#pragma once
#include "../../ds/mat/lib.hpp"
#include "../merge_lr/lib.hpp"
namespace tifa_libs {
template <class T, class Is0, class Ge>
requires requires(Is0 is0, Ge ge, T t, matrix<T> A, bool clear_u) {
{ is0(t) } -> std::same_as<bool>;
{ ge(A, clear_u) } -> std::same_as<i32>;
}
CEXP auto leqs_solver(matrix<T> CR A, matrix<T> CR b, Is0&& is0, Ge&& ge) NE {
cu32 r_ = A.row(), c_ = A.col();
assert(b.col() == 1 && r_ == b.row());
matrix<T> Ab = merge_lr_mat(A, b);
cu32 rk = (u32)abs(ge(Ab, false));
std::optional<matrix<T>> ret;
if (rk > c_) return ret;
if (!is0(Ab(rk - 1, c_))) {
bool f = true;
flt_ (u32, i, 0, c_)
if (!is0(Ab(rk - 1, i))) {
f = false;
break;
}
if (f) return ret;
}
flt_ (u32, i, rk, r_)
if (!is0(Ab(i, c_))) return ret;
vecb used(c_, false);
vecu idxs;
for (u32 i = 0, _ = 0; i < r_; ++i) {
while (i + _ < c_ && is0(Ab(i, i + _))) ++_;
if (i + _ >= c_) break;
used[i + _] = true, idxs.push_back(i + _);
}
matrix<T> sol(c_ - rk + 1, c_);
{
for (u32 y = rk - 1; ~y; --y) {
cu32 f = idxs[y];
sol(0, f) = Ab(y, c_);
flt_ (u32, x, f + 1, c_) sol(0, f) -= Ab(y, x) * sol(0, x);
sol(0, f) /= Ab(y, f);
}
}
for (u32 s = 0, _ = 0; s < c_; ++s) {
if (used[s]) continue;
cu32 rid = ++_;
sol(rid, s) = 1;
for (u32 y = rk - 1; ~y; --y) {
u32 f = idxs[y];
flt_ (u32, x, f + 1, c_) sol(rid, f) -= Ab(y, x) * sol(rid, x);
sol(rid, f) /= Ab(y, f);
}
}
ret.emplace(sol.trans());
return ret;
}
} // namespace tifa_libs
#line 2 "src/lalg/mat/leqs_solver/lib.hpp"
#line 2 "src/lalg/ds/mat/lib.hpp"
#line 2 "src/util/traits/others/lib.hpp"
// clang-format off
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
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) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<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 T, usz N> using carr = std::array<const 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 U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, 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) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 4 "src/util/traits/others/lib.hpp"
namespace tifa_libs {
//! only for template without non-type argument
template <class, template <class...> class> CEXP bool specialized_from_v = false;
template <template <class...> class T, class... Args> CEXP bool specialized_from_v<T<Args...>, T> = true;
static_assert(specialized_from_v<vecu, std::vector>);
template <class T> concept container_c = common_range<T> && !std::is_array_v<std::remove_cvref_t<T>> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;
template <class T> concept istream_c = std::derived_from<T, std::istream> || std::derived_from<T, std::wistream> || requires(T is) { is.peek(); };
template <class T> concept ostream_c = std::derived_from<T, std::ostream> || std::derived_from<T, std::wostream> || requires(T os) { os.flush(); };
} // namespace tifa_libs
// clang-format on
#line 4 "src/lalg/ds/mat/lib.hpp"
namespace tifa_libs {
#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 {
vec<T> d;
u32 r_, c_;
bool tr_;
public:
using val_t = T;
CEXP matrix(u32 row, u32 col, cT_(T) v = T{}) NE : d(row* col, v), r_{row}, c_{col}, tr_{false} { assert(row > 0 && col > 0); }
