Tifa's CP Library

:heavy_check_mark: bitmat (src/code/lalg/bitmat.hpp)

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#ifndef TIFALIBS_LALG_BITMAT
#define TIFALIBS_LALG_BITMAT

#include "mat.hpp"

namespace tifa_libs::math {

#define FOR1_(i, l, r) for (usz i = (l), i##ed__ = (r); i < i##ed__; ++i)
#define FOR2_(i, row_l, row_r, j, col_l, col_r) \
  FOR1_ (i, row_l, row_r)                       \
    FOR1_ (j, col_l, col_r)

template <usz R, usz C = R>
using bitmat = arr<std::bitset<C>, R>;

template <usz R, usz C>
CEXP matrix<bool> bitmat2mat(cT_(bitmat<R, C>) bmat) {
  matrix<bool> ret(R, C);
  ret.apply([&bmat](u32 i, u32 j, auto &b) { b = bmat[i][j]; });
  return ret;
}
template <usz R, usz C = R>
CEXP bitmat<R, C> mat2bitmat(cT_(matrix<bool>) mat) {
  const u32 r = mat.row(), c = mat.col();
  assert(r <= R && c <= C);
  bitmat<R, C> ret;
  FOR2_ (i, 0, r, j, 0, c) ret[i][j] = mat(i, j);
  return ret;
}
template <usz R, usz C>
std::istream &read_bitmat(std::istream &is, bitmat<R, C> &bmat, u32 r, u32 c) {
  assert(r <= R && c <= C);
  char ch;
  FOR2_ (i, 0, r, j, 0, c) is >> ch, bmat[i][j] = ch & 1;
  return is;
}
template <usz R, usz C>
std::istream &read_bitmat_trans(std::istream &is, bitmat<R, C> &bmat, u32 r, u32 c) {
  assert(r <= R && c <= C);
  char ch;
  FOR2_ (i, 0, r, j, 0, c) is >> ch, bmat[j][i] = ch & 1;
  return is;
}
template <usz R, usz C>
std::ostream &print_bitmat(std::ostream &os, bitmat<R, C> &bmat, u32 r, u32 c) {
  assert(r <= R && c <= C);
  FOR2_ (i, 0, r, j, 0, c)
    if (os << bmat[i][j]; j == c - 1 && i != r - 1) os << '\n';
  return os;
}
template <usz R, usz C>
std::istream &operator>>(std::istream &is, bitmat<R, C> &bmat) { return read_bitmat(is, bmat, R, C); }
template <usz R, usz C>
std::ostream &operator<<(std::ostream &os, bitmat<R, C> CR bmat) { return print_bitmat(os, bmat, R, C); }

#undef FOR1_
#undef FOR2_

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/lalg/bitmat.hpp"



#line 1 "src/code/lalg/mat.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/extc++.h>

#define CEXP constexpr
#define CEXPE constexpr explicit
#define TPN typename
#define CR const&

#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;
using f32 = float;
using f64 = double;
using f128 = long double;
using strn = std::string;
using strnv = std::string_view;

// clang-format off
template <class T, T v> using ic = std::integral_constant<T, v>;
template <class T> using ptt = std::pair<T, T>;
template <class T> struct edge_t {
  T w; u32 u, v;
  CEXP auto operator<=>(edge_t CR) const = default;
};
template <class T> struct pt3 {
  T _0, _1, _2;
  CEXP auto operator<=>(pt3 CR) const = default;
};
template <class T> struct pt4 {
  T _0, _1, _2, _3;
  CEXP auto operator<=>(pt4 CR) const = default;
};
template <class E> using itl = std::initializer_list<E>;
template <class T> using vec = std::vector<T>;
template <class T> using vvec = vec<vec<T>>;
template <class T> using v3ec = vec<vvec<T>>;
template <class T> using vecpt = vec<ptt<T>>;
template <class T> using vvecpt = vvec<ptt<T>>;
template <class T> using ptvec = ptt<vec<T>>;
template <class T> using ptvvec = ptt<vvec<T>>;

template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>;

template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
template <class T> using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;
// clang-format on

#define mk_(V, A, T) using V##A = V<T>;
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk_(spn, A, T) mk_(itl, A, T)
mk(b, bool) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64);
#undef mk
#undef mk_

using namespace std::literals;
CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }
CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }

using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) { eps_v<FP> = v; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };

namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
}  // namespace tifa_libs


#line 5 "src/code/lalg/mat.hpp"

namespace tifa_libs::math {

#define FOR1_(i, l, r) for (u32 i = (l), i##ed__ = (r); i < i##ed__; ++i)
#define FOR2_(i, row_l, row_r, j, col_l, col_r) \
  FOR1_ (i, row_l, row_r)                       \
    FOR1_ (j, col_l, col_r)

template <class T>
class matrix {
  vvec<T> d;

 public:
  using value_type = T;

