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NT/Misc/Bigint.hpp
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- Last update: 2024-05-25 22:48:50+07:00
- Include:
#include "NT/Misc/Bigint.hpp"
Code
#pragma once
template <long long base = 1000000LL, int digit = 6>
struct BigInt{
int sign = 1;
vector<long long> val;
constexpr BigInt(const long long _val = 0) noexcept {
if(_val != 0) val.assign(1, _val);
if(_val < 0) sign = -1;
}
constexpr BigInt(const vector<long long> &_val) noexcept : val(_val) {}
constexpr BigInt(const string &s) noexcept {
stoi(s);
}
private:
void normalize(){
while(!val.empty() && val.back() == 0) val.pop_back();
if(val.empty()) sign = 1;
}
vector<long long> karatsuba_algorithm(vector<long long> &a, vector<long long> &b){
const int n = (int) a.size();
const int h = n >> 1;
assert(a.size() == b.size());
assert((n & (n - 1)) == 0);
if(n <= 64){
vector<long long> res(2 * n - 1);
for(int i = 0; i < n; ++i){
for(int j = 0; j < n; ++j){
res[i + j] += a[i] * b[j];
}
}
return res;
}
vector<long long> p(h), q(h), r(h), s(h), t(h), u(h);
for(int i = 0; i < h; ++i){
p[i] = a[i + h];
q[i] = a[i];
r[i] = b[i + h];
s[i] = b[i];
t[i] = p[i] + q[i];
u[i] = r[i] + s[i];
}
p = karatsuba_algorithm(p, r);
q = karatsuba_algorithm(q, s);
t = karatsuba_algorithm(t, u);
vector<long long> res(2 * n - 1, 0);
for(int i = 0; i < n - 1; ++i){
res[i] += q[i];
res[i + h] += t[i] - p[i] - q[i];
res[i + n] += p[i];
}
return res;
}
pair<BigInt, BigInt> divide_naive(const BigInt& rhs) const {
assert(!rhs.val.empty());
const int k = base / (rhs.val.back() + 1);
const BigInt dividend = (sign == 1 ? *this : -(*this)) * k;
const BigInt divisor = (rhs.sign == 1 ? rhs : -rhs) * k;
BigInt quo, rem = 0;
quo.val.resize(dividend.val.size());
const int n = divisor.val.size();
for(int i = (int) dividend.val.size() - 1; i >= 0; --i){
rem.val.emplace(rem.val.begin(), dividend.val[i]);
quo.val[i] =
((n < (int) rem.val.size() ?
rem.val[n] * base : 0)
+ ((n - 1) < (int) rem.val.size() ? rem.val[n - 1] : 0))
/ divisor.val.back();
rem -= divisor * quo.val[i];
while (rem.sign == -1) {
rem += divisor;
--quo.val[i];
}
}
quo.sign = sign * rhs.sign;
quo.normalize();
rem.sign = sign;
rem.normalize();
return {quo, rem / k};
}
pair<BigInt, BigInt> divide_newton(const BigInt& rhs) const {
assert(!rhs.val.empty());
int preci = val.size() - rhs.val.size();
BigInt t(1);
BigInt two = BigInt(2) << rhs.val.size();
BigInt pre;
int lim = min(preci, 3);
int rhslim = min(int(rhs.val.size()), 6);
t <<= lim;
while(pre != t){
BigInt rb = rhs >> (rhs.val.size() - rhslim);
if(rhslim != (int) rhs.val.size()) rb += BigInt(1);
pre = t;
t *= (BigInt(2) << (rhslim + lim)) - rb * t;
t.val = vector<long long>(t.val.begin() + lim + rhslim, t.val.end());
}
if(lim != preci){
pre = BigInt();
while(pre != t){
BigInt rb = rhs >> (rhs.val.size() - rhslim);
if(rhslim != (int) rhs.val.size()) rb += BigInt(1);
pre = t;
t *= (BigInt(2) << (rhslim + lim)) - rb * t;
t.val = vector<long long>(t.val.begin() + lim + rhslim, t.val.end());
int next_lim = min(lim * 2 + 1, preci);
if (next_lim != lim) t <<= next_lim - lim;
int next_rhslim = min(rhslim * 2 + 1, int(rhs.val.size()));
lim = next_lim;
rhslim = next_rhslim;
}
}
BigInt quo = (*this) * t;
quo.val = vector<long long>(quo.val.begin() + val.size(), quo.val.end());
BigInt mul = quo * rhs;
while(mul + rhs <= (*this)){
quo += BigInt(1);
mul += rhs;
}
BigInt rem = *this - quo * rhs;
return {quo, rem};
}
public:
void stoi(string s){
if(s == "0") return;
int n = s.size(), idx = 0;
if(s[0] == '-'){
n -= 1;
sign = -1;
idx = 1;
}
