#include "ancient2.h"
#include <bits/stdc++.h>
using namespace std;
// Fast Fourier transform
// https://cp-algorithms.com/algebra/fft.html
// https://drive.google.com/file/d/1B9BIfATnI_qL6rYiE5hY9bh20SMVmHZ7/view
using cpx = complex<double>;
const double PI = acos(-1);
vector<cpx> roots = {{0, 0}, {1, 0}};
void ensure_capacity(int min_capacity) {
for (int len = roots.size(); len < min_capacity; len *= 2) {
for (int i = len >> 1; i < len; i++) {
roots.emplace_back(roots[i]);
double angle = 2 * PI * (2 * i + 1 - len) / (len * 2);
roots.emplace_back(cos(angle), sin(angle));
}
}
}
void fft(vector<cpx> &z, bool inverse) {
int n = z.size();
assert((n & (n - 1)) == 0);
ensure_capacity(n);
for (unsigned i = 1, j = 0; i < n; i++) {
int bit = n >> 1;
for (; j >= bit; bit >>= 1)
j -= bit;
j += bit;
if (i < j)
swap(z[i], z[j]);
}
for (int len = 1; len < n; len <<= 1) {
for (int i = 0; i < n; i += len * 2) {
for (int j = 0; j < len; j++) {
cpx root = inverse ? conj(roots[j + len]) : roots[j + len];
cpx u = z[i + j];
cpx v = z[i + j + len] * root;
z[i + j] = u + v;
z[i + j + len] = u - v;
}
}
}
if (inverse)
for (int i = 0; i < n; i++)
z[i] /= n;
}
vector<int> multiply_bigint(const vector<int> &a, const vector<int> &b, int base) {
int need = a.size() + b.size();
int n = 1;
while (n < need)
n <<= 1;
vector<cpx> p(n);
for (size_t i = 0; i < n; i++) {
p[i] = cpx(i < a.size() ? a[i] : 0, i < b.size() ? b[i] : 0);
}
fft(p, false);
// a[w[k]] = (p[w[k]] + conj(p[w[n-k]])) / 2
// b[w[k]] = (p[w[k]] - conj(p[w[n-k]])) / (2*i)
vector<cpx> ab(n);
cpx r(0, -0.25);
for (int i = 0; i < n; i++) {
int j = (n - i) & (n - 1);
ab[i] = (p[i] * p[i] - conj(p[j] * p[j])) * r;
}
fft(ab, true);
vector<int> result(need);
long long carry = 0;
for (int i = 0; i < need; i++) {
long long d = (long long)(ab[i].real() + 0.5) + carry;
carry = d / base;
result[i] = d % base;
}
return result;
}
vector<int> multiply_mod(const vector<int> &a, const vector<int> &b, int m) {
int need = a.size() + b.size() - 1;
int n = 1;
while (n < need)
n <<= 1;
vector<cpx> A(n);
for (size_t i = 0; i < a.size(); i++) {
int x = (a[i] % m + m) % m;
A[i] = cpx(x & ((1 << 15) - 1), x >> 15);
}
fft(A, false);
vector<cpx> B(n);
for (size_t i = 0; i < b.size(); i++) {
int x = (b[i] % m + m) % m;
B[i] = cpx(x & ((1 << 15) - 1), x >> 15);
}
fft(B, false);
vector<cpx> fa(n);
vector<cpx> fb(n);
for (int i = 0, j = 0; i < n; i++, j = n - i) {
cpx a1 = (A[i] + conj(A[j])) * cpx(0.5, 0);
cpx a2 = (A[i] - conj(A[j])) * cpx(0, -0.5);
cpx b1 = (B[i] + conj(B[j])) * cpx(0.5, 0);
cpx b2 = (B[i] - conj(B[j])) * cpx(0, -0.5);
fa[i] = a1 * b1 + a2 * b2 * cpx(0, 1);
fb[i] = a1 * b2 + a2 * b1;
}
fft(fa, true);
fft(fb, true);
vector<int> res(need);
for (int i = 0; i < need; i++) {
long long aa = (long long)(fa[i].real() + 0.5);
long long bb = (long long)(fb[i].real() + 0.5);
long long cc = (long long)(fa[i].imag() + 0.5);
res[i] = (aa % m + (bb % m << 15) + (cc % m << 30)) % m;
}
return res;
}
constexpr int digits(int base) noexcept {
return base <= 1 ? 0 : 1 + digits(base / 10);
}
constexpr int base = 1000'000'000;
constexpr int base_digits = digits(base);
constexpr int fft_base = 10'000; // fft_base^2 * n / fft_base_digits <= 10^15 for double
constexpr int fft_base_digits = digits(fft_base);
struct bigint {
// value == 0 is represented by empty z
vector<int> z; // digits
// sign == 1 <==> value >= 0
// sign == -1 <==> value < 0
int sign;
bigint(long long v = 0) { *this = v; }
bigint &operator=(long long v) {
sign = v < 0 ? -1 : 1;
v *= sign;
z.clear();
for (; v > 0; v = v / base)
z.push_back((int)(v % base));
return *this;
}
bigint(const string &s) { read(s); }
bigint &operator+=(const bigint &other) {
if (sign == other.sign) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] >= base;
if (carry)
z[i] -= base;
}
