結果
| 問題 | No.1073 無限すごろく |
| ユーザー |
 apricity
|
| 提出日時 | 2023-02-12 03:14:01 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
CE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 17,263 bytes |
| コンパイル時間 | 1,198 ms |
| コンパイル使用メモリ | 131,128 KB |
| 最終ジャッジ日時 | 2024-04-27 04:29:00 |
| 合計ジャッジ時間 | 1,797 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。（リジャッジ後のコンパイルエラーは公開されます）
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
コンパイルメッセージ
main.cpp:429:30: error: 'function' does not name a type; did you mean 'union'?
429 | P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const {
| ^~~~~~~~
| union
main.cpp:429:38: error: expected ',' or '...' before '<' token
429 | P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const {
| ^
main.cpp:456:16: error: 'function' does not name a type; did you mean 'union'?
456 | P sqrt(const function< T(T) > &get_sqrt, int deg = -1) const {
| ^~~~~~~~
| union
main.cpp:456:24: error: expected ',' or '...' before '<' token
456 | P sqrt(const function< T(T) > &get_sqrt, int deg = -1) const {
| ^
main.cpp:429:24: error: default argument missing for parameter 2 of 'FormalPowerSeries<T>::P FormalPowerSeries<T>::sqrt(int, int) const'
429 | P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const {
| ^~~~~~~~~~~~~~
main.cpp:429:14: note: ...following parameter 1 which has a default argument
429 | P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const {
| ~~~~^~~~~~~~
main.cpp: In member function 'FormalPowerSeries<T>::P FormalPowerSeries<T>::sqrt(int, int) const':
main.cpp:437:53: error: 'get_sqrt' was not declared in this scope
437 | auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);
| ^~~~~~~~
main.cpp: In member function 'FormalPowerSeries<T>::P FormalPowerSeries<T>::sqrt(int) const':
main.cpp:457:17: error: 'deg' was not declared in this scope
457 | return sqrt(deg, get_sqrt);
| ^~~
main.cpp:457:22: error: 'get_sqrt' was not declared in this scope
457 | return sqrt(deg, get_sqrt);
|
ソースコード
#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<deque>
#include<unordered_map>
#include<unordered_set>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#ifdef LOCAL
# include "debug_print.hpp"
# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
# define debug(...) (static_cast<void>(0))
#endif
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
#define rrep(i,n) for(int i=(n)-1; i>=0; i--)
#define FOR(i,a,b) for(int i=(a); i<(b); i++)
#define RFOR(i,a,b) for(int i=(b-1); i>=(a); i--)
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define pb push_back
using ll = long long;
using D = double;
using LD = long double;
using P = pair<int, int>;
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
namespace FastFourierTransform {
using real = double;
struct C {
real x, y;
C() : x(0), y(0) {}
C(real x, real y) : x(x), y(y) {}
inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }
inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }
inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }
inline C conj() const { return C(x, -y); }
};
const real PI = acosl(-1);
int base = 1;
vector< C > rts = { {0, 0},
{1, 0} };
vector< int > rev = {0, 1};
void ensure_base(int nbase) {
if(nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for(int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
while(base < nbase) {
real angle = PI * 2.0 / (1 << (base + 1));
for(int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
real angle_i = angle * (2 * i + 1 - (1 << base));
rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
}
++base;
}
}
void fft(vector< C > &a, int n) {
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for(int i = 0; i < n; i++) {
if(i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for(int k = 1; k < n; k <<= 1) {
for(int i = 0; i < n; i += 2 * k) {
for(int j = 0; j < k; j++) {
C z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
int need = (int) a.size() + (int) b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < sz; i++) {
int x = (i < (int) a.size() ? a[i] : 0);
int y = (i < (int) b.size() ? b[i] : 0);
fa[i] = C(x, y);
}
fft(fa, sz);
C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
for(int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
fa[i] = z;
}
for(int i = 0; i < (sz >> 1); i++) {
C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
fa[i] = A0 + A1 * s;
}
fft(fa, sz >> 1);
vector< int64_t > ret(need);
