// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/directedmst/
#include "../../../src/graph/mst/cle/lib.hpp"
#include "../../../src/io/container/lib.hpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 n, m, s;
std::cin >> n >> m >> s;
vec<edge_t<u64>> arcs(m);
for (auto& [w, u, v] : arcs) std::cin >> u >> v >> w;
auto res = cle(n, s, arcs);
u64 cost = 0;
vecu ans(n, -1_u32);
ans[s] = s;
for (auto [w, u, v] : res) cost += w, ans[v] = u;
std::cout << cost << '\n'
<< ans << '\n';
return 0;
}
#line 1 "test/cpv/library-checker-graph/directedmst.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/directedmst/
#line 2 "src/graph/mst/cle/lib.hpp"
#line 2 "src/ds/dsu/basic/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/ds/dsu/basic/lib.hpp"
namespace tifa_libs {
template <bool union_by_size = true>
class dsu_basic {
veci p;
public:
CEXPE dsu_basic(u32 sz) NE : p(sz, -1) {}
CEXP i32 find(u32 x) NE { retif_((p[x] < 0), (i32)x, p[x] = find((u32)p[x])); }
ND CEXP u32 size() CNE { return (u32)p.size(); }
CEXP u32 size(u32 x) NE { return (u32)-p[(u32)find(x)]; }
CEXP bool same(u32 x, u32 y) NE { return find(x) == find(y); }
CEXP bool merge(u32 x, u32 y) NE {
if ((x = (u32)find(x)) == (y = (u32)find(y))) return false;
if CEXP (union_by_size)
if (p[x] > p[y]) swap(x, y);
p[x] += p[y], p[y] = (i32)x;
return true;
}
};
} // namespace tifa_libs
#line 2 "src/ds/heap/skew/lib.hpp"
#line 4 "src/ds/heap/skew/lib.hpp"
namespace tifa_libs {
template <class T, class C = std::less<T>>
class skew_heap {
static CEXP C comp_{};
struct TIFA {
T k, lz;
u32 l, r, idx;
TIFA() = default;
TIFA(cT_(T) key, u32 i = -1_u32)
NE : k(key), lz(0), l{-1_u32}, r{-1_u32}, idx{i} {}
};
ND CEXP bool comp(u32 idxl, u32 idxr) CNE { return comp_(weight(idxl), weight(idxr)); }
CEXP void pd(u32 idx) NE {
if (d[idx].lz == 0) return;
if (~d[idx].l) d[d[idx].l].lz += d[idx].lz;
if (~d[idx].r) d[d[idx].r].lz += d[idx].lz;
d[idx].k += d[idx].lz, d[idx].lz = 0;
}
public:
vec<TIFA> d;
CEXP T weight(u32 idx) CNE { return d[idx].k + d[idx].lz; }
CEXP u32 newheap(cT_(T) key, u32 idx = -1_u32) NE {
d.emplace_back(key, idx);
return u32(d.size() - 1);
}
CEXP u32 merge(u32 x, u32 y) NE {
if (!~x || !~y) return ~(x ^ y);
if (!comp(x, y)) swap(x, y);
pd(x), swap(d[x].l, d[x].r = merge(d[x].r, y));
return x;
}
CEXP void apply(u32 x, cT_(T) lz) NE { d[x].lz += lz, pd(x); }
CEXP u32 push(u32 x, cT_(T) key, u32 idx = -1_u32) NE { return merge(x, newheap(key, idx)); }
CEXP u32 pop(u32 x) NE {
pd(x);
return merge(d[x].l, d[x].r);
}
};
} // namespace tifa_libs
#line 5 "src/graph/mst/cle/lib.hpp"
namespace tifa_libs {
template <class T>
CEXP vec<edge_t<T>> cle(u32 n, u32 root, vec<edge_t<T>> CR arcs) NE {
skew_heap<T> heap;
dsu_basic uf(n);
vecu used(n, -1_u32), from(n), come(n, -1_u32);
vec<T> from_cost(n);
used[root] = root;
vecu par_e(arcs.size(), -1_u32), stem(n, -1_u32), idxs;
flt_ (u32, i, 0, (u32)arcs.size()) {
auto [w, u, v] = arcs[i];
come[v] = heap.push(come[v], w, i);
}
T costs = 0;
flt_ (u32, start, 0, n) {
if (~used[start]) continue;
u32 now = start, cyc = 0;
vecu chi_e;
while (!~used[now] || used[now] == start) {
used[now] = start;
auto& node = heap.d[come[now]];
if (!~come[now]) return {};
u32 src = (u32)uf.find(arcs[node.idx].u);
T cost = heap.weight(come[now]);
u32 idx = node.idx;
if (come[now] = heap.pop(come[now]); src == now) continue;
if (from[now] = src, from_cost[now] = cost; !~stem[now]) stem[now] = idx;
costs += cost, idxs.push_back(idx);
while (cyc) par_e[chi_e.back()] = idx, chi_e.pop_back(), --cyc;
if (chi_e.push_back(idx); used[src] == start) {
u32 p = now;
do {
if (~come[p]) heap.apply(come[p], -from_cost[p]);
if (p != now) {
uf.merge(p, now);
u32 newheap = heap.merge(come[now], come[p]);
come[now = (u32)uf.find(now)] = newheap;
}
p = (u32)uf.find(from[p]), ++cyc;
} while (p != now);
} else now = src;
}
}
vecu vis_e(arcs.size());
vec<edge_t<T>> res;
for (u32 _ = (u32)idxs.size(); _--;) {
cu32 i = idxs[_];
if (vis_e[i]) continue;
auto [w, u, v] = arcs[i];
res.push_back(arcs[i]);
u32 x = stem[v];
while (x != i) vis_e[x] = true, x = par_e[x];
}
return res;
}
} // namespace tifa_libs
#line 2 "src/io/container/lib.hpp"
#line 2 "src/util/traits/others/lib.hpp"
// clang-format off
#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/io/container/lib.hpp"
namespace tifa_libs {
auto& operator>>(tifa_libs::istream_c auto& is, tifa_libs::container_c auto& x) NE {
for (auto& i : x) is >> i;
return is;
}
auto& operator<<(tifa_libs::ostream_c auto& os, tifa_libs::container_c auto CR x) NE {
if (begin(x) == end(x)) [[unlikely]]
return os;
auto it = begin(x);
for (os << *it++; it != end(x); ++it) os << ' ' << *it;
return os;
}
} // namespace tifa_libs
#line 4 "test/cpv/library-checker-graph/directedmst.cpp"
using namespace tifa_libs;
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 n, m, s;
std::cin >> n >> m >> s;
vec<edge_t<u64>> arcs(m);
for (auto& [w, u, v] : arcs) std::cin >> u >> v >> w;
auto res = cle(n, s, arcs);
u64 cost = 0;
vecu ans(n, -1_u32);
ans[s] = s;
for (auto [w, u, v] : res) cost += w, ans[v] = u;
std::cout << cost << '\n'
<< ans << '\n';
return 0;
}
test/cpv/library-checker-graph/directedmst.cpp