} else if (other != 0 /* prevent infinite loop */) {
*this -= -other;
}
return *this;
}
friend bigint operator+(bigint a, const bigint &b) {
a += b;
return a;
}
bigint &operator-=(const bigint &other) {
if (sign == other.sign) {
if ((sign == 1 && *this >= other) || (sign == -1 && *this <= other)) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] < 0;
if (carry)
z[i] += base;
}
trim();
} else {
*this = other - *this;
this->sign = -this->sign;
}
} else {
*this += -other;
}
return *this;
}
friend bigint operator-(bigint a, const bigint &b) {
a -= b;
return a;
}
bigint &operator*=(int v) {
if (v < 0)
sign = -sign, v = -v;
for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
long long cur = (long long)z[i] * v + carry;
carry = (int)(cur / base);
z[i] = (int)(cur % base);
}
trim();
return *this;
}
bigint operator*(int v) const { return bigint(*this) *= v; }
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 = (int)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 = (int)(((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 {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 = (int)(((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; }
bigint &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();
return *this;
}
bigint operator/(int v) const { return bigint(*this) /= v; }
int operator%(int v) const {
if (v < 0)
v = -v;
int m = 0;
for (int i = (int)z.size() - 1; i >= 0; --i)
m = (int)((z[i] + m * (long long)base) % v);
return m * sign;
}
bigint &operator*=(const bigint &v) {
*this = *this * v;
return *this;
}
bigint &operator/=(const bigint &v) {
*this = *this / v;
return *this;
}
bigint &operator%=(const bigint &v) {
*this = *this % v;
return *this;
}
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 = (int)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 sign == v.sign && z == v.z; }
bool operator!=(const bigint &v) const { return !(*this == v); }
void trim() {
while (!z.empty() && z.back() == 0)
z.pop_back();
if (z.empty())
sign = 1;
}
bool isZero() const { return z.empty(); }
friend bigint operator-(bigint v) {
if (!v.z.empty())
v.sign = -v.sign;
return v;
}
bigint abs() const { return sign == 1 ? *this : -*this; }
long long longValue() const {
long long res = 0;
for (int i = (int)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 < s.size() && (s[pos] == '-' || s[pos] == '+')) {
if (s[pos] == '-')
sign = -sign;
++pos;
}
for (int i = (int)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 < p.size(); i++)
p[i] = p[i - 1] * 10;
vector<int> res;
long long cur = 0;
int cur_digits = 0;
for (int v : a) {
cur += v * 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;
}
bigint operator*(const bigint &v) const {
if (min(z.size(), v.z.size()) < 150)
return mul_simple(v);
bigint res;
res.sign = sign * v.sign;
res.z = multiply_bigint(convert_base(z, base_digits, fft_base_digits),
convert_base(v.z, base_digits, fft_base_digits), fft_base);
res.z = convert_base(res.z, fft_base_digits, base_digits);
res.trim();
return res;
}
bigint mul_simple(const bigint &v) const {
bigint res;
res.sign = sign * v.sign;
res.z.resize(z.size() + v.z.size());
for (int i = 0; i < z.size(); ++i)
if (z[i])
for (int j = 0, carry = 0; j < v.z.size() || carry; ++j) {
long long cur = res.z[i + j] + (long long)z[i] * (j < v.z.size() ? v.z[j] : 0) + carry;
carry = (int)(cur / base);
res.z[i + j] = (int)(cur % base);
}
res.trim();
return res;
}
};
mt19937 rng(1);
bigint random_bigint(int n) {
string s;
for (int i = 0; i < n; i++) {
s += uniform_int_distribution<int>('0', '9')(rng);
}
return bigint(s);
}
namespace {
using namespace std;
bool is_prime(int p){
for(int q = 2; q * q <= p; q++){
if(p % q == 0) return false;
}
return true;
}
string my_solve(int N){
double log_prime_powers = 0;
int M = 600;
bigint res = 0;
bigint mod = 1;
for(int p = 2; p <= M; p++){
