// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/two_sat/
#include "../../../src/graph/sat2/lib.hpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
strn s;
std::cin >> s >> s;
u32 n, m;
std::cin >> n >> m;
i32 u, v, w;
sat2 s2(n);
flt_ (u32, i, 0, m) {
std::cin >> u >> v >> w;
bool fu = u > 0, fv = v > 0;
s2.add((u32)abs(u) - 1, fu, (u32)abs(v) - 1, fv);
}
auto ans = s2.solve();
if (!ans) {
std::cout << "s UNSATISFIABLE\n";
return 0;
}
std::cout << "s SATISFIABLE\nv";
for (i32 i = 0; (u32)i < n; ++i) std::cout << ' ' << (ans.value()[(u32)i] ? (i + 1) : -(i + 1));
std::cout << " 0\n";
return 0;
}
#line 1 "test/cpv/library-checker-other/two_sat.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/two_sat/
#line 2 "src/graph/sat2/lib.hpp"
#line 2 "src/graph/scc/tarjan/lib.hpp"
#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/graph/scc/tarjan/lib.hpp"
namespace tifa_libs {
struct tarjan {
u32 id;
vecu scc_id, dfn, low;
vvecu belongs;
CEXP void build(cT_(vvecu) g) NE {
u32 cnt = 0, n = u32(g.size());
vecu s;
vecb ins(n);
id = 0, dfn = low = scc_id = vecu(n, n);
auto dfs = [&](auto&& dfs, u32 u) NE -> void {
for (dfn[u] = low[u] = cnt++, s.push_back(u), ins[u] = true; auto v : g[u])
if (dfn[v] == n) dfs(dfs, v), low[u] = min(low[u], low[v]);
else if (ins[v]) low[u] = min(low[u], dfn[v]);
if (low[u] == dfn[u]) {
belongs.emplace_back();
do {
cu32 v = s.back();
s.pop_back();
ins[v] = false, belongs[scc_id[v] = id].push_back(v);
if (v == u) return void(++id);
} while (true);
}
};
flt_ (u32, i, 0, n)
if (dfn[i] == n) dfs(dfs, i);
}
};
} // namespace tifa_libs
#line 4 "src/graph/sat2/lib.hpp"
namespace tifa_libs {
class sat2 {
cu32 n;
// vecptu e;
tarjan tj;
vvecu g;
public:
CEXPE sat2(u32 n) NE : n{n}, g(n * 2 + 1) {}
// $(c_x = v_x) \lor (c_y = v_y)$
CEXP void add(u32 x, bool vx, u32 y, bool vy) NE {
x = x * 2 + vx, y = y * 2 + vy;
// e.emplace_back(x ^ 1, y), e.emplace_back(y ^ 1, x);
g[x ^ 1].push_back(y), g[y ^ 1].push_back(x);
}
// @return a, a_i == 1 if c_i is true else a_i == 0
CEXP auto solve() NE {
tj.build(g);
std::optional ans{vecb(n)};
flt_ (u32, i, 0, n)
if (tj.scc_id[i * 2] == tj.scc_id[i * 2 + 1]) {
ans = std::nullopt;
return ans;
} else ans.value()[i] = tj.scc_id[i * 2] > tj.scc_id[i * 2 + 1];
return ans;
}
};
} // namespace tifa_libs
#line 3 "test/cpv/library-checker-other/two_sat.cpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
strn s;
std::cin >> s >> s;
u32 n, m;
std::cin >> n >> m;
i32 u, v, w;
sat2 s2(n);
flt_ (u32, i, 0, m) {
std::cin >> u >> v >> w;
bool fu = u > 0, fv = v > 0;
s2.add((u32)abs(u) - 1, fu, (u32)abs(v) - 1, fv);
}
auto ans = s2.solve();
if (!ans) {
std::cout << "s UNSATISFIABLE\n";
return 0;
}
std::cout << "s SATISFIABLE\nv";
for (i32 i = 0; (u32)i < n; ++i) std::cout << ' ' << (ans.value()[(u32)i] ? (i + 1) : -(i + 1));
std::cout << " 0\n";
return 0;
}
test/cpv/library-checker-other/two_sat.cpp