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fps #92
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fps
shinchankosen 012a6a3
[auto-verifier] verify commit 4fb45552a6cada512926ce65f8f5fe25b9829cba
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fps, powとか
shinchankosen 250b8a2
Merge branch 'fps' of https://github.com/rainbou-kpr/library into fps
shinchankosen 93d0664
[auto-verifier] verify commit 250b8a2a728d755edbee787a3b61fcee3158c5f1
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partition
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Merge branch 'fps' of https://github.com/rainbou-kpr/library into fps
shinchankosen 191e717
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remove q, r
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Merge branch 'main' of https://github.com/rainbou-kpr/library into fps
shinchankosen 9763484
fps >>=
shinchankosen 884de15
Merge branch 'fps' of https://github.com/rainbou-kpr/library into fps
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,13 @@ | ||
| { | ||
| "files.associations": { | ||
| "array": "cpp", | ||
| "deque": "cpp", | ||
| "list": "cpp", | ||
| "string": "cpp", | ||
| "unordered_map": "cpp", | ||
| "vector": "cpp", | ||
| "string_view": "cpp", | ||
| "initializer_list": "cpp", | ||
| "valarray": "cpp" | ||
| } | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,225 @@ | ||
| #pragma once | ||
|
|
||
| #include <algorithm> | ||
| #include "number-theory.hpp" | ||
|
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||
| template <typename mint> struct FPS : std::vector<mint> { | ||
| using std::vector<mint>::vector; | ||
|
|
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| // constructor | ||
| FPS(const std::vector<mint>& r) : std::vector<mint>(r) {} | ||
|
|
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| // core operator | ||
| inline FPS pre(int siz) const { | ||
| return FPS(begin(*this), begin(*this) + std::min((int)this->size(), siz)); | ||
| } | ||
| inline FPS rev() const { | ||
| FPS res = *this; | ||
| reverse(begin(res), end(res)); | ||
| return res; | ||
| } | ||
| inline FPS& normalize() { | ||
| while (!this->empty() && this->back() == 0) this->pop_back(); | ||
| return *this; | ||
| } | ||
|
|
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| // basic operator | ||
| inline FPS operator - () const noexcept { | ||
| FPS res = (*this); | ||
| for (int i = 0; i < (int)res.size(); ++i) res[i] = -res[i]; | ||
| return res; | ||
| } | ||
| inline FPS operator + (const mint& v) const { return FPS(*this) += v; } | ||
| inline FPS operator + (const FPS& r) const { return FPS(*this) += r; } | ||
| inline FPS operator - (const mint& v) const { return FPS(*this) -= v; } | ||
| inline FPS operator - (const FPS& r) const { return FPS(*this) -= r; } | ||
| inline FPS operator * (const mint& v) const { return FPS(*this) *= v; } | ||
| inline FPS operator * (const FPS& r) const { return FPS(*this) *= r; } | ||
| inline FPS operator / (const mint& v) const { return FPS(*this) /= v; } | ||
| inline FPS operator << (int x) const { return FPS(*this) <<= x; } | ||
| inline FPS operator >> (int x) const { return FPS(*this) >>= x; } | ||
| inline FPS& operator += (const mint& v) { | ||
| if (this->empty()) this->resize(1); | ||
| (*this)[0] += v; | ||
| return *this; | ||
| } | ||
| inline FPS& operator += (const FPS& r) { | ||
| if (r.size() > this->size()) this->resize(r.size()); | ||
| for (int i = 0; i < (int)r.size(); ++i) (*this)[i] += r[i]; | ||
| return this->normalize(); | ||
| } | ||
| inline FPS& operator -= (const mint& v) { | ||
| if (this->empty()) this->resize(1); | ||
| (*this)[0] -= v; | ||
| return *this; | ||
| } | ||
| inline FPS& operator -= (const FPS& r) { | ||
| if (r.size() > this->size()) this->resize(r.size()); | ||
