C++ Library for Competitive Programming
#include "emthrm/math/convolution/kronecker_power-vector_multiplication.hpp"
$G \in K^{d \times d},\ \boldsymbol{v} \in K^{d^n}$ に対して $G^{\otimes n} \boldsymbol{v}$ を求める。ここで
\[A \otimes B \mathrel{:=} \begin{pmatrix} a_{11} B & \cdots & a_{1n} B \\ \vdots & \ddots & \vdots \\ a_{m1} B & \cdots & a_{mn} B \end{pmatrix} \quad (A \in K^{m \times n})\]はクロネッカー積である。
$O(N D^{N + 1})$
名前 | 戻り値 |
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template <typename T> std::vector<T> kronecker_power_vector_multiplication(const Matrix<T>& g, std::vector<T> v);
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$G^{\otimes n} \boldsymbol{v}$ |
https://atcoder.jp/contests/abc288/submissions/39117221
#ifndef EMTHRM_MATH_CONVOLUTION_KRONECKER_POWER_VECTOR_MULTIPLICATION_HPP_
#define EMTHRM_MATH_CONVOLUTION_KRONECKER_POWER_VECTOR_MULTIPLICATION_HPP_
#include <cassert>
#include <cmath>
#include <vector>
#include "emthrm/math/matrix/matrix.hpp"
namespace emthrm {
template <typename T>
std::vector<T> kronecker_power_vector_multiplication(const Matrix<T>& g,
std::vector<T> v) {
const int d = g.nrow(), n = v.size();
assert(std::llround(std::pow(d, std::log(n) / std::log(d))) == n);
Matrix<T> tmp(d, 1);
for (int block = 1; block < n; block *= d) {
for (int i = 0; i < n; i += block * d) {
for (int j = 0; j < block; ++j) {
for (int x = 0; x < d; ++x) {
tmp[x][0] = v[i + j + block * x];
}
tmp = g * tmp;
for (int x = 0; x < d; ++x) {
v[i + j + block * x] = tmp[x][0];
}
}
}
}
return v;
}
} // namespace emthrm
#endif // EMTHRM_MATH_CONVOLUTION_KRONECKER_POWER_VECTOR_MULTIPLICATION_HPP_
#line 1 "include/emthrm/math/convolution/kronecker_power-vector_multiplication.hpp"
#include <cassert>
#include <cmath>
#include <vector>
#line 1 "include/emthrm/math/matrix/matrix.hpp"
#line 5 "include/emthrm/math/matrix/matrix.hpp"
namespace emthrm {
template <typename T>
struct Matrix {
explicit Matrix(const int m, const int n, const T def = 0)
: data(m, std::vector<T>(n, def)) {}
int nrow() const { return data.size(); }
int ncol() const { return data.empty() ? 0 : data.front().size(); }
Matrix pow(long long exponent) const {
const int n = nrow();
Matrix<T> res(n, n, 0), tmp = *this;
for (int i = 0; i < n; ++i) {
res[i][i] = 1;
}
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
inline const std::vector<T>& operator[](const int i) const { return data[i]; }
inline std::vector<T>& operator[](const int i) { return data[i]; }
Matrix& operator=(const Matrix& x) = default;
Matrix& operator+=(const Matrix& x) {
const int m = nrow(), n = ncol();
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
data[i][j] += x[i][j];
}
}
return *this;
}
Matrix& operator-=(const Matrix& x) {
const int m = nrow(), n = ncol();
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
data[i][j] -= x[i][j];
}
}
return *this;
}
Matrix& operator*=(const Matrix& x) {
const int m = nrow(), l = ncol(), n = x.ncol();
std::vector<std::vector<T>> res(m, std::vector<T>(n, 0));
for (int i = 0; i < m; ++i) {
for (int k = 0; k < l; ++k) {
for (int j = 0; j < n; ++j) {
res[i][j] += data[i][k] * x[k][j];
}
}
}
data.swap(res);
return *this;
}
Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; }
Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; }
Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; }
private:
std::vector<std::vector<T>> data;
};
} // namespace emthrm
#line 9 "include/emthrm/math/convolution/kronecker_power-vector_multiplication.hpp"
namespace emthrm {
template <typename T>
std::vector<T> kronecker_power_vector_multiplication(const Matrix<T>& g,
std::vector<T> v) {
const int d = g.nrow(), n = v.size();
assert(std::llround(std::pow(d, std::log(n) / std::log(d))) == n);
Matrix<T> tmp(d, 1);
for (int block = 1; block < n; block *= d) {
for (int i = 0; i < n; i += block * d) {
for (int j = 0; j < block; ++j) {
for (int x = 0; x < d; ++x) {
tmp[x][0] = v[i + j + block * x];
}
tmp = g * tmp;
for (int x = 0; x < d; ++x) {
v[i + j + block * x] = tmp[x][0];
}
}
}
}
return v;
}
} // namespace emthrm