int len = (n + digit - 1) / digit, rem = n % digit;
if(rem == 0) rem += digit;
val.resize(len);
for(int i = len - 1; i >= 0; --i){
if(i == len - 1){
val[i] = stoll(s.substr(idx, rem));
idx += rem;
}else{
val[i] = stoll(s.substr(idx, digit));
idx += digit;
}
}
}
string itos() const {
string res = "";
if(sign == -1) res += "-";
bool flag = false;
for(int i = (int) val.size() - 1; i >= 0; --i){
if(val[i] > 0 && !flag){
res += to_string(val[i]);
flag = true;
}else if(flag){
string rem = to_string(val[i]);
res += string(digit - rem.size(), '0') + rem;
}
}
return (res.empty() || res == "-") ? "0" : res;
}
BigInt getReminder(const BigInt& rhs, const BigInt& div){
assert(!rhs.val.empty());
BigInt ans = *this - (div) * rhs;
return ans;
}
BigInt& shift(){
for(int i = 0; i < (int) val.size() - 1; ++i){
if(val[i] >= 0){
val[i + 1] += val[i] / base;
val[i] %= base;
}else{
long long x = (-val[i] + base - 1) / base;
val[i] += x * base;
val[i + 1] -= x;
}
}
while(val.back() >= base){
val.emplace_back(val.back() / base);
val[val.size() - 2] %= base;
}
return *this;
}
BigInt& operator=(const BigInt& x) = default;
inline BigInt& operator+=(const BigInt& rhs) noexcept {
if(rhs.val.empty()) return *this;
if(sign != rhs.sign) return *this -= -rhs;
if(val.size() < rhs.val.size()){
val.resize(rhs.val.size());
}
for(int i = 0; i < (int) rhs.val.size(); ++i){
val[i] += rhs.val[i];
}
return (*this).shift();
}
inline BigInt& operator-=(const BigInt& rhs) noexcept {
if(rhs.val.empty()) return *this;
if(sign != rhs.sign) return *this += -rhs;
if((sign == 1 ? *this : -*this) < (rhs.sign == 1 ? rhs : -rhs)){
return *this = -(rhs - *this);
}
for(int i = 0; i < (int) rhs.val.size(); ++i){
val[i] -= rhs.val[i];
}
shift();
while(!val.empty() && val.back() == 0) val.pop_back();
if(val.empty()) sign = 1;
return *this;
}
// Karatsuba Algorithm (O(N^(1.58)))
inline BigInt& operator*=(const BigInt& rhs) noexcept {
if(val.empty() || rhs.val.empty()){
*this = BigInt();
return *this;
}
sign *= rhs.sign;
/*
vector<long long> rhsval = rhs.val;
int k = 1;
while(k < (int) max(val.size(), rhsval.size())){
k *= 2;
}
val.resize(k), rhsval.resize(k);
val = karatsuba_algorithm(val, rhsval);
*/
val = atcoder::convolution_ll(val, rhs.val);
shift();
while(!val.empty() && val.back() == 0) val.pop_back();
if(val.empty()) sign = 1;
return *this;
}
// Newton method
inline BigInt& operator/=(const BigInt& rhst) noexcept {
assert(!rhst.val.empty());
if(val.empty()) return *this;
BigInt rhs = rhst;
int mulsign = sign * rhs.sign;
sign = 1, rhs.sign = 1;
if(*this < rhs){
*this = BigInt();
return *this;
}
if((int) val.size() <= 32 && (int) rhs.val.size() <= 32){
*this = divide_naive(rhs).first;
return *this;
}
*this = divide_newton(rhs).first;
sign = mulsign;
normalize();
return *this;
}
inline BigInt& operator%=(const BigInt& rhs) noexcept {
assert(!rhs.val.empty());
BigInt ans = *this - (*this / rhs) * rhs;
*this = ans;
return *this;
}
inline BigInt& operator++() { return *this += 1; }
inline BigInt operator++(int) {
const BigInt res = *this;
++(*this);
return res;
}
inline BigInt& operator--() { return *this -= 1; }
inline BigInt operator--(int) {
const BigInt res = *this;
--(*this);
return res;
}
inline BigInt operator+() const { return *this; }
inline BigInt operator-() const {
BigInt res = *this;
if (!res.val.empty()) res.sign = -res.sign;
return res;
}
inline BigInt& operator<<=(const unsigned int rhs){
if(val.back() >= 1 || (int) val.size() >= 2){
vector<long long> tmp(rhs, 0);
val.insert(val.begin(), tmp.begin(), tmp.end());
}
return *this;
}
inline BigInt& operator>>=(const unsigned int rhs){
