#ifndef EMTHRM_MATH_POLYNOMIAL_HPP_
#define EMTHRM_MATH_POLYNOMIAL_HPP_
#include <algorithm>
#include <cassert>
#include <functional>
#include <initializer_list>
#include <iterator>
#include <numeric>
#include <utility>
#include <vector>
namespace emthrm {
template <typename T>
struct Polynomial {
std::vector<T> coef;
explicit Polynomial(const int deg = 0) : coef(deg + 1, 0) {}
explicit Polynomial(const std::vector<T>& coef) : coef(coef) {}
Polynomial(const std::initializer_list<T> init)
: coef(init.begin(), init.end()) {}
template <typename InputIter>
explicit Polynomial(const InputIter first, const InputIter last)
: coef(first, last) {}
inline const T& operator[](const int term) const { return coef[term]; }
inline T& operator[](const int term) { return coef[term]; }
using Mult = std::function<std::vector<T>(const std::vector<T>&,
const std::vector<T>&)>;
static void set_mult(const Mult mult) { get_mult() = mult; }
void resize(const int deg) { coef.resize(deg + 1, 0); }
void shrink() {
while (coef.size() > 1 && coef.back() == 0) coef.pop_back();
}
int degree() const { return std::ssize(coef) - 1; }
Polynomial& operator=(const std::vector<T>& coef_) {
coef = coef_;
return *this;
}
Polynomial& operator=(const Polynomial& x) = default;
Polynomial& operator+=(const Polynomial& x) {
const int deg_x = x.degree();
if (deg_x > degree()) resize(deg_x);
for (int i = 0; i <= deg_x; ++i) {
coef[i] += x[i];
}
return *this;
}
Polynomial& operator-=(const Polynomial& x) {
const int deg_x = x.degree();
if (deg_x > degree()) resize(deg_x);
for (int i = 0; i <= deg_x; ++i) {
coef[i] -= x[i];
}
return *this;
}
Polynomial& operator*=(const T x) {
for (T& e : coef) e *= x;
return *this;
}
Polynomial& operator*=(const Polynomial& x) {
return *this = get_mult()(coef, x.coef);
}
Polynomial& operator/=(const T x) {
assert(x != 0);
return *this *= static_cast<T>(1) / x;
}
std::pair<Polynomial, Polynomial> divide(Polynomial x) const {
x.shrink();
Polynomial rem = *this;
const int n = rem.degree(), m = x.degree(), deg = n - m;
if (deg < 0) return {Polynomial{0}, rem};
Polynomial quo(deg);
for (int i = 0; i <= deg; ++i) {
quo[deg - i] = rem[n - i] / x[m];
for (int j = 0; j <= m; ++j) {
rem[n - i - j] -= x[m - j] * quo[deg - i];
}
}
rem.resize(deg);
return {quo, rem};
}
Polynomial& operator/=(const Polynomial& x) {
return *this = divide(x).first;
}
Polynomial& operator%=(const Polynomial& x) {
return *this = divide(x).second;
}
Polynomial& operator<<=(const int n) {
coef.insert(coef.begin(), n, 0);
return *this;
}
bool operator==(Polynomial x) const {
x.shrink();
Polynomial y = *this;
y.shrink();
return x.coef == y.coef;
}
Polynomial operator+() const { return *this; }
Polynomial operator-() const {
Polynomial res = *this;
for (T& e : res.coef) e = -e;
return res;
}
Polynomial operator+(const Polynomial& x) const {
return Polynomial(*this) += x;
}
Polynomial operator-(const Polynomial& x) const {
return Polynomial(*this) -= x;
}
Polynomial operator*(const T x) const {
return Polynomial(*this) *= x;
}
Polynomial operator*(const Polynomial& x) const {
return Polynomial(*this) *= x;
}
Polynomial operator/(const T x) const { return Polynomial(*this) /= x; }
Polynomial operator/(const Polynomial& x) const {
return Polynomial(*this) /= x;
}