// if p is prime, multiply log_prime_powers by p^k where p^k <= M
if(is_prime(p)){
int q = 1;
while(q * p <= M) q *= p;
log_prime_powers += log(q) / log(2);
vector<int> A(q);
vector<int> B(q);
for(int i = 0; i < q; i++){
A[i] = (2*i) % q;
B[i] = (2*i+1) % q;
}
int val = Query(q, A, B);
while(res % q != val) res += mod;
mod *= q;
}
}
cerr << log_prime_powers << '\n';
string ans;
for(int i = 0; i < N; i++){
if(res % 2 == 0) ans += '0';
else ans += '1';
res /= 2;
}
reverse(ans.begin(), ans.end());
return ans;
}
} // namespace
std::string Solve(int N) {
return my_solve(N);
}
Compilation message
ancient2.cpp: In function 'void fft(std::vector<std::complex<double> >&, bool)':
ancient2.cpp:28:35: warning: comparison of integer expressions of different signedness: 'unsigned int' and 'int' [-Wsign-compare]
28 | for (unsigned i = 1, j = 0; i < n; i++) {
| ~~^~~
ancient2.cpp:30:18: warning: comparison of integer expressions of different signedness: 'unsigned int' and 'int' [-Wsign-compare]
30 | for (; j >= bit; bit >>= 1)
| ~~^~~~~~
ancient2.cpp: In function 'std::vector<int> multiply_bigint(const std::vector<int>&, const std::vector<int>&, int)':
ancient2.cpp:58:26: warning: comparison of integer expressions of different signedness: 'size_t' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
58 | for (size_t i = 0; i < n; i++) {
| ~~^~~
ancient2.cpp: In member function 'bigint& bigint::operator+=(const bigint&)':
ancient2.cpp:156:42: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
156 | for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
| ~~^~~~~~~~~~~~~~~~
ancient2.cpp:157:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
157 | if (i == z.size())
| ~~^~~~~~~~~~~
ancient2.cpp:159:36: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
159 | z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
| ~~^~~~~~~~~~~~~~~~
ancient2.cpp: In member function 'bigint& bigint::operator-=(const bigint&)':
ancient2.cpp:178:46: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
178 | for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
| ~~^~~~~~~~~~~~~~~~
ancient2.cpp:179:40: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
179 | z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
| ~~^~~~~~~~~~~~~~~~
ancient2.cpp: In member function 'bigint& bigint::operator*=(int)':
ancient2.cpp:203:38: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
203 | for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
| ~~^~~~~~~~~~
ancient2.cpp:204:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
204 | if (i == z.size())
| ~~^~~~~~~~~~~
ancient2.cpp: In member function 'void bigint::read(const string&)':
ancient2.cpp:380:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::__cxx11::basic_string<char>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
380 | while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) {
| ~~~~^~~~~~~~~~
ancient2.cpp: In static member function 'static std::vector<int> bigint::convert_base(const std::vector<int>&, int, int)':
ancient2.cpp:413:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
413 | for (int i = 1; i < p.size(); i++)
| ~~^~~~~~~~~~
ancient2.cpp: In member function 'bigint bigint::mul_simple(const bigint&) const':
ancient2.cpp:449:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
449 | for (int i = 0; i < z.size(); ++i)
| ~~^~~~~~~~~~
ancient2.cpp:451:46: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
451 | for (int j = 0, carry = 0; j < v.z.size() || carry; ++j) {
| ~~^~~~~~~~~~~~
ancient2.cpp:452:73: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
452 | long long cur = res.z[i + j] + (long long)z[i] * (j < v.z.size() ? v.z[j] : 0) + carry;
| ~~^~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
6 ms |
572 KB |
Wrong Answer [3] |
| 2 |
Halted |
0 ms |
0 KB |
- |