if(rhs == 0) return *this;
if(rhs > val.size()) val = {0};
else val = vector<long long>(val.begin() + rhs, val.end());
return *this;
}
inline bool operator<(const BigInt& rhs) const {
if(sign != rhs.sign) return sign < rhs.sign;
if(val.size() != rhs.val.size()) return sign * val.size() < rhs.sign * rhs.val.size();
for(int i = (int) val.size() - 1; i >= 0; --i){
if(val[i] != rhs.val[i]) return sign * val[i] < rhs.sign * rhs.val[i];
}
return false;
}
inline bool operator>(const BigInt& rhs) const { return rhs < (*this); }
inline bool operator<=(const BigInt& rhs) const { return !((*this) > rhs); }
inline bool operator>=(const BigInt& rhs) const { return !((*this) < rhs); }
friend inline BigInt operator+(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) += rhs; }
friend inline BigInt operator-(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) -= rhs; }
friend inline BigInt operator*(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) *= rhs; }
friend inline BigInt operator/(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) /= rhs; }
friend inline BigInt operator%(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) %= rhs; }
friend inline BigInt operator<<(const BigInt& lhs, const unsigned int rhs) noexcept { return BigInt(lhs) <<= rhs; }
friend inline BigInt operator>>(const BigInt& lhs, const unsigned int rhs) noexcept { return BigInt(lhs) >>= rhs; }
friend inline bool operator==(const BigInt& lhs, const BigInt& rhs) noexcept { return lhs.val == rhs.val; }
friend inline bool operator!=(const BigInt& lhs, const BigInt& rhs) noexcept { return lhs.val != rhs.val; }
friend inline istream& operator>>(istream& is, BigInt& x) noexcept {
string s;
is >> s;
x.stoi(s);
return is;
}
friend inline ostream& operator<<(ostream& os, const BigInt& x) noexcept { return os << x.itos(); }
};#line 2 "NT/Misc/Bigint.hpp"
template <long long base = 1000000LL, int digit = 6>
struct BigInt{
int sign = 1;
vector<long long> val;
constexpr BigInt(const long long _val = 0) noexcept {
if(_val != 0) val.assign(1, _val);
if(_val < 0) sign = -1;
}
constexpr BigInt(const vector<long long> &_val) noexcept : val(_val) {}
constexpr BigInt(const string &s) noexcept {
stoi(s);
}
private:
void normalize(){
while(!val.empty() && val.back() == 0) val.pop_back();
if(val.empty()) sign = 1;
}
vector<long long> karatsuba_algorithm(vector<long long> &a, vector<long long> &b){
const int n = (int) a.size();
const int h = n >> 1;
assert(a.size() == b.size());
assert((n & (n - 1)) == 0);
if(n <= 64){
vector<long long> res(2 * n - 1);
for(int i = 0; i < n; ++i){
for(int j = 0; j < n; ++j){
res[i + j] += a[i] * b[j];
}
}
return res;
}
vector<long long> p(h), q(h), r(h), s(h), t(h), u(h);
for(int i = 0; i < h; ++i){
p[i] = a[i + h];
q[i] = a[i];
r[i] = b[i + h];
s[i] = b[i];
t[i] = p[i] + q[i];
u[i] = r[i] + s[i];
}
p = karatsuba_algorithm(p, r);
q = karatsuba_algorithm(q, s);
t = karatsuba_algorithm(t, u);
vector<long long> res(2 * n - 1, 0);
for(int i = 0; i < n - 1; ++i){
res[i] += q[i];
res[i + h] += t[i] - p[i] - q[i];
res[i + n] += p[i];
}
return res;
}
pair<BigInt, BigInt> divide_naive(const BigInt& rhs) const {
assert(!rhs.val.empty());
const int k = base / (rhs.val.back() + 1);
const BigInt dividend = (sign == 1 ? *this : -(*this)) * k;
const BigInt divisor = (rhs.sign == 1 ? rhs : -rhs) * k;
BigInt quo, rem = 0;
quo.val.resize(dividend.val.size());
const int n = divisor.val.size();
for(int i = (int) dividend.val.size() - 1; i >= 0; --i){
rem.val.emplace(rem.val.begin(), dividend.val[i]);
quo.val[i] =
((n < (int) rem.val.size() ?
