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-rw-r--r--math/bigint.cpp514
1 files changed, 275 insertions, 239 deletions
diff --git a/math/bigint.cpp b/math/bigint.cpp
index e25ebe3..1753200 100644
--- a/math/bigint.cpp
+++ b/math/bigint.cpp
@@ -1,240 +1,276 @@
-// Bislang keine Division. Multiplikation nach Schulmethode.
-#define PLUS 0
-#define MINUS 1
-#define BASE 1000000000
-#define EXPONET 9
-
+// base and base_digits must be consistent
+constexpr ll base = 1000000;
+constexpr ll base_digits = 6;
struct bigint {
- int sign;
- vector<ll> digits;
-
- // Initialisiert mit 0.
- bigint(void) { sign = PLUS; }
-
- // Initialisiert mit kleinem Wert.
- bigint(ll value) {
- if (value == 0) sign = PLUS;
- else {
- sign = value >= 0 ? PLUS : MINUS;
- value = abs(value);
- while (value) {
- digits.push_back(value % BASE);
- value /= BASE;
- }}}
-
- // Initialisiert mit C-String. Kann nicht mit Vorzeichen umgehen.
- bigint(char *str, int length) {
- int base = 1;
- ll digit = 0;
- for (int i = length - 1; i >= 0; i--) {
- digit += base * (str[i] - '0');
- if (base * 10 == BASE) {
- digits.push_back(digit);
- digit = 0;
- base = 1;
- } else base *= 10;
- }
- if (digit != 0) digits.push_back(digit);
- sign = PLUS;
- }
-
- // Löscht führende Nullen und macht -0 zu 0.
- void trim() {
- while (digits.size() > 0 && digits[digits.size() - 1] == 0)
- digits.pop_back();
- if (digits.size() == 0 && sign == MINUS) sign = PLUS;
- }
-
- // Gibt die Zahl aus.
- void print() {
- if (digits.size() == 0) { printf("0"); return; }
- if (sign == MINUS) printf("-");
- printf("%lld", digits[digits.size() - 1]);
- for (int i = digits.size() - 2; i >= 0; i--) {
- printf("%09lld", digits[i]); // Anpassen, wenn andere Basis gewählt wird.
- }}
-};
-
-// Kleiner-oder-gleich-Vergleich.
-bool operator<=(bigint &a, bigint &b) {
- if (a.digits.size() == b.digits.size()) {
- int idx = a.digits.size() - 1;
- while (idx >= 0) {
- if (a.digits[idx] < b.digits[idx]) return true;
- else if (a.digits[idx] > b.digits[idx]) return false;
- idx--;
- }
- return true;
- }
- return a.digits.size() < b.digits.size();
-}
-
-// Kleiner-Vergeleich.
-bool operator<(bigint &a, bigint &b) {
- if (a.digits.size() == b.digits.size()) {
- int idx = a.digits.size() - 1;
- while (idx >= 0) {
- if (a.digits[idx] < b.digits[idx]) return true;
- else if (a.digits[idx] > b.digits[idx]) return false;
- idx--;
- }
- return false;
- }
- return a.digits.size() < b.digits.size();
-}
-
-void sub(bigint *a, bigint *b, bigint *c);
-
-// a + b = c. a, b, c dürfen gleich sein.
-void add(bigint *a, bigint *b, bigint *c) {
- if (a->sign == b->sign) c->sign = a->sign;
- else {
- if (a->sign == MINUS) {
- a->sign ^= 1;
- sub(b, a, c);
- a->sign ^= 1;
- } else {
- b->sign ^= 1;
- sub(a, b, c);
- b->sign ^= 1;
- }
- return;
- }
-
- c->digits.resize(max(a->digits.size(), b->digits.size()));
- ll carry = 0;
- int i = 0;
- for (; i < (int)min(a->digits.size(), b->digits.size()); i++) {
- ll sum = carry + a->digits[i] + b->digits[i];
- c->digits[i] = sum % BASE;
- carry = sum / BASE;
- }
- if (i < (int)a->digits.size()) {
- for (; i< (int)a->digits.size(); i++) {
- ll sum = carry + a->digits[i];
- c->digits[i] = sum % BASE;
- carry = sum / BASE;
- }
- } else {
- for (; i< (int)b->digits.size(); i++) {
- ll sum = carry + b->digits[i];
- c->digits[i] = sum % BASE;
- carry = sum / BASE;
- }}
- if (carry) c->digits.push_back(carry);
-}
-
-// a - b = c. c darf a oder b sein. a und b müssen verschieden sein.