Polynomial operator%(const Polynomial& x) const {
return Polynomial(*this) %= x;
}
Polynomial operator<<(const int n) const { return Polynomial(*this) <<= n; }
T horner(const T x) const {
return std::accumulate(
coef.rbegin(), coef.rend(), static_cast<T>(0),
[x](const T l, const T r) -> T { return l * x + r; });
}
Polynomial differential() const {
const int deg = degree();
assert(deg >= 0);
Polynomial res(std::max(deg - 1, 0));
for (int i = 1; i <= deg; ++i) {
res[i - 1] = coef[i] * i;
}
return res;
}
Polynomial pow(int exponent) const {
Polynomial res{1}, base = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= base;
base *= base;
}
return res;
}
Polynomial translate(const T c) const {
const int n = coef.size();
std::vector<T> fact(n, 1), inv_fact(n, 1);
for (int i = 1; i < n; ++i) {
fact[i] = fact[i - 1] * i;
}
inv_fact[n - 1] = static_cast<T>(1) / fact[n - 1];
for (int i = n - 1; i > 0; --i) {
inv_fact[i - 1] = inv_fact[i] * i;
}
std::vector<T> g(n), ex(n);
for (int i = 0; i < n; ++i) {
g[i] = coef[i] * fact[i];
}
std::reverse(g.begin(), g.end());
T pow_c = 1;
for (int i = 0; i < n; ++i) {
ex[i] = pow_c * inv_fact[i];
pow_c *= c;
}
const std::vector<T> conv = get_mult()(g, ex);
Polynomial res(n - 1);
for (int i = 0; i < n; ++i) {
res[i] = conv[n - 1 - i] * inv_fact[i];
}
return res;
}
private:
static Mult& get_mult() {
static Mult mult = [](const std::vector<T>& a, const std::vector<T>& b)
-> std::vector<T> {
const int n = a.size(), m = b.size();
std::vector<T> res(n + m - 1, 0);
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
res[i + j] += a[i] * b[j];
}
}
return res;
};
return mult;
}
};
} // namespace emthrm
#endif // EMTHRM_MATH_POLYNOMIAL_HPP_
#line 1 "include/emthrm/math/polynomial.hpp"
#include <algorithm>
#include <cassert>
#include <functional>
#include <initializer_list>
#include <iterator>
#include <numeric>
#include <utility>
#include <vector>
namespace emthrm {
template <typename T>
struct Polynomial {
std::vector<T> coef;
explicit Polynomial(const int deg = 0) : coef(deg + 1, 0) {}
explicit Polynomial(const std::vector<T>& coef) : coef(coef) {}
Polynomial(const std::initializer_list<T> init)
: coef(init.begin(), init.end()) {}
template <typename InputIter>
explicit Polynomial(const InputIter first, const InputIter last)
: coef(first, last) {}
inline const T& operator[](const int term) const { return coef[term]; }
inline T& operator[](const int term) { return coef[term]; }
using Mult = std::function<std::vector<T>(const std::vector<T>&,
const std::vector<T>&)>;
static void set_mult(const Mult mult) { get_mult() = mult; }
void resize(const int deg) { coef.resize(deg + 1, 0); }
void shrink() {
while (coef.size() > 1 && coef.back() == 0) coef.pop_back();
}
int degree() const { return std::ssize(coef) - 1; }
Polynomial& operator=(const std::vector<T>& coef_) {
coef = coef_;
return *this;
}
Polynomial& operator=(const Polynomial& x) = default;
Polynomial& operator+=(const Polynomial& x) {
const int deg_x = x.degree();
if (deg_x > degree()) resize(deg_x);
for (int i = 0; i <= deg_x; ++i) {
coef[i] += x[i];
}
return *this;
}
Polynomial& operator-=(const Polynomial& x) {
const int deg_x = x.degree();
if (deg_x > degree()) resize(deg_x);
for (int i = 0; i <= deg_x; ++i) {
coef[i] -= x[i];
}
return *this;
}