rem.val[n] * base : 0)
+ ((n - 1) < (int) rem.val.size() ? rem.val[n - 1] : 0))
/ divisor.val.back();
rem -= divisor * quo.val[i];
while (rem.sign == -1) {
rem += divisor;
--quo.val[i];
}
}
quo.sign = sign * rhs.sign;
quo.normalize();
rem.sign = sign;
rem.normalize();
return {quo, rem / k};
}
pair<BigInt, BigInt> divide_newton(const BigInt& rhs) const {
assert(!rhs.val.empty());
int preci = val.size() - rhs.val.size();
BigInt t(1);
BigInt two = BigInt(2) << rhs.val.size();
BigInt pre;
int lim = min(preci, 3);
int rhslim = min(int(rhs.val.size()), 6);
t <<= lim;
while(pre != t){
BigInt rb = rhs >> (rhs.val.size() - rhslim);
if(rhslim != (int) rhs.val.size()) rb += BigInt(1);
pre = t;
t *= (BigInt(2) << (rhslim + lim)) - rb * t;
t.val = vector<long long>(t.val.begin() + lim + rhslim, t.val.end());
}
if(lim != preci){
pre = BigInt();
while(pre != t){
BigInt rb = rhs >> (rhs.val.size() - rhslim);
if(rhslim != (int) rhs.val.size()) rb += BigInt(1);
pre = t;
t *= (BigInt(2) << (rhslim + lim)) - rb * t;
t.val = vector<long long>(t.val.begin() + lim + rhslim, t.val.end());
int next_lim = min(lim * 2 + 1, preci);
if (next_lim != lim) t <<= next_lim - lim;
int next_rhslim = min(rhslim * 2 + 1, int(rhs.val.size()));
lim = next_lim;
rhslim = next_rhslim;
}
}
BigInt quo = (*this) * t;
quo.val = vector<long long>(quo.val.begin() + val.size(), quo.val.end());
BigInt mul = quo * rhs;
while(mul + rhs <= (*this)){
quo += BigInt(1);
mul += rhs;
}
BigInt rem = *this - quo * rhs;
return {quo, rem};
}
public:
void stoi(string s){
if(s == "0") return;
int n = s.size(), idx = 0;
if(s[0] == '-'){
n -= 1;
sign = -1;
idx = 1;
}
int len = (n + digit - 1) / digit, rem = n % digit;
if(rem == 0) rem += digit;
val.resize(len);
for(int i = len - 1; i >= 0; --i){
if(i == len - 1){
val[i] = stoll(s.substr(idx, rem));
idx += rem;
}else{
val[i] = stoll(s.substr(idx, digit));
idx += digit;
}
}
}
string itos() const {
string res = "";
if(sign == -1) res += "-";
bool flag = false;
for(int i = (int) val.size() - 1; i >= 0; --i){
if(val[i] > 0 && !flag){
res += to_string(val[i]);
flag = true;
}else if(flag){
string rem = to_string(val[i]);
res += string(digit - rem.size(), '0') + rem;
}
}
return (res.empty() || res == "-") ? "0" : res;
}
BigInt getReminder(const BigInt& rhs, const BigInt& div){
assert(!rhs.val.empty());
BigInt ans = *this - (div) * rhs;
return ans;
}
BigInt& shift(){
for(int i = 0; i < (int) val.size() - 1; ++i){
if(val[i] >= 0){
val[i + 1] += val[i] / base;
val[i] %= base;
}else{
long long x = (-val[i] + base - 1) / base;
val[i] += x * base;
val[i + 1] -= x;
}
}
while(val.back() >= base){
val.emplace_back(val.back() / base);
val[val.size() - 2] %= base;
}
return *this;
}
BigInt& operator=(const BigInt& x) = default;
inline BigInt& operator+=(const BigInt& rhs) noexcept {
if(rhs.val.empty()) return *this;
if(sign != rhs.sign) return *this -= -rhs;
if(val.size() < rhs.val.size()){
val.resize(rhs.val.size());
}
for(int i = 0; i < (int) rhs.val.size(); ++i){
val[i] += rhs.val[i];
}
return (*this).shift();
}
inline BigInt& operator-=(const BigInt& rhs) noexcept {
if(rhs.val.empty()) return *this;
if(sign != rhs.sign) return *this += -rhs;
if((sign == 1 ? *this : -*this) < (rhs.sign == 1 ? rhs : -rhs)){
return *this = -(rhs - *this);
}
for(int i = 0; i < (int) rhs.val.size(); ++i){
val[i] -= rhs.val[i];
}
shift();
while(!val.empty() && val.back() == 0) val.pop_back();
if(val.empty()) sign = 1;
return *this;
}
// Karatsuba Algorithm (O(N^(1.58)))
inline BigInt& operator*=(const BigInt& rhs) noexcept {
