fps/formal_power_series.hpp

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• Last update: 2024-07-01 23:39:10+09:00
• Include: #include "fps/formal_power_series.hpp"

Depends on

• template/const.hpp
• template/inout_old.hpp
• template/template.hpp
• template/utils.hpp

Required by

• fps/fps_arbitrary.hpp
• fps/fps_atcoder.hpp
• fps/fps_modint.hpp
• fps/fps_ntt.hpp
• fps/multipoint_evaluation.hpp
• fps/sample_point_shift.hpp

Verified with

• test/fps/Convolution1000000007.test.cpp
• test/fps/Inv_of_Formal_Power_Series.test.cpp
• test/fps/Multipoint_Evaluation_Geometric_Sequence.test.cpp
• test/fps/Shift_of_Sampling_Points_of_Polynomial.test.cpp
• test/fps/convolution.test.cpp
• test/tree/FrequencyTableofTreeDistance.test.cpp

Code

#pragma once

#include"../template/template.hpp"

namespace noya2{

template<typename T>
concept Field = requires (T a, T b){
    a + b; a - b; a / b; a * b;
    T(0); T(1);
};

template<class Info>
concept Fps_Info = requires {
    typename Info::value_type;
    requires Field<typename Info::value_type>;
    {Info::multiply(declval<vector<typename Info::value_type>>(),declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typename Info::value_type>>;
    {Info::inv(declval<vector<typename Info::value_type>>(),declval<int>())} -> convertible_to<vector<typename Info::value_type>>;
    {Info::integral(declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typename Info::value_type>>;
};

template<Fps_Info Info>
struct FormalPowerSeries : vector<typename Info::value_type> {
    using T = typename Info::value_type;
    using vector<T>::vector;
    using vector<T>::operator=;
    using FPS = FormalPowerSeries;
    FormalPowerSeries (const vector<T> &init_ = {}){ (*this) = init_; }
    void shrink(){ while (!(*this).empty() && (*this).back() == T(0)) (*this).pop_back(); }
    FPS &operator+=(const T &r){
        if ((*this).empty()) (*this).resize(1);
        (*this)[0] += r;
        return *this;
    }
    FPS &operator-=(const T &r){
        if ((*this).empty()) (*this).resize(1);
        (*this)[0] -= r;
        return *this;
    }
    FPS &operator*=(const T &r){
        for (auto &x : *this) x *= r;
        return *this;
    }
    FPS &operator/=(const T &r){
        (*this) *= T(1)/r;
        return *this;
    }
    FPS &operator<<=(const int &d){
        (*this).insert((*this).begin(),d,T(0));
        return *this;
    }
    FPS &operator>>=(const int &d){
        if ((int)(*this).size() <= d) (*this).clear();
        else (*this).erase((*this).begin(),(*this).begin()+d);
        return *this;
    }
    FPS &operator+=(const FPS &r){
        if ((*this).size() < r.size()) (*this).resize(r.size());
        for (int i = 0; i < (int)(r.size()); i++) (*this)[i] += r[i];
        return *this;
    }
    FPS &operator-=(const FPS &r){
        if ((*this).size() < r.size()) (*this).resize(r.size());