CEXP matrix(u32 row, u32 col, spn<T> data) NE : d(data), r_{row}, c_{col}, tr_{false} { assert(row > 0 && col > 0 && d.size() == row * col); }
CEXP matrix(vvec<T> CR data) NE : d(data.size() * data[0].size()), r_((u32)data.size()), c_((u32)data[0].size()), tr_{false} {
assert(data.size() > 0 && data[0].size() > 0);
FOR1_ (i, 1, r_) assert((u32)data[i].size() == c_);
FOR2_ (i, 0, r_, j, 0, c_) (*this)(i, j) = data[i][j];
}
ND CEXP u32 row() CNE { retif_((tr_), c_, r_); }
ND CEXP u32 col() CNE { retif_((tr_), r_, c_); }
ND CEXP vec<T> CR data() CNE { return d; }
CEXP vec<T>& data() NE { return d; }
CEXP TPN vec<T>::reference operator()(u32 r, u32 c) NE { retif_((tr_), d[c * c_ + r], d[r * c_ + c]); }
CEXP TPN vec<T>::const_reference operator()(u32 r, u32 c) CNE { retif_((tr_), d[c * c_ + r], d[r * c_ + c]); }
CEXP matrix& trans() NE {
tr_ = !tr_;
return *this;
}
template <class F>
CEXP void apply(F&& f) NE { 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) NE {
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 auto& operator>>(istream_c auto& is, matrix& mat) NE {
cu32 r_ = mat.row(), c_ = mat.col();
FOR2_ (i, 0, r_, j, 0, c_) is >> mat(i, j);
return is;
}
friend auto& operator<<(ostream_c auto& os, matrix CR mat) NE {
cu32 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;
}
ND CEXP matrix submat(u32 row_l, u32 row_r, u32 col_l, u32 col_r) CNE {
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);
FOR2_ (i, row_l, row_r, j, col_l, col_r) ret(i - row_l, j - col_l) = (*this)(i, j);
return ret;
}
CEXP void swap_row(u32 r1, u32 r2) NE {
if (assert(r1 < row() && r2 < row()); r1 == r2) return;
FOR1_ (j, 0, col()) swap((*this)(r1, j), (*this)(r2, j));
}
CEXP void swap_col(u32 c1, u32 c2) NE {
if (assert(c1 < col() && c2 < col()); c1 == c2) return;
FOR1_ (i, 0, row()) swap((*this)(i, c1), (*this)(i, c2));
}
CEXP matrix operator-() CNE {
if CEXP (std::is_same_v<T, bool>) return *this;
else {
matrix ret = *this;
ret.apply([](u32, u32, T& v) NE { v = -v; });
return ret;
}
}
friend CEXP matrix operator+(matrix l, cT_(T) v) NE { return l += v; }
friend CEXP matrix operator+(cT_(T) v, matrix l) NE { return l += v; }
CEXP matrix& operator+=(cT_(T) v) NE {
if CEXP (std::is_same_v<T, bool>) apply([&v](u32, u32, auto& val) NE { val = val ^ v; });
else apply([&v](u32, u32, T& val) NE { val += v; });
return *this;
}
friend CEXP matrix operator-(matrix l, cT_(T) v) NE { return l -= v; }
CEXP matrix& operator-=(cT_(T) v) NE {
if CEXP (std::is_same_v<T, bool>) apply([&v](u32, u32, auto& val) NE { val = val ^ v; });
else apply([&v](u32, u32, T& val) NE { val -= v; });
return *this;
}
friend CEXP matrix operator*(matrix l, cT_(T) v) NE { return l *= v; }
friend CEXP matrix operator*(cT_(T) v, matrix l) NE { return l *= v; }
CEXP matrix& operator*=(cT_(T) v) NE {
if CEXP (std::is_same_v<T, bool>) {
if (!v) fill(begin(d), end(d), false);
return *this;
} else apply([&v](u32, u32, T& val) NE { val *= v; });
return *this;
}
friend CEXP matrix operator+(matrix l, matrix CR r) NE { return l += r; }
CEXP matrix& operator+=(matrix CR r) NE {
assert(row() == r.row() && col() == r.col());
