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-rw-r--r--content/math/bigint.cpp271
1 files changed, 271 insertions, 0 deletions
diff --git a/content/math/bigint.cpp b/content/math/bigint.cpp
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+++ b/content/math/bigint.cpp
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+// base and base_digits must be consistent
+constexpr ll base = 1'000'000;
+constexpr ll base_digits = 6;
+struct bigint {
+ using vll = vector<ll>;
+ vll a; ll sign;
+
+ bigint() : sign(1) {}
+
+ bigint(ll v) {*this = v;}
+
+ bigint(const string &s) {read(s);}
+
+ 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 < max(sz(a), sz(v.a)) || carry; ++i) {
+ if (i == sz(res.a))
+ res.a.push_back(0);
+ res.a[i] += carry + (i < sz(a) ? 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 < sz(v.a) || carry; ++i) {
+ res.a[i] -= carry + (i < sz(v.a) ? 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 < sz(a) || carry; ++i) {
+ if (i == sz(a)) 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(sz(a.a));
+ for (ll i = sz(a.a) - 1; i >= 0; i--) {
+ r *= base;
+ r += a.a[i];
+ ll s1 = sz(r.a) <= sz(b.a) ? 0 : r.a[sz(b.a)];
+ ll s2 = sz(r.a) <= sz(b.a) - 1 ? 0 : r.a[sz(b.a) - 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 = sz(a) - 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 = sz(a) - 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 (sz(a) != sz(v.a))
+ return sz(a) * sign < sz(v.a) * v.sign;
+ for (ll i = sz(a) - 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() || (sz(a) == 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 = sz(a) - 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 < sz(s) && (s[pos] == '-' || s[pos] == '+')) {
+ if (s[pos] == '-') sign = -sign;
+ ++pos;
+ }
+ for (ll i = sz(s) - 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 = sz(v.a) - 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 = sz(a);
+ 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 < sz(a1b1); i++) r[i] -= a1b1[i];
+ for (ll i = 0; i < sz(a2b2); i++) r[i] -= a2b2[i];
+ for (ll i = 0; i < sz(r); i++) res[i + k] += r[i];
+ for (ll i = 0; i < sz(a1b1); i++) res[i] += a1b1[i];
+ for (ll i = 0; i < sz(a2b2); i++) res[i + n] += a2b2[i];
+ return res;
+ }
+
+ bigint operator*(const bigint& v) const {
+ vll ta(a.begin(), a.end());
+ vll va(v.a.begin(), v.a.end());
+ while (sz(ta) < sz(va)) ta.push_back(0);
+ while (sz(va) < sz(ta)) va.push_back(0);
+ while (sz(ta) & (sz(ta) - 1))
+ ta.push_back(0), va.push_back(0);
+ vll ra = karatsubaMultiply(ta, va);
+ bigint res;
+ res.sign = sign * v.sign;
+ for (ll i = 0, carry = 0; i < sz(ra); i++) {
+ ll cur = ra[i] + carry;
+ res.a.push_back(cur % base);
+ carry = cur / base;
+ }
+ res.trim();
+ return res;
+ }
+};
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