  CEXP matrix(u32 row, u32 col, cT_(T) v = T{}) : d(row, vec<T>(col, v)) { assert(row > 0 && col > 0); }
  CEXPE matrix(cT_(vvec<T>) data) : d(data) { assert(data.size() > 0 && data[0].size() > 0); }

  CEXP u32 row() const { return (u32)d.size(); }
  CEXP u32 col() const { return (u32)d[0].size(); }
  CEXP vvec<T> CR data() const { return d; }
  CEXP vvec<T> &data() { return d; }
  CEXP TPN vec<T>::reference operator()(u32 r, u32 c) { return d[r][c]; }
  CEXP TPN vec<T>::const_reference operator()(u32 r, u32 c) const { return d[r][c]; }
  template <class F>
  CEXP void apply(F &&f) { apply_range(0, row(), 0, col(), std::forward<F>(f)); }
  template <class F>
  requires requires(F f, u32 i, u32 j, T &val) { f(i, j, val); }
  CEXP void apply_range(u32 row_l, u32 row_r, u32 col_l, u32 col_r, F &&f) {
    assert(row_l < row_r && row_r <= row() && col_l < col_r && col_r <= col());
    T val;
    FOR2_ (i, row_l, row_r, j, col_l, col_r) f(i, j, val = (*this)(i, j)), (*this)(i, j) = val;
  }

  friend std::istream &operator>>(std::istream &is, matrix &mat) {
    const u32 r_ = mat.row(), c_ = mat.col();
    FOR2_ (i, 0, r_, j, 0, c_) is >> mat(i, j);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, matrix CR mat) {
    const u32 r_ = mat.row(), c_ = mat.col();
    FOR2_ (i, 0, r_ - 1, j, 0, c_) os << mat(i, j) << " \n"[j + 1 == c_];
    os << mat(r_ - 1, 0);
    FOR1_ (j, 1, c_) os << ' ' << mat(r_ - 1, j);
    return os;
  }
  CEXP matrix submat(u32 row_l, u32 row_r, u32 col_l, u32 col_r) const {
    assert(row_l < row_r && row_r <= row() && col_l < col_r && col_r <= col());
    matrix ret(row_r - row_l, col_r - col_l);
    return ret.apply_range(0, ret.row(), 0, ret.col(), [this, row_l, col_l](u32 i, u32 j, T &v) { v = (*this)(i + row_l, j + col_l); }), ret;
  }
  CEXP void swap_row(u32 r1, u32 r2) {
    assert(r1 < row() && r2 < row());
    if (r1 == r2) return;
    swap(d[r1], d[r2]);
  }
  CEXP void swap_col(u32 c1, u32 c2) {
    assert(c1 < col() && c2 < col());
    if (c1 == c2) return;
    FOR1_ (i, 0, row()) swap((*this)(i, c1), (*this)(i, c2));
  }
  CEXP matrix operator-() const {
    if CEXP (std::is_same_v<T, bool>) return *this;
    else {
      matrix ret = *this;
      return ret.apply_range(0, row(), 0, col(), [](u32, u32, T &v) { v = -v; }), ret;
    }
  }
  friend CEXP matrix operator+(matrix l, cT_(T) v) { return l += v; }
  friend CEXP matrix operator+(cT_(T) v, matrix l) { return l += v; }
  CEXP matrix &operator+=(cT_(T) v) {
    if CEXP (std::is_same_v<T, bool>) apply_range(0, row(), 0, col(), [&v](u32, u32, auto &val) { val = val ^ v; });
    else apply_range(0, row(), 0, col(), [&v](u32, u32, T &val) { val += v; });
    return *this;
  }
  friend CEXP matrix operator-(matrix l, cT_(T) v) { return l -= v; }
  CEXP matrix &operator-=(cT_(T) v) {
    if CEXP (std::is_same_v<T, bool>) apply_range(0, row(), 0, col(), [&v](u32, u32, auto &val) { val = val ^ v; });
    else apply_range(0, row(), 0, col(), [&v](u32, u32, T &val) { val -= v; });
    return *this;
  }
  friend CEXP matrix operator*(matrix l, cT_(T) v) { return l *= v; }
  friend CEXP matrix operator*(cT_(T) v, matrix l) { return l *= v; }
  CEXP matrix &operator*=(cT_(T) v) {
    if CEXP (std::is_same_v<T, bool>) {
      if (!v)
        for (auto &i : d) i.clear(), i.resize(col());
      return *this;
    } else apply_range(0, row(), 0, col(), [&v](u32, u32, T &val) { val *= v; });
    return *this;
  }
  friend CEXP matrix operator+(matrix l, matrix CR r) { return l += r; }
  CEXP matrix &operator+=(matrix CR r) {
    assert(row() == r.row() && col() == r.col());
    if CEXP (std::is_same_v<T, bool>) apply_range(0, row(), 0, col(), [&r](u32 i, u32 j, auto &val) { val = val ^ r(i, j); });
    else apply_range(0, row(), 0, col(), [&r](u32 i, u32 j, T &val) { val += r(i, j); });
    return *this;
  }
  friend CEXP matrix operator-(matrix l, matrix CR r) { return l -= r; }
  CEXP matrix &operator-=(matrix CR r) {
    assert(row() == r.row() && col() == r.col());
    if CEXP (std::is_same_v<T, bool>) apply_range(0, row(), 0, col(), [&r](u32 i, u32 j, auto &val) { val = val ^ r(i, j); });
    else apply_range(0, row(), 0, col(), [&r](u32 i, u32 j, T &val) { val -= r(i, j); });
    return *this;
  }
  friend CEXP matrix operator*(matrix CR l, matrix CR r) {
    const u32 i_ = l.row(), j_ = l.col(), k_ = r.col();
    assert(j_ == r.row());
    matrix ret(i_, k_);
    FOR1_ (i, 0, i_)
      FOR1_ (j, 0, j_)
        FOR1_ (k, 0, k_)
          if CEXP (std::is_same_v<T, bool>) ret(i, k) = ret(i, k) ^ (l(i, j) && r(j, k));
          else ret(i, k) += l(i, j) * r(j, k);
    return ret;
  }
  CEXP matrix &operator*=(matrix CR r) { return *this = *this * r; }
  CEXP vec<T> lproj(spn<T> x) const {
    const u32 r_ = row(), c_ = col();
    assert(r_ == x.size());
    vec<T> ret(c_);
    flt_ (u32, i, 0, c_)
      if CEXP (std::is_same_v<T, bool>) ret[i] = std::transform_reduce(d[i].begin(), d[i].end(), x.begin(), false, std::bit_xor<bool>{}, std::bit_and<bool>{});
      else ret[i] = std::transform_reduce(d[i].begin(), d[i].end(), x.begin(), T{});
    return ret;
  }
  CEXP bool operator==(matrix CR r) const {
    if (row() != r.row() || col() != r.col()) return 0;
    FOR1_ (i, 0, row())
      if (d[i] != r.d[i]) return 0;
    return 1;
  }
};

