You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
447 lines
12 KiB
C++
447 lines
12 KiB
C++
#include <vector>
|
|
#include <cstdlib>
|
|
#include <iostream>
|
|
#include <iomanip>
|
|
#include <string>
|
|
#include <ctime>
|
|
#include <cstdio>
|
|
#include <cmath>
|
|
using namespace std;
|
|
|
|
// base and base_digits must be consistent
|
|
const int base = 1000000000;
|
|
const int base_digits = 9;
|
|
|
|
struct bigint {
|
|
vector<int> 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<bigint, bigint> 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<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
|
|
vector<long long> 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<int> 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<long long> 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<int> a6 = convert_base(this->z, base_digits, 6);
|
|
vector<int> 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;
|
|
}
|