if(val.empty() || rhs.val.empty()){
*this = BigInt();
return *this;
}
sign *= rhs.sign;
/*
vector<long long> rhsval = rhs.val;
int k = 1;
while(k < (int) max(val.size(), rhsval.size())){
k *= 2;
}
val.resize(k), rhsval.resize(k);
val = karatsuba_algorithm(val, rhsval);
*/
val = atcoder::convolution_ll(val, rhs.val);
shift();
while(!val.empty() && val.back() == 0) val.pop_back();
if(val.empty()) sign = 1;
return *this;
}
// Newton method
inline BigInt& operator/=(const BigInt& rhst) noexcept {
assert(!rhst.val.empty());
if(val.empty()) return *this;
BigInt rhs = rhst;
int mulsign = sign * rhs.sign;
sign = 1, rhs.sign = 1;
if(*this < rhs){
*this = BigInt();
return *this;
}
if((int) val.size() <= 32 && (int) rhs.val.size() <= 32){
*this = divide_naive(rhs).first;
return *this;
}
*this = divide_newton(rhs).first;
sign = mulsign;
normalize();
return *this;
}
inline BigInt& operator%=(const BigInt& rhs) noexcept {
assert(!rhs.val.empty());
BigInt ans = *this - (*this / rhs) * rhs;
*this = ans;
return *this;
}
inline BigInt& operator++() { return *this += 1; }
inline BigInt operator++(int) {
const BigInt res = *this;
++(*this);
return res;
}
inline BigInt& operator--() { return *this -= 1; }
inline BigInt operator--(int) {
const BigInt res = *this;
--(*this);
return res;
}
inline BigInt operator+() const { return *this; }
inline BigInt operator-() const {
BigInt res = *this;
if (!res.val.empty()) res.sign = -res.sign;
return res;
}
inline BigInt& operator<<=(const unsigned int rhs){
if(val.back() >= 1 || (int) val.size() >= 2){
vector<long long> tmp(rhs, 0);
val.insert(val.begin(), tmp.begin(), tmp.end());
}
return *this;
}
inline BigInt& operator>>=(const unsigned int rhs){
if(rhs == 0) return *this;
if(rhs > val.size()) val = {0};
else val = vector<long long>(val.begin() + rhs, val.end());
return *this;
}
inline bool operator<(const BigInt& rhs) const {
if(sign != rhs.sign) return sign < rhs.sign;
if(val.size() != rhs.val.size()) return sign * val.size() < rhs.sign * rhs.val.size();
for(int i = (int) val.size() - 1; i >= 0; --i){
if(val[i] != rhs.val[i]) return sign * val[i] < rhs.sign * rhs.val[i];
}
return false;
}
inline bool operator>(const BigInt& rhs) const { return rhs < (*this); }
inline bool operator<=(const BigInt& rhs) const { return !((*this) > rhs); }
inline bool operator>=(const BigInt& rhs) const { return !((*this) < rhs); }
friend inline BigInt operator+(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) += rhs; }
friend inline BigInt operator-(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) -= rhs; }
friend inline BigInt operator*(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) *= rhs; }
friend inline BigInt operator/(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) /= rhs; }
friend inline BigInt operator%(const BigInt& lhs, const BigInt& rhs) noexcept { return BigInt(lhs) %= rhs; }
friend inline BigInt operator<<(const BigInt& lhs, const unsigned int rhs) noexcept { return BigInt(lhs) <<= rhs; }
friend inline BigInt operator>>(const BigInt& lhs, const unsigned int rhs) noexcept { return BigInt(lhs) >>= rhs; }
friend inline bool operator==(const BigInt& lhs, const BigInt& rhs) noexcept { return lhs.val == rhs.val; }
friend inline bool operator!=(const BigInt& lhs, const BigInt& rhs) noexcept { return lhs.val != rhs.val; }
friend inline istream& operator>>(istream& is, BigInt& x) noexcept {
string s;
is >> s;
x.stoi(s);
return is;
}
friend inline ostream& operator<<(ostream& os, const BigInt& x) noexcept { return os << x.itos(); }
};