| for (int i = 0; i < (int)r.size(); ++i) (*this)[i] -= r[i]; | ||
| return this->normalize(); | ||
| } | ||
| inline FPS& operator *= (const mint& v) { | ||
| for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= v; | ||
| return *this; | ||
| } | ||
| inline FPS& operator *= (const FPS& r) { | ||
| return *this = convolution((*this), r); | ||
| } | ||
| inline FPS& operator /= (const mint& v) { | ||
| assert(v != 0); | ||
| mint iv = v.inv(); | ||
| for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= iv; | ||
| return *this; | ||
| } | ||
| inline FPS& operator <<= (int x) { | ||
| FPS res(x, 0); | ||
| res.insert(res.end(), begin(*this), end(*this)); | ||
| return *this = res; | ||
| } | ||
| inline FPS& operator >>= (int x) { | ||
| FPS res; | ||
| res.insert(res.end(), begin(*this) + x, end(*this)); | ||
| return *this = res; | ||
| } | ||
| inline mint eval(const mint& v){ | ||
| mint res = 0; | ||
| for (int i = (int)this->size()-1; i >= 0; --i) { | ||
| res *= v; | ||
| res += (*this)[i]; | ||
| } | ||
| return res; | ||
| } | ||
| inline friend FPS gcd(const FPS& f, const FPS& g) { | ||
| if (g.empty()) return f; | ||
| return gcd(g, f % g); | ||
| } | ||
|
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| // advanced operation | ||
| // df/dx | ||
| inline friend FPS diff(const FPS& f) { | ||
| int n = (int)f.size(); | ||
| FPS res(n-1); | ||
| for (int i = 1; i < n; ++i) res[i-1] = f[i] * i; | ||
| return res; | ||
| } | ||
|
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| // \int f dx | ||
| inline friend FPS intg(const FPS& f) { | ||
| int n = (int)f.size(); | ||
| FPS res(n+1, 0); | ||
| for (int i = 0; i < n; ++i) res[i+1] = f[i] / (i+1); | ||
| return res; | ||
| } | ||
|
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| // inv(f), f[0] must not be 0 | ||
| inline friend FPS inv(const FPS& f, int deg) { | ||
| assert(f[0] != 0); | ||
| if (deg < 0) deg = (int)f.size(); | ||
| FPS res({mint(1) / f[0]}); | ||
| for (int i = 1; i < deg; i <<= 1) { | ||
| res = (res + res - res * res * f.pre(i << 1)).pre(i << 1); | ||
| } | ||
| res.resize(deg); | ||
| return res; | ||
| } | ||
| inline friend FPS inv(const FPS& f) { | ||
| return inv(f, f.size()); | ||
| } | ||
|
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| // division, r must be normalized (r.back() must not be 0) | ||
| inline FPS& operator /= (const FPS& r) { | ||
| assert(!r.empty()); | ||
| assert(r.back() != 0); | ||
| this->normalize(); | ||
| if (this->size() < r.size()) { | ||
| this->clear(); | ||
| return *this; | ||
| } | ||
| int need = (int)this->size() - (int)r.size() + 1; | ||
| *this = ((*this).rev().pre(need) * inv(r.rev(), need)).pre(need).rev(); | ||
| return *this; | ||
| } | ||
| inline FPS& operator %= (const FPS &r) { | ||
| assert(!r.empty()); | ||
| assert(r.back() != 0); | ||
| this->normalize(); | ||
| FPS q = (*this) / r; | ||
| return *this -= q * r; | ||
| } | ||
| inline FPS operator / (const FPS& r) const { return FPS(*this) /= r; } | ||
| inline FPS operator % (const FPS& r) const { return FPS(*this) %= r; } | ||
|
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| // log(f) = \int f'/f dx, f[0] must be 1 | ||
| inline friend FPS log(const FPS& f, int deg) { | ||
| assert(f[0] == 1); | ||
| FPS res = intg(diff(f) * inv(f, deg)); | ||
| res.resize(deg); | ||
| return res; | ||
| } | ||
| inline friend FPS log(const FPS& f) { | ||
| return log(f, f.size()); | ||
| } | ||
|
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| // exp(f), f[0] must be 0 | ||
| inline friend FPS exp(const FPS& f, int deg) { | ||
| assert(f[0] == 0); | ||
| FPS res(1, 1); | ||
| for (int i = 1; i < deg; i <<= 1) { | ||
| res = res * (f.pre(i<<1) - log(res, i<<1) + 1).pre(i<<1); | ||
| } | ||
| res.resize(deg); | ||
| return res; | ||
| } | ||