for(int i = 0; i < need; i++) {
ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
}
return ret;
}
};
/*
* @brief Arbitrary Mod Convolution(任意mod畳み込み)
*/
template< typename T >
struct ArbitraryModConvolution {
using real = FastFourierTransform::real;
using C = FastFourierTransform::C;
ArbitraryModConvolution() = default;
static vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
if(need == -1) need = a.size() + b.size() - 1;
int nbase = 0;
while((1 << nbase) < need) nbase++;
FastFourierTransform::ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < a.size(); i++) {
fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
}
fft(fa, sz);
vector< C > fb(sz);
if(a == b) {
fb = fa;
} else {
for(int i = 0; i < b.size(); i++) {
fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
}
fft(fb, sz);
}
real ratio = 0.25 / sz;
C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
for(int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C a1 = (fa[i] + fa[j].conj());
C a2 = (fa[i] - fa[j].conj()) * r2;
C b1 = (fb[i] + fb[j].conj()) * r3;
C b2 = (fb[i] - fb[j].conj()) * r4;
if(i != j) {
C c1 = (fa[j] + fa[i].conj());
C c2 = (fa[j] - fa[i].conj()) * r2;
C d1 = (fb[j] + fb[i].conj()) * r3;
C d2 = (fb[j] - fb[i].conj()) * r4;
fa[i] = c1 * d1 + c2 * d2 * r5;
fb[i] = c1 * d2 + c2 * d1;
}
fa[j] = a1 * b1 + a2 * b2 * r5;
fb[j] = a1 * b2 + a2 * b1;
}
fft(fa, sz);
fft(fb, sz);
vector< T > ret(need);
for(int i = 0; i < need; i++) {
int64_t aa = llround(fa[i].x);
int64_t bb = llround(fb[i].x);
int64_t cc = llround(fa[i].y);
aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
ret[i] = aa + (bb << 15) + (cc << 30);
}
return ret;
}
};
/**
* @brief Formal Power Series(形式的冪級数)
*/
template< typename T >
struct FormalPowerSeries : vector< T > {
using vector< T >::vector;
using P = FormalPowerSeries;
using Conv = ArbitraryModConvolution< T >;
P pre(int deg) const {
return P(begin(*this), begin(*this) + min((int) this->size(), deg));
}
P rev(int deg = -1) const {
P ret(*this);
if(deg != -1) ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
void shrink() {
while(this->size() && this->back() == T(0)) this->pop_back();
}
P operator+(const P &r) const { return P(*this) += r; }
P operator+(const T &v) const { return P(*this) += v; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator-(const T &v) const { return P(*this) -= v; }
P operator*(const P &r) const { return P(*this) *= r; }
P operator*(const T &v) const { return P(*this) *= v; }
P operator/(const P &r) const { return P(*this) /= r; }
P operator%(const P &r) const { return P(*this) %= r; }
P &operator+=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] += r[i];
return *this;
}
P &operator-=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i];
return *this;
}
// https://judge.yosupo.jp/problem/convolution_mod
P &operator*=(const P &r) {
if(this->empty() || r.empty()) {
this->clear();
return *this;
}
auto ret = Conv::multiply(*this, r);
return *this = {begin(ret), end(ret)};
}
P &operator/=(const P &r) {
if(this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
}
P &operator%=(const P &r) {
return *this -= *this / r * r;
}
// https://judge.yosupo.jp/problem/division_of_polynomials
pair< P, P > div_mod(const P &r) {
P q = *this / r;
return make_pair(q, *this - q * r);
}
P operator-() const {
P ret(this->size());
for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
P &operator+=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
P &operator-=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] -= r;
return *this;
}
P &operator*=(const T &v) {
for(int i = 0; i < this->size(); i++) (*this)[i] *= v;
return *this;
}
P dot(P r) const {
P ret(min(this->size(), r.size()));
for(int i = 0; i < ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
P operator>>(int sz) const {
if(this->size() <= sz) return {};
P ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
P operator<<(int sz) const {
P ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
T operator()(T x) const {
T r = 0, w = 1;
for(auto &v : *this) {
r += w * v;
w *= x;
}
return r;
}
P diff() const {
const int n = (int) this->size();
P ret(max(0, n - 1));
for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
return ret;
}
P integral() const {
const int n = (int) this->size();
P ret(n + 1);
ret[0] = T(0);
for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
return ret;
}
