add(left._bits, left._sign, right._bits, -right._sign); else left = Subtract(left._bits, left._sign, right._bits, right._sign); return left; }
friend _Self& operator *=(_Self& left, const _Self& right) { return left = left * right; }
friend _Self& operator /=(_Self& left, const _Self& right) { return left = left / right; }
friend _Self& operator %=(_Self& left, const _Self& right) { if (!left._sign) return left; if (left.size() < right.size()) return left; Divide(left.data(), left.size(), right.data(), right.size(), container().data(), 0); return left = _Self(std::move(left._bits), left._sign < 0); }
friend _Self operator <<(const _Self& value, int shift) { if (shift == 0) return value; else if (shift == INT_MIN) return (value >> INT_MAX) >> 1; else if (shift < 0) return value >> -shift; int ds = shift / kcbitUint, ss = shift - (ds * kcbitUint); container xd; int xl; bool negx = GetPartsForBitManipulation(value, xd, xl); int zl = xl + ds + 1; container zd = container(zl); if (ss == 0) for (int i = 0; i < xl; i++) zd[i + ds] = xd[i]; else { int carryShift = kcbitUint - ss, i; uint carry = 0, rot; for (i = 0; i < xl; i++) rot = xd[i], zd[i + ds] = rot << ss | carry, carry = rot >> carryShift; zd[i + ds] = carry; } return _Self(zd, negx); }
friend _Self operator >>(const _Self& value, int shift) { if (shift == 0) return value; else if (shift == INT_MIN) return ((value << INT_MAX) << 1); else if (shift < 0) return value << -shift; int ds = shift / kcbitUint, ss = shift - (ds * kcbitUint); container xd; int xl; bool negx = GetPartsForBitManipulation(value, xd, xl); if (negx) { if (shift >= (kcbitUint * xl)) return _Self(-1LL); xd.resize(xl), DangerousMakeTwosComplement(xd); } int zl = xl - ds; if (zl < 0) zl = 0; container zd = container(zl); if (ss == 0) for (int i = xl - 1; i >= ds; i--) zd[i - ds] = xd[i]; else { int carryShift = kcbitUint - ss; uint carry = 0, rot; for (int i = xl - 1; i >= ds; i--) { rot = xd[i]; zd[i - ds] = (rot >> ss) | ((negx && i == xl - 1) ? (0xFFFFFFFF << carryShift) : carry); carry = (rot << carryShift); } } if (negx) DangerousMakeTwosComplement(zd); return _Self(zd, negx); }
private: static int Compare(const uint* l, int ll, const uint* r, int rl) { if (ll ^ rl) return (ll < rl) ? -1 : 1; for (int i = ll - 1; i >= 0; i--) if (l[i] ^ r[i]) return (l[i] < r[i]) ? -1 : 1; return 0; }
static void StripLeadingZero(container& bits) { const uint* data = bits.data(); uint len = bits.size(); while (len > 0 && data[len - 1] == 0) --len; bits.resize(len); }
static _Self Add(container left, int ls, container right, int rs) { container *l = &left, *s = &right; if (l->size() < s->size()) std::swap(l, s); uint ll = l->size(), sl = s->size(); long res = AddSelf(l->data(), ll, s->data(), sl); if (res) l->push_back(res); return _Self(std::move(*l), ls < 0); }
static _Self Subtract(container left, int ls, container right, int rs) { container *l = &left, *s = &right; if (Compare(l->data(), l->size(), s->data(), s->size()) < 0) std::swap(l, s), ls = -ls; uint ll = l->size(), sl = s->size(); SubtractSelf(l->data(), ll, s->data(), sl); StripLeadingZero(*l); return _Self(std::move(*l), ls < 0); }
static long AddSelf(uint* l, int ll, const uint* r, int rl) { long c = 0; for (int i = 0; i < rl; i++) c = (l[i] + c) + r[i], l[i] = c, c >>= 32; for (int i = rl; c != 0 && i < ll; i++) c = l[i] + c, l[i] = c, c >>= 32; return c; }
static long SubtractSelf(uint* l, int ll, const uint* r, int rl) { long c = 0; for (int i = 0; i < rl; i++) c = (l[i] + c) - r[i], l[i] = c, c >>= 32; for (int i = rl; c != 0 && i < ll; i++) c = l[i] + c, l[i] = c, c >>= 32; return c; }