| inline friend FPS exp(const FPS& f) { | ||
| return exp(f, f.size()); | ||
| } | ||
|
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| // pow(f) = exp(e * log f) | ||
| inline friend FPS pow(const FPS& f, long long e, int deg) { | ||
| if(e == 0) { | ||
| auto ret = FPS(deg, 0); | ||
| ret[0] = 1; | ||
| return ret; | ||
| } | ||
| long long i = 0; | ||
| while (i < (int)f.size() && f[i] == 0) ++i; | ||
| if (i == (int)f.size()) return FPS(deg, 0); | ||
| if ((i >= 1 and e >= deg) or i * e >= deg) return FPS(deg, 0); | ||
| mint k = f[i]; | ||
| FPS res = exp(log((f >> i) / k, deg) * e, deg) * k.pow(e) << (e * i); | ||
| res.resize(deg); | ||
| return res; | ||
| } | ||
| inline friend FPS pow(const FPS& f, long long e) { | ||
| return pow(f, e, f.size()); | ||
| } | ||
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| inline friend FPS taylor_shift(FPS f, mint a) { | ||
| int n = f.size(); | ||
| std::vector<mint> fac(n, 1), inv(n, 1), finv(n, 1); | ||
| int mod = mint::mod(); | ||
| for(int i = 2; i < n; i ++) { | ||
| fac[i] = fac[i - 1] * i; | ||
| inv[i] = -inv[mod % i] * (mod / i); | ||
| finv[i] = finv[i - 1] * inv[i]; | ||
| } | ||
| for(int i = 0; i < n; i ++) f[i] *= fac[i]; | ||
| std::reverse(f.begin(), f.end()); | ||
| FPS<mint> g(n, 1); | ||
| for(int i = 1; i < n; i ++) g[i] = g[i - 1] * a * inv[i]; | ||
| f = (f * g).pre(n); | ||
| std::reverse(f.begin(), f.end()); | ||
| for(int i = 0; i < n; i ++) f[i] *= finv[i]; | ||
| return f; | ||
| } | ||
| }; | ||
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| template <typename mint> FPS<mint> modpow(const FPS<mint> &f, long long n, const FPS<mint> &m) { | ||
| if (n == 0) return FPS<mint>(1, 1); | ||
| auto t = modpow(f, n / 2, m); | ||
| t = (t * t) % m; | ||
| if (n & 1) t = (t * f) % m; | ||
| auto q = t / m; | ||
| auto r = t % m; | ||
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|
||
| return t; | ||
| } | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,16 @@ | ||
| #define PROBLEM "https://judge.yosupo.jp/problem/exp_of_formal_power_series" | ||
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| #include "../cpp/fps.hpp" | ||
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| using mint = modint998244353; | ||
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| int main() { | ||
| long long n; | ||
| std::cin >> n; | ||
| FPS<mint> a(n); | ||
| for(auto& x : a) std::cin >> x; | ||
| auto f = exp(a); | ||
| for(auto e : f) std::cout << e << " "; | ||
| std::cout << std::endl; | ||
| return 0; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,16 @@ | ||
| #define PROBLEM "https://judge.yosupo.jp/problem/inv_of_formal_power_series" | ||
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| #include "../cpp/fps.hpp" | ||
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| using mint = modint998244353; | ||
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| int main() { | ||
| long long n; | ||
| std::cin >> n; | ||
| FPS<mint> a(n); | ||
| for(auto& x : a) std::cin >> x; | ||
| auto f = inv(a); | ||
| for(auto e : f) std::cout << e << " "; | ||
| std::cout << std::endl; | ||
| return 0; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,16 @@ | ||
| #define PROBLEM "https://judge.yosupo.jp/problem/log_of_formal_power_series" | ||
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| #include "../cpp/fps.hpp" | ||
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| using mint = modint998244353; | ||
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| int main() { | ||
| long long n; | ||
| std::cin >> n; | ||
| FPS<mint> a(n); | ||
| for(auto& x : a) std::cin >> x; | ||
| auto f = log(a); | ||
| for(auto e : f) std::cout << e << " "; | ||
| std::cout << std::endl; | ||
| return 0; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,19 @@ | ||