// https://judge.yosupo.jp/problem/inv_of_formal_power_series
// F(0) must not be 0
P inv(int deg = -1) const {
assert(((*this)[0]) != T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
P ret({T(1) / (*this)[0]});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
}
return ret.pre(deg);
}
// https://judge.yosupo.jp/problem/log_of_formal_power_series
// F(0) must be 1
P log(int deg = -1) const {
assert((*this)[0] == T(1));
const int n = (int) this->size();
if(deg == -1) deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
// https://judge.yosupo.jp/problem/sqrt_of_formal_power_series
P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
if((*this)[0] == T(0)) {
for(int i = 1; i < n; i++) {
if((*this)[i] != T(0)) {
if(i & 1) return {};
if(deg - i / 2 <= 0) break;
auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);
if(ret.empty()) return {};
ret = ret << (i / 2);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return P(deg, 0);
}
auto sqr = T(get_sqrt((*this)[0]));
if(sqr * sqr != (*this)[0]) return {};
P ret{sqr};
T inv2 = T(1) / T(2);
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
}
return ret.pre(deg);
}
P sqrt(const function< T(T) > &get_sqrt, int deg = -1) const {
return sqrt(deg, get_sqrt);
}
// https://judge.yosupo.jp/problem/exp_of_formal_power_series
// F(0) must be 0
P exp(int deg = -1) const {
if(deg == -1) deg = this->size();
assert((*this)[0] == T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
P ret({T(1)});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
// https://judge.yosupo.jp/problem/pow_of_formal_power_series
P pow(int64_t k, int deg = -1) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
for(int i = 0; i < n; i++) {
if((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
if(i * k > deg) return P(deg, T(0));
ret = (ret << (i * k)).pre(deg);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return *this;
}
// https://yukicoder.me/problems/no/215
P mod_pow(int64_t k, P g) const {
P modinv = g.rev().inv();
auto get_div = [&](P base) {
if(base.size() < g.size()) {
base.clear();
return base;
}
int n = base.size() - g.size() + 1;
return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
};
P x(*this), ret{1};
while(k > 0) {
if(k & 1) {
ret *= x;
ret -= get_div(ret) * g;
ret.shrink();
}
x *= x;
x -= get_div(x) * g;
x.shrink();
k >>= 1;
}
return ret;
}
// https://judge.yosupo.jp/problem/polynomial_taylor_shift
P taylor_shift(T c) const {
int n = (int) this->size();
vector< T > fact(n), rfact(n);
fact[0] = rfact[0] = T(1);
for(int i = 1; i < n; i++) fact[i] = fact[i - 1] * T(i);
rfact[n - 1] = T(1) / fact[n - 1];
for(int i = n - 1; i > 1; i--) rfact[i - 1] = rfact[i] * T(i);
P p(*this);
for(int i = 0; i < n; i++) p[i] *= fact[i];
p = p.rev();
P bs(n, T(1));
for(int i = 1; i < n; i++) bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];
p = (p * bs).pre(n);
p = p.rev();
for(int i = 0; i < n; i++) p[i] *= rfact[i];
return p;
}
};
template< int mod >
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += mod - p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int) (1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const ModInt &p) {
return os << p.x;
}
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt< mod >(t);
return (is);
}
static int get_mod() { return mod; }
};
constexpr int mod = 1000000007;
using mint = ModInt< mod >;
template< typename Mint >
using FPS = FormalPowerSeries< Mint >;
using fps = FPS<mint>;
/**
* @brief Coeff of Rational Function
* @docs docs/coeff-of-rational-function.md
*/
template< template< typename > class FPS, typename Mint >
Mint coeff_of_rational_function(FPS< Mint > P, FPS< Mint > Q, int64_t k) {
// compute the coefficient [x^k] P/Q of rational power series
Mint ret = 0;
if(P.size() >= Q.size()) {
auto R = P / Q;
P -= R * Q;
P.shrink();
if(k < (int) R.size()) ret += R[k];
}
if(P.empty()) return ret;
P.resize((int) Q.size() - 1);
auto sub = [&](const FPS< Mint > &as, bool odd) {
FPS< Mint > bs((as.size() + !odd) / 2);
for(int i = odd; i < (int) as.size(); i += 2) bs[i >> 1] = as[i];
return bs;
};
while(k > 0) {
auto Q2(Q);
for(int i = 1; i < (int) Q2.size(); i += 2) Q2[i] = -Q2[i];
P = sub(P * Q2, k & 1);
Q = sub(Q * Q2, 0);
k >>= 1;
}
return ret + P[0];
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
ll n; in(n);
fps f = {1};
mint x = (mint)1 / (mint)6;
fps g = {1,-x,-x,-x,-x,-x,-x};
out(coeff_of_rational_function(f,g,n));
}