        for (int i = 0; i < (int)(r.size()); i++) (*this)[i] -= r[i];
        return *this;
    }
    FPS &operator*=(const FPS &r){
        if ((*this).empty() || r.empty()){
            (*this).clear();
            return *this;
        }
        (*this) = Info::multiply(*this,r);
        return *this;
    }
    FPS operator+(const T &r) const { return FPS(*this) += r; }
    FPS operator-(const T &r) const { return FPS(*this) -= r; }
    FPS operator*(const T &r) const { return FPS(*this) *= r; }
    FPS operator/(const T &r) const { return FPS(*this) /= r; }
    FPS operator<<(const int &d) const { return FPS(*this) <<= d; }
    FPS operator>>(const int &d) const { return FPS(*this) >>= d; }
    FPS operator+(const FPS &r) const { return FPS(*this) += r; }
    FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
    FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
    FPS operator+() const { return *this; }
    FPS operator-() const {
        FPS res(*this);
        for (auto &x : res) x = -x;
        return res;
    }
    T eval(const T &x) const {
        T res = T(0), w = T(1);
        for (auto &e : *this) res += e * w, w *= x;
        return res;
    }
    static FPS dot(const FPS &lhs, const FPS &rhs){
        FPS res(min(lhs.size(),rhs.size()));
        for (int i = 0; i < (int)res.size(); i++) res[i] = lhs[i] * rhs[i];
        return res;
    }
    FPS pre(int siz) const {
        FPS ret((*this).begin(), (*this).begin() + min((int)this->size(), siz));
        if ((int)ret.size() < siz) ret.resize(siz);
        return ret;
    }
    FPS rev() const {
        FPS ret(*this);
        reverse(ret.begin(), ret.end());
        return ret;
    }
    FPS diff() const {
        const int n = (int)this->size();
        FPS ret(max(0, n - 1));
        T one(1), coeff(1);
        for (int i = 1; i < n; i++) {
            ret[i - 1] = (*this)[i] * coeff;
            coeff += one;
        }
        return ret;
    }
    FPS integral() const {
        FPS ret = Info::integral(*this);
        return ret;
    }
    FPS inv(int d = -1) const {
        FPS ret = Info::inv(*this,d);
        return ret;
    }
    FPS exp(int d = -1) const {
        const int n = (*this).size();
        if (d == -1) d = n;
        FPS f = {T(1)+(*this)[0],(*this)[1]}, res = {1,(n > 1 ? (*this)[1] : 0)};
        for (int sz = 2; sz < d; sz <<= 1){
            f.insert(f.end(),(*this).begin()+min(n,sz),(*this).begin()+min(n,sz*2));
            if ((int)f.size() < sz*2) f.resize(sz*2);
            res = res * (f - res.log(2*sz));
            res.resize(sz*2);
        }
        res.resize(d);
        return res;
    }
    FPS log(int d = -1) const {
        assert(!(*this).empty() && (*this)[0] == T(1));
        if (d == -1) d = (*this).size();
        return (this->diff() * this->inv(d)).pre(d - 1).integral();
    }
};