-void sub(bigint *a, bigint *b, bigint *c) {
- if (a->sign == MINUS || b->sign == MINUS) {
- b->sign ^= 1;
- add(a, b, c);
- b->sign ^= 1;
- return;
- }
-
- if (a < b) {
- sub(b, a, c);
- c->sign = MINUS;
- c->trim();
- return;
- }
-
- c->digits.resize(a->digits.size());
- ll borrow = 0;
- int i = 0;
- for (; i < (int)b->digits.size(); i++) {
- ll diff = a->digits[i] - borrow - b->digits[i];
- if (a->digits[i] > 0) borrow = 0;
- if (diff < 0) {
- diff += BASE;
- borrow = 1;
- }
- c->digits[i] = diff % BASE;
- }
- for (; i < (int)a->digits.size(); i++) {
- ll diff = a->digits[i] - borrow;
- if (a->digits[i] > 0) borrow = 0;
- if (diff < 0) {
- diff += BASE;
- borrow = 1;
- }
- c->digits[i] = diff % BASE;
- }
- c->trim();
-}
-
-// Ziffernmultiplikation a * b = c. b und c dürfen gleich sein.
-// a muss kleiner BASE sein.
-void digitMul(ll a, bigint *b, bigint *c) {
- if (a == 0) {
- c->digits.clear();
- c->sign = PLUS;
- return;
- }
- c->digits.resize(b->digits.size());
- ll carry = 0;
- for (int i = 0; i < (int)b->digits.size(); i++) {
- ll prod = carry + b->digits[i] * a;
- c->digits[i] = prod % BASE;
- carry = prod / BASE;
- }
- if (carry) c->digits.push_back(carry);
- c->sign = (a > 0) ? b->sign : 1 ^ b->sign;
- c->trim();
-}
-
-// Zifferndivision b / a = c. b und c dürfen gleich sein.
-// a muss kleiner BASE sein.
-void digitDiv(ll a, bigint *b, bigint *c) {
- c->digits.resize(b->digits.size());
- ll carry = 0;
- for (int i = (int)b->digits.size() - 1; i>= 0; i--) {
- ll quot = (carry * BASE + b->digits[i]) / a;
- carry = carry * BASE + b->digits[i] - quot * a;
- c->digits[i] = quot;
- }
- c->sign = b->sign ^ (a < 0);
- c->trim();
-}
-
-// a * b = c. c darf weder a noch b sein. a und b dürfen gleich sein.
-void mult(bigint *a, bigint *b, bigint *c) {
- bigint row = *a, tmp;
- c->digits.clear();
- for (int i = 0; i < (int)b->digits.size(); i++) {
- digitMul(b->digits[i], &row, &tmp);
- add(&tmp, c, c);
- row.digits.insert(row.digits.begin(), 0);
- }
- c->sign = a->sign != b->sign;
- c->trim();
-}
-
-// Berechnet eine kleine Zehnerpotenz.
-inline ll pow10(int n) {
- ll res = 1;
- for (int i = 0; i < n; i++) res *= 10;
- return res;
-}
-
-// Berechnet eine große Zehnerpotenz.
-void power10(ll e, bigint *out) {
- out->digits.assign(e / EXPONET + 1, 0);
- if (e % EXPONET)
- out->digits[out->digits.size() - 1] = pow10(e % EXPONET);
- else out->digits[out->digits.size() - 1] = 1;
-}
-
-// Nimmt eine Zahl module einer Zehnerpotenz 10^e.
-void mod10(int e, bigint *a) {
- int idx = e / EXPONET;
- if ((int)a->digits.size() < idx + 1) return;
- if (e % EXPONET) {
- a->digits.resize(idx + 1);
- a->digits[idx] %= pow10(e % EXPONET);
- } else {
- a->digits.resize(idx);
- }
- a->trim();
-}
+ vll a; ll sign;
+
+ bigint() : sign(1) {}
+
+ bigint(ll v) {*this = v;}
+
+ bigint(const string &s) {read(s);}
+
+ void operator=(const bigint& v) {
+ sign = v.sign;
+ a = v.a;
+ }
+
+ void operator=(ll v) {
+ sign = 1;
+ if (v < 0) sign = -1, v = -v;
+ a.clear();
+ for (; v > 0; v = v / base)
+ a.push_back(v % base);
+ }
+
+ bigint operator+(const bigint& v) const {
+ if (sign == v.sign) {
+ bigint res = v;
+ for (ll i = 0, carry = 0; i < (ll)max(a.size(), v.a.size()) || carry; ++i) {
+ if (i == (ll)res.a.size())
+ res.a.push_back(0);
+ res.a[i] += carry + (i < (ll)a.size() ? a[i] : 0);
+ carry = res.a[i] >= base;
+ if (carry)
+ res.a[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 (ll i = 0, carry = 0; i < (ll)v.a.size() || carry; ++i) {
+ res.a[i] -= carry + (i < (ll)v.a.size() ? v.a[i] : 0);
+ carry = res.a[i] < 0;
+ if (carry) res.a[i] += base;
+ }
+ res.trim();
+ return res;
+ }
+ return -(v - *this);
+ }
+ return *this + (-v);
+ }
+
+ void operator*=(ll v) {
+ if (v < 0) sign = -sign, v = -v;