static void Multiply(const uint* l, int ll, const uint* r, int rl, uint* b, int bl) { if (rl < MultiplyThreshold) { for (int i = 0; i < rl; i++) { ulong c = 0; for (int j = 0; j < ll; j++) c = b[i + j] + c + (ulong)l[j] * r[i], b[i + j] = c, c >>= 32; b[i + ll] = c; } } else { int n = rl >> 1, n2 = n << 1; const uint *llo = l, *lhi = l + n, *rlo = r, *rhi = r + n; int llol = n, lhil = ll - n, rlol = n, rhil = rl - n; uint *blo = b, *bhi = b + n2; int blol = n2, bhil = bl - n2; Multiply(llo, llol, rlo, rlol, blo, blol); Multiply(lhi, lhil, rhi, rhil, bhi, bhil); int lfl = lhil + 1, rfl = rhil + 1, col = lfl + rfl; container lf(lhi, lhi + lhil); lf.resize(lfl); AddSelf(lf.data(), lfl, llo, llol); container rf(rhi, rhi + rhil); rf.resize(rfl); AddSelf(rf.data(), rfl, rlo, rlol); container co = container(col); Multiply(lf.data(), lfl, rf.data(), rfl, co.data(), col); SubtractSelf(co.data(), col, bhi, bhil); SubtractSelf(co.data(), col, blo, blol); AddSelf(b + n, bl - n, co.data(), col); } }
static void Divide(uint* l, int ll, const uint* r, int rl, uint* b, int bl) { uint dHi = r[rl - 1], dLo = rl > 1 ? r[rl - 2] : 0; int sh = __builtin_clz(dHi), bsh = 32 - sh; if (sh > 0) { uint dNx = rl > 2 ? r[rl - 3] : 0; dHi = (dHi << sh) | (dLo >> bsh); dLo = (dLo << sh) | (dNx >> bsh); } for (int i = ll; i >= rl; i--) { int n = i - rl; uint t = i < ll ? l[i] : 0; ulong vHi = ((ulong)t << 32) | l[i - 1]; uint vLo = i > 1 ? l[i - 2] : 0; if (sh > 0) { uint vNx = i > 2 ? l[i - 3] : 0; vHi = (vHi << sh) | (vLo >> bsh); vLo = (vLo << sh) | (vNx >> bsh); } ulong d = std::min(vHi / dHi, 0xFFFFFFFFULL); while (DivideGuessTooBig(d, vHi, vLo, dHi, dLo)) --d; if (d > 0 && SubtractDivisor(l + n, ll - n, r, rl, d) != t) AddDivisor(l + n, ll - n, r, rl), --d; if (bl != 0) b[n] = (uint)d; if (i < ll) l[i] = 0; } }
static uint AddDivisor(uint* l, int ll, const uint* r, int rl) { ulong c = 0; for (int i = 0; i < rl; i++) c = (l[i] + c) + r[i], l[i] = c, c >>= 32; return c; }
static uint SubtractDivisor(uint* l, int ll, const uint* r, int rl, ulong q) { ulong c = 0; for (int i = 0; i < rl; i++) { c += r[i] * q; uint digit = (uint)c; c = (c >> 32) + (l[i] < digit), l[i] -= digit; } return c; }
static bool DivideGuessTooBig(ulong q, ulong vHi, uint vLo, uint dHi, uint dLo) { ulong cHi = dHi * q, cLo = dLo * q; cHi = cHi + (cLo >> 32), cLo = cLo & 0xFFFFFFFF; if (cHi ^ vHi) return cHi > vHi; if (cLo ^ vLo) return cLo > vLo; return false; }
inline static bool GetPartsForBitManipulation(const _Self& x, container& xd, int& xl) { if (x._bits.empty()) xd.assign(1, (x._sign < 0) ? (uint)-x._sign : (uint)x._sign); else xd = x._bits; xl = (x._bits.empty() ? 1 : x._bits.size()); return x._sign < 0; }
static void DangerousMakeTwosComplement(container& d) { if (!d.empty() && d.size() > 0) { d[0] = ~d[0] + 1; uint i = 1; for (; d[i - 1] == 0 && i < d.size(); i++) d[i] = ~d[i] + 1; for (; i < d.size(); i++) d[i] = ~d[i]; } }
static std::string FormatBigInt(const _Self& value) { if (value._sign == 0) return "0"; const uint kuBase = 1000000000; const int kcchBase = 9; int d = 0, cs = value._bits.size(), cd = 0; container rd = container(cs * 10 / 9 + 2); for (int is = cs; --is >= 0;) { uint uc = value._bits[is]; for (int id = 0; id < cd; id++) { ulong ur = ((ulong)rd[id] << kcbitUint) | uc; rd[id] = (uint)(ur % kuBase), uc = (uint)(ur / kuBase); } if (uc != 0) { rd[cd++] = uc % kuBase, uc /= kuBase; if (uc != 0) rd[cd++] = uc; } } int cm = cd * kcchBase; if (d > 0 && d > cm) cm = d; if (value._sign < 0) cm = cm + 1; char* s = new char[cm + 1]; int id = cm; for (int iuDst = 0; iuDst < cd - 1; iuDst++) { uint ud = rd[iuDst]; for (int cch = kcchBase; --cch >= 0;) s[--id] = (char)('0' + ud % 10), ud /= 10; } for (uint uDig = rd[cd - 1]; uDig != 0;) s[--id] = (char)('0' + uDig % 10), uDig /= 10; for (int t = cm - id; d > 0 && d > t;) s[--id] = '0', d--; if (value._sign < 0) s[--id] = '-'; return std::string(s + id, s + cm); } };
#undef long }
namespace std { inline csl::BigInt abs(const csl::BigInt& x) { return x.abs(); } inline string to_string(const csl::BigInt& x) { return x.to_string(); } }
#endif /* BIGINT_H_ */
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