} // namespace noya2

#line 2 "fps/formal_power_series.hpp"

#line 2 "template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "template/inout_old.hpp"
namespace noya2 {

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...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "template/utils.hpp"

#line 6 "template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 4 "fps/formal_power_series.hpp"

namespace noya2{

template<typename T>
concept Field = requires (T a, T b){
    a + b; a - b; a / b; a * b;
    T(0); T(1);
};

template<class Info>
concept Fps_Info = requires {
    typename Info::value_type;
    requires Field<typename Info::value_type>;
    {Info::multiply(declval<vector<typename Info::value_type>>(),declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typename Info::value_type>>;
    {Info::inv(declval<vector<typename Info::value_type>>(),declval<int>())} -> convertible_to<vector<typename Info::value_type>>;
    {Info::integral(declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typename Info::value_type>>;
};

template<Fps_Info Info>
struct FormalPowerSeries : vector<typename Info::value_type> {
    using T = typename Info::value_type;
    using vector<T>::vector;
    using vector<T>::operator=;
    using FPS = FormalPowerSeries;
    FormalPowerSeries (const vector<T> &init_ = {}){ (*this) = init_; }
    void shrink(){ while (!(*this).empty() && (*this).back() == T(0)) (*this).pop_back(); }
    FPS &operator+=(const T &r){
        if ((*this).empty()) (*this).resize(1);
        (*this)[0] += r;
        return *this;
    }
    FPS &operator-=(const T &r){
        if ((*this).empty()) (*this).resize(1);
        (*this)[0] -= r;
        return *this;
    }
    FPS &operator*=(const T &r){
        for (auto &x : *this) x *= r;
        return *this;
    }
    FPS &operator/=(const T &r){
        (*this) *= T(1)/r;
        return *this;
    }
    FPS &operator<<=(const int &d){
        (*this).insert((*this).begin(),d,T(0));
        return *this;
    }
    FPS &operator>>=(const int &d){
        if ((int)(*this).size() <= d) (*this).clear();
        else (*this).erase((*this).begin(),(*this).begin()+d);
        return *this;
    }
    FPS &operator+=(const FPS &r){
        if ((*this).size() < r.size()) (*this).resize(r.size());
        for (int i = 0; i < (int)(r.size()); i++) (*this)[i] += r[i];
        return *this;
    }
    FPS &operator-=(const FPS &r){
        if ((*this).size() < r.size()) (*this).resize(r.size());
        for (int i = 0; i < (int)(r.size()); i++) (*this)[i] -= r[i];
        return *this;
    }
    FPS &operator*=(const FPS &r){
        if ((*this).empty() || r.empty()){
            (*this).clear();
            return *this;
        }
        (*this) = Info::multiply(*this,r);
        return *this;
    }
    FPS operator+(const T &r) const { return FPS(*this) += r; }
    FPS operator-(const T &r) const { return FPS(*this) -= r; }
    FPS operator*(const T &r) const { return FPS(*this) *= r; }
    FPS operator/(const T &r) const { return FPS(*this) /= r; }
    FPS operator<<(const int &d) const { return FPS(*this) <<= d; }
    FPS operator>>(const int &d) const { return FPS(*this) >>= d; }
    FPS operator+(const FPS &r) const { return FPS(*this) += r; }
    FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
    FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
    FPS operator+() const { return *this; }
    FPS operator-() const {
        FPS res(*this);
        for (auto &x : res) x = -x;
        return res;
    }
    T eval(const T &x) const {
        T res = T(0), w = T(1);
        for (auto &e : *this) res += e * w, w *= x;
        return res;
    }
    static FPS dot(const FPS &lhs, const FPS &rhs){
        FPS res(min(lhs.size(),rhs.size()));
        for (int i = 0; i < (int)res.size(); i++) res[i] = lhs[i] * rhs[i];
        return res;
    }
    FPS pre(int siz) const {
        FPS ret((*this).begin(), (*this).begin() + min((int)this->size(), siz));
        if ((int)ret.size() < siz) ret.resize(siz);
        return ret;
    }
    FPS rev() const {
        FPS ret(*this);
        reverse(ret.begin(), ret.end());
        return ret;
    }
    FPS diff() const {
        const int n = (int)this->size();
        FPS ret(max(0, n - 1));
        T one(1), coeff(1);
        for (int i = 1; i < n; i++) {
            ret[i - 1] = (*this)[i] * coeff;
            coeff += one;
        }
        return ret;
    }
    FPS integral() const {
        FPS ret = Info::integral(*this);
        return ret;
    }
    FPS inv(int d = -1) const {
        FPS ret = Info::inv(*this,d);
        return ret;
    }
    FPS exp(int d = -1) const {
        const int n = (*this).size();
        if (d == -1) d = n;
        FPS f = {T(1)+(*this)[0],(*this)[1]}, res = {1,(n > 1 ? (*this)[1] : 0)};
        for (int sz = 2; sz < d; sz <<= 1){
            f.insert(f.end(),(*this).begin()+min(n,sz),(*this).begin()+min(n,sz*2));
            if ((int)f.size() < sz*2) f.resize(sz*2);
            res = res * (f - res.log(2*sz));
            res.resize(sz*2);
        }
        res.resize(d);
        return res;
    }
    FPS log(int d = -1) const {
        assert(!(*this).empty() && (*this)[0] == T(1));
        if (d == -1) d = (*this).size();
        return (this->diff() * this->inv(d)).pre(d - 1).integral();
    }
};

} // namespace noya2

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