+ for (ll i = 0, carry = 0; i < (ll)a.size() || carry; ++i) {
+ if (i == (ll)a.size()) a.push_back(0);
+ ll cur = a[i] * v + carry;
+ carry = cur / base;
+ a[i] = cur % base;
+ }
+ trim();
+ }
+
+ bigint operator*(ll v) const {
+ bigint res = *this;
+ res *= v;
+ return res;
+ }
+
+ friend pair<bigint, bigint> divmod(const bigint& a1, const bigint& b1) {
+ ll norm = base / (b1.a.back() + 1);
+ bigint a = a1.abs() * norm;
+ bigint b = b1.abs() * norm;
+ bigint q, r;
+ q.a.resize(a.a.size());
+ for (ll i = (ll)a.a.size() - 1; i >= 0; i--) {
+ r *= base;
+ r += a.a[i];
+ ll s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
+ ll s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
+ ll d = (base * s1 + s2) / b.a.back();
+ r -= b * d;
+ while (r < 0)
+ r += b, --d;
+ q.a[i] = d;
+ }
+ q.sign = a1.sign * b1.sign;
+ r.sign = a1.sign;
+ q.trim();
+ r.trim();
+ return make_pair(q, r / 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/=(ll v) {
+ if (v < 0) sign = -sign, v = -v;
+ for (ll i = (ll)a.size() - 1, rem = 0; i >= 0; --i) {
+ ll cur = a[i] + rem * base;
+ a[i] = cur / v;
+ rem = cur % v;
+ }
+ trim();
+ }
+
+ bigint operator/(ll v) const {
+ bigint res = *this;
+ res /= v;
+ return res;
+ }
+
+ ll operator%(ll v) const {
+ if (v < 0) v = -v;
+ ll m = 0;
+ for (ll i = (ll)a.size() - 1; i >= 0; --i)
+ m = (a[i] + m * 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 (a.size() != v.a.size())
+ return a.size() * sign < v.a.size() * v.sign;
+ for (ll i = (ll)a.size() - 1; i >= 0; i--)
+ if (a[i] != v.a[i])
+ return a[i] * sign < v.a[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 (!a.empty() && !a.back()) a.pop_back();
+ if (a.empty()) sign = 1;
+ }
+
+ bool isZero() const {
+ return a.empty() || (a.size() == 1 && a[0] == 0);
+ }
+
+ bigint operator-() const {
+ bigint res = *this;
+ res.sign = -sign;
+ return res;
+ }
+
+ bigint abs() const {
+ bigint res = *this;
+ res.sign *= res.sign;
+ return res;
+ }
+
+ ll longValue() const {
+ ll res = 0;
+ for (ll i = (ll)a.size() - 1; i >= 0; i--)
+ res = res * base + a[i];
+ return res * sign;
+ }
+
+ void read(const string& s) {
+ sign = 1;
+ a.clear();
+ ll pos = 0;
+ while (pos < (ll)s.size() && (s[pos] == '-' || s[pos] == '+')) {
+ if (s[pos] == '-') sign = -sign;
+ ++pos;
+ }
+ for (ll i = (ll)s.size() - 1; i >= pos; i -= base_digits) {
+ ll x = 0;
+ for (ll j = max(pos, i - base_digits + 1); j <= i; j++)
+ x = x * 10 + s[j] - '0';
+ a.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.a.empty() ? 0 : v.a.back());
+ for (ll i = (ll)v.a.size() - 2; i >= 0; --i)
+ stream << setw(base_digits) << setfill('0') << v.a[i];
+ return stream;
+ }
+
+ static vll karatsubaMultiply(const vll& a, const vll& b) {
+ ll n = a.size();
+ vll res(n + n);
+ if (n <= 32) {
+ for (ll i = 0; i < n; i++)
+ for (ll j = 0; j < n; j++)
+ res[i + j] += a[i] * b[j];
+ return res;
+ }
+ ll 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 (ll i = 0; i < k; i++) a2[i] += a1[i];
+ for (ll i = 0; i < k; i++) b2[i] += b1[i];
+ vll r = karatsubaMultiply(a2, b2);
+ for (ll i = 0; i < (ll)a1b1.size(); i++) r[i] -= a1b1[i];
+ for (ll i = 0; i < (ll)a2b2.size(); i++) r[i] -= a2b2[i];
+ for (ll i = 0; i < (ll)r.size(); i++) res[i + k] += r[i];
+ for (ll i = 0; i < (ll)a1b1.size(); i++) res[i] += a1b1[i];
+ for (ll i = 0; i < (ll)a2b2.size(); i++) res[i + n] += a2b2[i];
+ return res;
+ }
+
+ bigint operator*(const bigint& v) const {
+ vll a(this->a.begin(), this->a.end());
+ vll b(v.a.begin(), v.a.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 (ll i = 0, carry = 0; i < (ll)c.size(); i++) {
+ ll cur = c[i] + carry;
+ res.a.push_back(cur % base);
+ carry = cur / base;
+ }
+ res.trim();
+ return res;
+ }
+}; \ No newline at end of file
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