ベクトル (src/LinearAlgebra/Vector.hpp)

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• Last update: 2024-08-28 13:54:11+09:00
• Include: #include "src/LinearAlgebra/Vector.hpp"

Vector<K> クラス

$K$ 上の $n$ 次元数ベクトル空間 $K^n$ のベクトルを表すクラス．

K=bool は特殊化して有限体 $\mathbb{F}_2$ の意味で用いる(定数倍高速化)

コンストラクタ	概要
Vector()	次元数 $0$ (invalid)
Vector(n)	次元数 $n$
Vector(n,a)	次元数 $n$, 全成分が $a$
Vector({...})	initializer_list

メンバ関数	概要	計算量
operator[](i)	ランダムアクセス．第 $i$ 成分 $v_i$ を返す．	$O(1)$
size()	ベクトルの次元数 $n$ を返す．	$O(1)$

演算子オーバーロード	概要	計算量
operator-(v)	$-\boldsymbol{v}$ を返す	$O(n)$
operator+(v,u)	$\boldsymbol{v}+\boldsymbol{u}$ を返す	$O(n)$
operator-(v,u)	$\boldsymbol{v}-\boldsymbol{u}$ を返す	$O(n)$
operator*(v,a)	スカラー倍 $a\boldsymbol{v}$ を返す	$O(n)$
operator*(a,v)	スカラー倍 $a\boldsymbol{v}$ を返す	$O(n)$
operator==(v,u)	$\boldsymbol{v}=\boldsymbol{u}$ なら true	$O(n)$
operator!=(a,v)	$\boldsymbol{v}\ne\boldsymbol{u}$ なら true	$O(n)$
operator+=(v,u)	$\boldsymbol{v}\leftarrow\boldsymbol{v}+\boldsymbol{u}$	$O(n)$
operator-=(v,u)	$\boldsymbol{v}\leftarrow\boldsymbol{v}-\boldsymbol{u}$	$O(n)$
operator*=(v,a)	$\boldsymbol{v}\leftarrow a\boldsymbol{v}$	$O(n)$
bool(v)	次元数が 1 以上なら true	$O(1)$

その他関数	概要	計算量
dot(u,v)	内積 $\boldsymbol{u}^{\top}\boldsymbol{v}$ を返す	$O(n)$

Required by

• 行列の特性多項式 他 (src/LinearAlgebra/characteristic_polynomial.hpp)
• LU分解 (src/LinearAlgebra/LU_Decomposition.hpp)
• 行列 (src/LinearAlgebra/Matrix.hpp)
• 行列の最小多項式 (src/LinearAlgebra/MinimalPolynomial.hpp)

Verified with

• test/alone/mat.unit_test.cpp
• test/alone/vec.unit_test.cpp
• test/aoj/1328.test.cpp
• test/aoj/2397.MinPoly.test.cpp
• test/aoj/2397.SparseMat.test.cpp
• test/aoj/2397.test.cpp
• test/aoj/2530.test.cpp
• test/aoj/2624.test.cpp
• test/atcoder/abc236_g.test.cpp
• test/atcoder/abc323_g.test.cpp
• test/atcoder/abc336_g.test.cpp
• test/atcoder/agc051_d.test.cpp
• test/loj/3350.test.cpp
• test/sample_test/abc009_4.test.cpp
• test/sample_test/abc276_ex.test.cpp
• test/sample_test/arc027_4.test.cpp
• test/sample_test/ddcc2019_final_d.test.cpp
• test/sample_test/ddcc2020_final_b.test.cpp
• test/sample_test/yahoo_procon2019_final_d.test.cpp
• test/sample_test/yukicoder_1421.Nimber.test.cpp
• test/sample_test/yukicoder_1421.test.cpp
• test/yosupo/characteristic_polynomial.test.cpp
• test/yosupo/counting_eulerian_circuits.test.cpp
• test/yosupo/counting_spanning_tree_directed.test.cpp
• test/yosupo/counting_spanning_tree_undirected.test.cpp
• test/yosupo/inverse_matrix.test.cpp
• test/yosupo/inverse_matrix_mod_2.test.cpp
• test/yosupo/linear_equations.test.cpp
• test/yosupo/matrix_det.test.cpp
• test/yosupo/matrix_det_arbitrary_mod.test.cpp
• test/yosupo/matrix_det_mod_2.test.cpp
• test/yosupo/matrix_product.test.cpp
• test/yosupo/matrix_product_mod_2.test.cpp
• test/yosupo/matrix_rank.test.cpp
• test/yosupo/matrix_rank_mod_2.test.cpp
• test/yosupo/sparse_matrix_det.test.cpp
• test/yosupo/unionfind_with_potential_non_commutative_group.test.cpp
• test/yosupo/unionfind_with_potential_non_commutative_group.UFPU.test.cpp
• test/yukicoder/1303.test.cpp
• test/yukicoder/1340.test.cpp
• test/yukicoder/1750.MinPoly.test.cpp
• test/yukicoder/1750.SparseMat.test.cpp
• test/yukicoder/1750.test.cpp
• test/yukicoder/184.test.cpp
• test/yukicoder/1907.test.cpp
• test/yukicoder/310.test.cpp
• test/yukicoder/426.test.cpp
• test/yukicoder/650.HLD.test.cpp
• test/yukicoder/650.LCT.test.cpp
• test/yukicoder/803.test.cpp
• test/yukicoder/950.test.cpp