#undef FOR1_
#undef FOR2_

}  // namespace tifa_libs::math


#line 5 "src/code/lalg/bitmat.hpp"

namespace tifa_libs::math {

#define FOR1_(i, l, r) for (usz i = (l), i##ed__ = (r); i < i##ed__; ++i)
#define FOR2_(i, row_l, row_r, j, col_l, col_r) \
  FOR1_ (i, row_l, row_r)                       \
    FOR1_ (j, col_l, col_r)

template <usz R, usz C = R>
using bitmat = arr<std::bitset<C>, R>;

template <usz R, usz C>
CEXP matrix<bool> bitmat2mat(cT_(bitmat<R, C>) bmat) {
  matrix<bool> ret(R, C);
  ret.apply([&bmat](u32 i, u32 j, auto &b) { b = bmat[i][j]; });
  return ret;
}
template <usz R, usz C = R>
CEXP bitmat<R, C> mat2bitmat(cT_(matrix<bool>) mat) {
  const u32 r = mat.row(), c = mat.col();
  assert(r <= R && c <= C);
  bitmat<R, C> ret;
  FOR2_ (i, 0, r, j, 0, c) ret[i][j] = mat(i, j);
  return ret;
}
template <usz R, usz C>
std::istream &read_bitmat(std::istream &is, bitmat<R, C> &bmat, u32 r, u32 c) {
  assert(r <= R && c <= C);
  char ch;
  FOR2_ (i, 0, r, j, 0, c) is >> ch, bmat[i][j] = ch & 1;
  return is;
}
template <usz R, usz C>
std::istream &read_bitmat_trans(std::istream &is, bitmat<R, C> &bmat, u32 r, u32 c) {
  assert(r <= R && c <= C);
  char ch;
  FOR2_ (i, 0, r, j, 0, c) is >> ch, bmat[j][i] = ch & 1;
  return is;
}
template <usz R, usz C>
std::ostream &print_bitmat(std::ostream &os, bitmat<R, C> &bmat, u32 r, u32 c) {
  assert(r <= R && c <= C);
  FOR2_ (i, 0, r, j, 0, c)
    if (os << bmat[i][j]; j == c - 1 && i != r - 1) os << '\n';
  return os;
}
template <usz R, usz C>
std::istream &operator>>(std::istream &is, bitmat<R, C> &bmat) { return read_bitmat(is, bmat, R, C); }
template <usz R, usz C>
std::ostream &operator<<(std::ostream &os, bitmat<R, C> CR bmat) { return print_bitmat(os, bmat, R, C); }

#undef FOR1_
#undef FOR2_

}  // namespace tifa_libs::math


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