if CEXP (std::is_same_v<T, bool>) apply([&r](u32 i, u32 j, auto& val) NE { val = val ^ r(i, j); });
else apply([&r](u32 i, u32 j, T& val) NE { val += r(i, j); });
return *this;
}
friend CEXP matrix operator-(matrix l, matrix CR r) NE { return l -= r; }
CEXP matrix& operator-=(matrix CR r) NE {
assert(row() == r.row() && col() == r.col());
if CEXP (std::is_same_v<T, bool>) apply([&r](u32 i, u32 j, auto& val) NE { val = val ^ r(i, j); });
else apply([&r](u32 i, u32 j, T& val) NE { val -= r(i, j); });
return *this;
}
friend CEXP matrix operator*(matrix CR l, matrix CR r) NE {
cu32 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) NE { return *this = *this * r; }
ND CEXP vec<T> lproj(spn<T> x) CNE {
cu32 r_ = row(), c_ = col();
assert(r_ == x.size());
vec<T> ret(c_);
FOR1_ (j, 0, c_)
if CEXP (std::is_same_v<T, bool>) {
bool v = false;
FOR1_ (i, 0, r_) v = v ^ ((*this)(i, j) && x[i]);
ret[j] = v;
} else {
T v{};
FOR1_ (i, 0, r_) v += (*this)(i, j) * x[i];
ret[j] = v;
}
return ret;
}
CEXP bool operator==(matrix CR r) CNE {
if (row() != r.row() || col() != r.col()) return false;
FOR2_ (i, 0, row(), j, 0, col())
if ((*this)(i, j) != r(i, j)) return false;
return true;
}
};
#undef FOR1_
#undef FOR2_
} // namespace tifa_libs
#line 2 "src/lalg/mat/merge_lr/lib.hpp"
#line 4 "src/lalg/mat/merge_lr/lib.hpp"
namespace tifa_libs {
// [l] [r] -> [l r]
template <class T>
CEXP matrix<T> merge_lr_mat(matrix<T> CR l, matrix<T> CR r) NE {
cu32 r_ = l.row();
assert(r_ == r.row());
cu32 lc_ = l.col(), rc_ = r.col(), c_ = lc_ + rc_;
matrix<T> ret(r_, c_);
ret.apply_range(0, r_, 0, lc_, [&l](u32 i, u32 j, T& val) NE { val = l(i, j); });
ret.apply_range(0, r_, lc_, c_, [lc_, &r](u32 i, u32 j, T& val) NE { val = r(i, j - lc_); });
return ret;
}
} // namespace tifa_libs
#line 5 "src/lalg/mat/leqs_solver/lib.hpp"
namespace tifa_libs {
template <class T, class Is0, class Ge>
requires requires(Is0 is0, Ge ge, T t, matrix<T> A, bool clear_u) {
{ is0(t) } -> std::same_as<bool>;
{ ge(A, clear_u) } -> std::same_as<i32>;
}
CEXP auto leqs_solver(matrix<T> CR A, matrix<T> CR b, Is0&& is0, Ge&& ge) NE {
cu32 r_ = A.row(), c_ = A.col();
assert(b.col() == 1 && r_ == b.row());
matrix<T> Ab = merge_lr_mat(A, b);
cu32 rk = (u32)abs(ge(Ab, false));
std::optional<matrix<T>> ret;
if (rk > c_) return ret;
if (!is0(Ab(rk - 1, c_))) {
bool f = true;
flt_ (u32, i, 0, c_)
if (!is0(Ab(rk - 1, i))) {
f = false;
break;
}
if (f) return ret;
}
flt_ (u32, i, rk, r_)
if (!is0(Ab(i, c_))) return ret;
vecb used(c_, false);
vecu idxs;
for (u32 i = 0, _ = 0; i < r_; ++i) {
while (i + _ < c_ && is0(Ab(i, i + _))) ++_;
if (i + _ >= c_) break;
used[i + _] = true, idxs.push_back(i + _);
}
matrix<T> sol(c_ - rk + 1, c_);
{
for (u32 y = rk - 1; ~y; --y) {
cu32 f = idxs[y];
sol(0, f) = Ab(y, c_);
flt_ (u32, x, f + 1, c_) sol(0, f) -= Ab(y, x) * sol(0, x);
sol(0, f) /= Ab(y, f);
}
}
for (u32 s = 0, _ = 0; s < c_; ++s) {
if (used[s]) continue;
cu32 rid = ++_;
sol(rid, s) = 1;
for (u32 y = rk - 1; ~y; --y) {
u32 f = idxs[y];
flt_ (u32, x, f + 1, c_) sol(rid, f) -= Ab(y, x) * sol(rid, x);
sol(rid, f) /= Ab(y, f);
}
}
ret.emplace(sol.trans());
return ret;
}
} // namespace tifa_libs
src/lalg/mat/leqs_solver/lib.hpp