Code

#pragma once
#include <cstdint>
#include <iostream>
#include <valarray>
namespace _la_internal {
using namespace std;
template <class R> struct Vector {
 valarray<R> dat;
 Vector()= default;
 Vector(size_t n): dat(n) {}
 Vector(size_t n, const R &v): dat(v, n) {}
 Vector(const initializer_list<R> &v): dat(v) {}
 R &operator[](int i) { return dat[i]; }
 const R &operator[](int i) const { return dat[i]; }
 bool operator==(const Vector &r) const {
  if (dat.size() != r.dat.size()) return false;
  for (int i= dat.size(); i--;)
   if (dat[i] != r.dat[i]) return false;
  return true;
 }
 bool operator!=(const Vector &r) const { return !(*this == r); }
 explicit operator bool() const { return dat.size(); }
 Vector operator-() const { return Vector(dat.size())-= *this; }
 Vector &operator+=(const Vector &r) { return dat+= r.dat, *this; }
 Vector &operator-=(const Vector &r) { return dat-= r.dat, *this; }
 Vector &operator*=(const R &r) { return dat*= r, *this; }
 Vector operator+(const Vector &r) const { return Vector(*this)+= r; }
 Vector operator-(const Vector &r) const { return Vector(*this)-= r; }
 Vector operator*(const R &r) const { return Vector(*this)*= r; }
 size_t size() const { return dat.size(); }
 friend R dot(const Vector<R> &a, const Vector<R> &b) { return assert(a.size() == b.size()), (a.dat * b.dat).sum(); }
};
using u128= __uint128_t;
using u64= uint64_t;
using u8= uint8_t;
class Ref {
 u128 *ref;
 u8 i;
public:
 Ref(u128 *ref, u8 i): ref(ref), i(i) {}
 Ref &operator=(const Ref &r) { return *this= bool(r); }
 Ref &operator=(bool b) { return *ref&= ~(u128(1) << i), *ref|= u128(b) << i, *this; }
 Ref &operator|=(bool b) { return *ref|= u128(b) << i, *this; }
 Ref &operator&=(bool b) { return *ref&= ~(u128(!b) << i), *this; }
 Ref &operator^=(bool b) { return *ref^= u128(b) << i, *this; }
 operator bool() const { return (*ref >> i) & 1; }
};
template <> class Vector<bool> {
 size_t n;
public:
 valarray<u128> dat;
 Vector(): n(0) {}
 Vector(size_t n): n(n), dat((n + 127) >> 7) {}
 Vector(size_t n, bool b): n(n), dat(-u128(b), (n + 127) >> 7) {
  if (int k= n & 127; k) dat[dat.size() - 1]&= (u128(1) << k) - 1;
 }
 Vector(const initializer_list<bool> &v): n(v.size()), dat((n + 127) >> 7) {
  int i= 0;
  for (bool b: v) dat[i >> 7]|= u128(b) << (i & 127), ++i;
 }
 Ref operator[](int i) { return {begin(dat) + (i >> 7), u8(i & 127)}; }
 bool operator[](int i) const { return (dat[i >> 7] >> (i & 127)) & 1; }
 bool operator==(const Vector &r) const {
  if (dat.size() != r.dat.size()) return false;
  for (int i= dat.size(); i--;)
   if (dat[i] != r.dat[i]) return false;
  return true;
 }
 bool operator!=(const Vector &r) const { return !(*this == r); }
 explicit operator bool() const { return n; }
 Vector operator-() const { return Vector(*this); }
 Vector &operator+=(const Vector &r) { return dat^= r.dat, *this; }
 Vector &operator-=(const Vector &r) { return dat^= r.dat, *this; }
 Vector &operator*=(bool b) { return dat*= b, *this; }
 Vector operator+(const Vector &r) const { return Vector(*this)+= r; }
 Vector operator-(const Vector &r) const { return Vector(*this)-= r; }
 Vector operator*(bool b) const { return Vector(*this)*= b; }
 size_t size() const { return n; }
 friend bool dot(const Vector<bool> &a, const Vector<bool> &b) {
  assert(a.size() == b.size());
  u128 v= 0;
  for (int i= a.dat.size(); i--;) v^= a.dat[i] & b.dat[i];
  return __builtin_parityll(v >> 64) ^ __builtin_parityll(u64(v));
 }
};
template <class R> Vector<R> operator*(const R &r, const Vector<R> &v) { return v * r; }
template <class R> ostream &operator<<(ostream &os, const Vector<R> &v) {
 os << '[';
 for (int _= 0, __= v.size(); _ < __; ++_) os << (_ ? ", " : "") << v[_];
 return os << ']';
}
}
using _la_internal::Vector;