Polynomial& operator*=(const T x) {
for (T& e : coef) e *= x;
return *this;
}
Polynomial& operator*=(const Polynomial& x) {
return *this = get_mult()(coef, x.coef);
}
Polynomial& operator/=(const T x) {
assert(x != 0);
return *this *= static_cast<T>(1) / x;
}
std::pair<Polynomial, Polynomial> divide(Polynomial x) const {
x.shrink();
Polynomial rem = *this;
const int n = rem.degree(), m = x.degree(), deg = n - m;
if (deg < 0) return {Polynomial{0}, rem};
Polynomial quo(deg);
for (int i = 0; i <= deg; ++i) {
quo[deg - i] = rem[n - i] / x[m];
for (int j = 0; j <= m; ++j) {
rem[n - i - j] -= x[m - j] * quo[deg - i];
}
}
rem.resize(deg);
return {quo, rem};
}
Polynomial& operator/=(const Polynomial& x) {
return *this = divide(x).first;
}
Polynomial& operator%=(const Polynomial& x) {
return *this = divide(x).second;
}
Polynomial& operator<<=(const int n) {
coef.insert(coef.begin(), n, 0);
return *this;
}
bool operator==(Polynomial x) const {
x.shrink();
Polynomial y = *this;
y.shrink();
return x.coef == y.coef;
}
Polynomial operator+() const { return *this; }
Polynomial operator-() const {
Polynomial res = *this;
for (T& e : res.coef) e = -e;
return res;
}
Polynomial operator+(const Polynomial& x) const {
return Polynomial(*this) += x;
}
Polynomial operator-(const Polynomial& x) const {
return Polynomial(*this) -= x;
}
Polynomial operator*(const T x) const {
return Polynomial(*this) *= x;
}
Polynomial operator*(const Polynomial& x) const {
return Polynomial(*this) *= x;
}
Polynomial operator/(const T x) const { return Polynomial(*this) /= x; }
Polynomial operator/(const Polynomial& x) const {
return Polynomial(*this) /= x;
}
Polynomial operator%(const Polynomial& x) const {
return Polynomial(*this) %= x;
}
Polynomial operator<<(const int n) const { return Polynomial(*this) <<= n; }
T horner(const T x) const {
return std::accumulate(
coef.rbegin(), coef.rend(), static_cast<T>(0),
[x](const T l, const T r) -> T { return l * x + r; });
}
Polynomial differential() const {
const int deg = degree();
assert(deg >= 0);
Polynomial res(std::max(deg - 1, 0));
for (int i = 1; i <= deg; ++i) {
res[i - 1] = coef[i] * i;
}
return res;
}
Polynomial pow(int exponent) const {
Polynomial res{1}, base = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= base;
base *= base;
}
return res;
}
Polynomial translate(const T c) const {
const int n = coef.size();
std::vector<T> fact(n, 1), inv_fact(n, 1);
for (int i = 1; i < n; ++i) {
fact[i] = fact[i - 1] * i;
}
inv_fact[n - 1] = static_cast<T>(1) / fact[n - 1];
for (int i = n - 1; i > 0; --i) {
inv_fact[i - 1] = inv_fact[i] * i;
}
std::vector<T> g(n), ex(n);
for (int i = 0; i < n; ++i) {
g[i] = coef[i] * fact[i];
}
std::reverse(g.begin(), g.end());
T pow_c = 1;
for (int i = 0; i < n; ++i) {
ex[i] = pow_c * inv_fact[i];
pow_c *= c;
}
const std::vector<T> conv = get_mult()(g, ex);
Polynomial res(n - 1);
for (int i = 0; i < n; ++i) {
res[i] = conv[n - 1 - i] * inv_fact[i];
}
return res;
}
private:
static Mult& get_mult() {
static Mult mult = [](const std::vector<T>& a, const std::vector<T>& b)
-> std::vector<T> {
const int n = a.size(), m = b.size();
std::vector<T> res(n + m - 1, 0);
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
res[i + j] += a[i] * b[j];
}
}
return res;
};
return mult;
}
};
} // namespace emthrm