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#define PROBLEM "https://judge.yosupo.jp/problem/directedmst" #include "../../template/template.hpp" #include "../../graph/mst/directed-mst.hpp" int main() { int n, m, r; cin >> n >> m >> r; Edges< int64_t > edges; for(int i = 0; i < m; ++i) { int a, b; int64_t w; cin >> a >> b >> w; edges.emplace_back(a, b, w); } auto res = directed_mst(n, r, edges); cout << res.cost << "\n"; vector< int > ans(n); ans[r] = r; for(auto &e : res.edges) { ans[e.to] = e.from; } cout << ans << "\n"; }
#line 1 "test/verify/yosupo-directedmst.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/directedmst" #line 1 "template/template.hpp" #include<bits/stdc++.h> using namespace std; using int64 = long long; const int mod = 1e9 + 7; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 >& p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { explicit FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } #line 4 "test/verify/yosupo-directedmst.test.cpp" #line 2 "graph/mst/directed-mst.hpp" #line 2 "graph/graph-template.hpp" /** * @brief Graph Template(グラフテンプレート) */ template< typename T = int > struct Edge { int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template< typename T = int > struct Graph { vector< vector< Edge< T > > > g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const { return g.size(); } void add_directed_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false) { for(int i = 0; i < M; i++) { int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if(weighted) cin >> c; if(directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } inline vector< Edge< T > > &operator[](const int &k) { return g[k]; } inline const vector< Edge< T > > &operator[](const int &k) const { return g[k]; } }; template< typename T = int > using Edges = vector< Edge< T > >; #line 1 "structure/heap/skew-heap.hpp" /** * @brief Skew-Heap */ template< typename T, bool isMin = true > struct SkewHeap { struct Node { T key, lazy; Node *l, *r; int idx; explicit Node(const T &key, int idx) : key(key), idx(idx), lazy(0), l(nullptr), r(nullptr) {} }; SkewHeap() = default; Node *alloc(const T &key, int idx = -1) { return new Node(key, idx); } Node *propagate(Node *t) { if(t && t->lazy != 0) { if(t->l) t->l->lazy += t->lazy; if(t->r) t->r->lazy += t->lazy; t->key += t->lazy; t->lazy = 0; } return t; } Node *meld(Node *x, Node *y) { propagate(x), propagate(y); if(!x || !y) return x ? x : y; if((x->key < y->key) ^ isMin) swap(x, y); x->r = meld(y, x->r); swap(x->l, x->r); return x; } Node *push(Node *t, const T &key, int idx = -1) { return meld(t, alloc(key, idx)); } Node *pop(Node *t) { assert(t != nullptr); return meld(t->l, t->r); } Node *add(Node *t, const T &lazy) { if(t) { t->lazy += lazy; propagate(t); } return t; } Node *make_root() { return nullptr; } }; #line 5 "graph/mst/directed-mst.hpp" /** * @brief Directed MST(最小有向全域木) * @docs docs/directed-mst.md */ template< typename T > struct MinimumSpanningTree { T cost; Edges< T > edges; }; template< typename T > MinimumSpanningTree< T > directed_mst(int V, int root, Edges< T > edges) { for(int i = 0; i < V; ++i) { if(i != root) edges.emplace_back(i, root, 0); } int x = 0; vector< int > par(2 * V, -1), vis(par), link(par); using Heap = SkewHeap< T, true >; using Node = typename Heap::Node; Heap heap; vector< Node * > ins(2 * V, heap.make_root()); for(int i = 0; i < (int) edges.size(); i++) { auto &e = edges[i]; ins[e.to] = heap.push(ins[e.to], e.cost, i); } vector< int > st; auto go = [&](int x) { x = edges[ins[x]->idx].from; while(link[x] != -1) { st.emplace_back(x); x = link[x]; } for(auto &p : st) { link[p] = x; } st.clear(); return x; }; for(int i = V; ins[x]; i++) { for(; vis[x] == -1; x = go(x)) vis[x] = 0; for(; x != i; x = go(x)) { auto w = ins[x]->key; auto v = heap.pop(ins[x]); v = heap.add(v, -w); ins[i] = heap.meld(ins[i], v); par[x] = i; link[x] = i; } for(; ins[x] && go(x) == x; ins[x] = heap.pop(ins[x])); } T cost = 0; Edges< T > ans; for(int i = root; i != -1; i = par[i]) { vis[i] = 1; } for(int i = x; i >= 0; i--) { if(vis[i] == 1) continue; cost += edges[ins[i]->idx].cost; ans.emplace_back(edges[ins[i]->idx]); for(int j = edges[ins[i]->idx].to; j != -1 && vis[j] == 0; j = par[j]) { vis[j] = 1; } } return {cost, ans}; } #line 6 "test/verify/yosupo-directedmst.test.cpp" int main() { int n, m, r; cin >> n >> m >> r; Edges< int64_t > edges; for(int i = 0; i < m; ++i) { int a, b; int64_t w; cin >> a >> b >> w; edges.emplace_back(a, b, w); } auto res = directed_mst(n, r, edges); cout << res.cost << "\n"; vector< int > ans(n); ans[r] = r; for(auto &e : res.edges) { ans[e.to] = e.from; } cout << ans << "\n"; }