#line 2 "src/LinearAlgebra/Vector.hpp"
#include <cstdint>
#include <iostream>
#include <valarray>
namespace _la_internal {
using namespace std;
template <class R> struct Vector {
 valarray<R> dat;
 Vector()= default;
 Vector(size_t n): dat(n) {}
 Vector(size_t n, const R &v): dat(v, n) {}
 Vector(const initializer_list<R> &v): dat(v) {}
 R &operator[](int i) { return dat[i]; }
 const R &operator[](int i) const { return dat[i]; }
 bool operator==(const Vector &r) const {
  if (dat.size() != r.dat.size()) return false;
  for (int i= dat.size(); i--;)
   if (dat[i] != r.dat[i]) return false;
  return true;
 }
 bool operator!=(const Vector &r) const { return !(*this == r); }
 explicit operator bool() const { return dat.size(); }
 Vector operator-() const { return Vector(dat.size())-= *this; }
 Vector &operator+=(const Vector &r) { return dat+= r.dat, *this; }
 Vector &operator-=(const Vector &r) { return dat-= r.dat, *this; }
 Vector &operator*=(const R &r) { return dat*= r, *this; }
 Vector operator+(const Vector &r) const { return Vector(*this)+= r; }
 Vector operator-(const Vector &r) const { return Vector(*this)-= r; }
 Vector operator*(const R &r) const { return Vector(*this)*= r; }
 size_t size() const { return dat.size(); }
 friend R dot(const Vector<R> &a, const Vector<R> &b) { return assert(a.size() == b.size()), (a.dat * b.dat).sum(); }
};
using u128= __uint128_t;
using u64= uint64_t;
using u8= uint8_t;
class Ref {
 u128 *ref;
 u8 i;
public:
 Ref(u128 *ref, u8 i): ref(ref), i(i) {}
 Ref &operator=(const Ref &r) { return *this= bool(r); }
 Ref &operator=(bool b) { return *ref&= ~(u128(1) << i), *ref|= u128(b) << i, *this; }
 Ref &operator|=(bool b) { return *ref|= u128(b) << i, *this; }
 Ref &operator&=(bool b) { return *ref&= ~(u128(!b) << i), *this; }
 Ref &operator^=(bool b) { return *ref^= u128(b) << i, *this; }
 operator bool() const { return (*ref >> i) & 1; }
};
template <> class Vector<bool> {
 size_t n;
public:
 valarray<u128> dat;
 Vector(): n(0) {}
 Vector(size_t n): n(n), dat((n + 127) >> 7) {}
 Vector(size_t n, bool b): n(n), dat(-u128(b), (n + 127) >> 7) {
  if (int k= n & 127; k) dat[dat.size() - 1]&= (u128(1) << k) - 1;
 }
 Vector(const initializer_list<bool> &v): n(v.size()), dat((n + 127) >> 7) {
  int i= 0;
  for (bool b: v) dat[i >> 7]|= u128(b) << (i & 127), ++i;
 }
 Ref operator[](int i) { return {begin(dat) + (i >> 7), u8(i & 127)}; }
 bool operator[](int i) const { return (dat[i >> 7] >> (i & 127)) & 1; }
 bool operator==(const Vector &r) const {
  if (dat.size() != r.dat.size()) return false;
  for (int i= dat.size(); i--;)
   if (dat[i] != r.dat[i]) return false;
  return true;
 }
 bool operator!=(const Vector &r) const { return !(*this == r); }
 explicit operator bool() const { return n; }
 Vector operator-() const { return Vector(*this); }
 Vector &operator+=(const Vector &r) { return dat^= r.dat, *this; }
 Vector &operator-=(const Vector &r) { return dat^= r.dat, *this; }
 Vector &operator*=(bool b) { return dat*= b, *this; }
 Vector operator+(const Vector &r) const { return Vector(*this)+= r; }
 Vector operator-(const Vector &r) const { return Vector(*this)-= r; }
 Vector operator*(bool b) const { return Vector(*this)*= b; }
 size_t size() const { return n; }
 friend bool dot(const Vector<bool> &a, const Vector<bool> &b) {
  assert(a.size() == b.size());
  u128 v= 0;
  for (int i= a.dat.size(); i--;) v^= a.dat[i] & b.dat[i];
  return __builtin_parityll(v >> 64) ^ __builtin_parityll(u64(v));
 }
};
template <class R> Vector<R> operator*(const R &r, const Vector<R> &v) { return v * r; }
template <class R> ostream &operator<<(ostream &os, const Vector<R> &v) {
 os << '[';
 for (int _= 0, __= v.size(); _ < __; ++_) os << (_ ? ", " : "") << v[_];
 return os << ']';
}
}
using _la_internal::Vector;

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