| #define PROBLEM "https://judge.yosupo.jp/problem/partition_function" | ||
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| #include "../cpp/fps.hpp" | ||
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| using mint = modint998244353; | ||
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| int main() { | ||
| long long n; | ||
| std::cin >> n; | ||
| FPS<mint> f(n + 1, 0); | ||
| for(int i = 1; i <= n; i ++) { | ||
| mint inv = mint(i).inv(); | ||
| for(int j = i; j <= n; j += i) f[j] += inv; | ||
| } | ||
| f = exp(f); | ||
| for(auto x : f) std::cout << x << " "; | ||
| std::cout << std::endl; | ||
| return 0; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,23 @@ | ||
| #define PROBLEM "https://judge.yosupo.jp/problem/partition_function" | ||
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| #include "../cpp/fps.hpp" | ||
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| using mint = modint998244353; | ||
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| int main() { | ||
| long long n; | ||
| std::cin >> n; | ||
| FPS<mint> f(n + 1, 0); | ||
| for(int i = 0;; i ++) { | ||
| if(i * (3 * i - 1) > n * 2) break; | ||
| f[i * (3 * i - 1) / 2] = (i % 2 ? -1 : 1); | ||
| } | ||
| for(int i = -1;; i --) { | ||
| if(i * (3 * i - 1) > n * 2) break; | ||
| f[i * (3 * i - 1) / 2] = (i % 2 ? -1 : 1); | ||
| } | ||
| f = inv(f); | ||
| for(auto x : f) std::cout << x << " "; | ||
| std::cout << std::endl; | ||
| return 0; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,16 @@ | ||
| #define PROBLEM "https://judge.yosupo.jp/problem/polynomial_taylor_shift" | ||
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| #include "../cpp/fps.hpp" | ||
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| using mint = modint998244353; | ||
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| int main() { | ||
| long long n, c; | ||
| std::cin >> n >> c; | ||
| FPS<mint> a(n); | ||
| for(auto& x : a) std::cin >> x; | ||
| auto f = taylor_shift(a, c); | ||
| for(auto e : f) std::cout << e << " "; | ||
| std::cout << std::endl; | ||
| return 0; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,16 @@ | ||
| #define PROBLEM "https://judge.yosupo.jp/problem/pow_of_formal_power_series" | ||
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| #include "../cpp/fps.hpp" | ||
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| using mint = modint998244353; | ||
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| int main() { | ||
| long long n, m; | ||
| std::cin >> n >> m; | ||
| FPS<mint> a(n); | ||
| for(auto& x : a) std::cin >> x; | ||
| auto f = pow(a, m); | ||
| for(auto e : f) std::cout << e << " "; | ||
| std::cout << std::endl; | ||
| return 0; | ||
| } |
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これ、drkenさんのライブラリでそうなってたのの引用かと思うんですが、
res * ...をしてからの.pre(i<<1)にしたら早そうで、(というか...の計算結果はi<<1項なので.pre(i<<1)の意味がなさそう)それじゃだめなんですかね？
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両方実行してみます
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nyaanさんの方にはexpがみあたらなかったです。https://ei1333.github.io/library/math/fps/formal-power-series.hpp
うしさんのを見るとけんちょんさんのと同じことをしているっぽいのでそのままにします。
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いえ、うしさんは
ではなく
です
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https://judge.yosupo.jp/submission/165847
https://judge.yosupo.jp/submission/165848
あんまりかわらない…
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(f.pre(i<<1) - log(res, i<<1) + 1)はすでにi<<1項なので(f.pre(i<<1) - log(res, i<<1) + 1).pre(i<<1)は意味がないres * (f.pre(i<<1) - log(res, i<<1) + 1).pre(i<<1)は掛け算の結果項の数が多くなってるがほしいのはmod.pre(i<<1)をつけるのが正しいという主張でした
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時間的には全部変わらないですね。どうしましょう？
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時間が変わらないのは意外ですが、任せます
（個人的には変なので変えたい）