#line 1 "template/template.hpp" #include #if __has_include() #include #endif using namespace std; using int64 = long long; 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 ostream& operator<<(ostream& os, const pair& p) { os << p.first << " " << p.second; return os; } template istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (size_t i = 0; i < v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template istream& operator>>(istream& is, vector& v) { for (T& in : v) is >> in; return is; } template bool chmax(T1& a, T2 b) { return a < b && (a = b, true); } template bool chmin(T1& a, T2 b) { return a > b && (a = b, true); } template vector make_v(size_t a) { return vector(a); } template auto make_v(size_t a, Ts... ts) { return vector(ts...))>(a, make_v(ts...)); } template enable_if_t == 0> fill_v(T& t, const V& v) { t = v; } template enable_if_t != 0> fill_v(T& t, const V& v) { for (auto& e : t) fill_v(e, v); } template struct FixPoint : F { explicit FixPoint(F&& f) : F(std::forward(f)) {} template decltype(auto) operator()(Args&&... args) const { return F::operator()(*this, std::forward(args)...); } }; template decltype(auto) MFP(F&& f) { return FixPoint{std::forward(f)}; } #line 2 "graph/flow/push-relabel.hpp" #include #include #include #include #include class Stack { private: const int N, H; std::vector node; public: Stack(const int N, const int H) : N(N), H(H), node(N + H) { clear(); } inline bool empty(const int h) const { return node[N + h] == N + h; } inline int top(const int h) const { return node[N + h]; } inline void pop(const int h) { node[N + h] = node[node[N + h]]; } inline void push(const int h, const int u) { node[u] = node[N + h], node[N + h] = u; } inline void clear() { std::iota(node.begin() + N, node.end(), N); } }; class List { public: struct node { int prev, next; }; const int N, H; std::vector dat; List(const int N, const int H) : N(N), H(H), dat(N + H) { clear(); } inline bool empty(const int h) const { return (dat[N + h].next == N + h); } inline bool more_one(const int h) const { return dat[N + h].prev != dat[N + h].next; } inline void insert(const int h, const int u) { dat[u].prev = dat[N + h].prev, dat[u].next = N + h; dat[dat[N + h].prev].next = u, dat[N + h].prev = u; } inline void erase(const int u) { dat[dat[u].prev].next = dat[u].next, dat[dat[u].next].prev = dat[u].prev; } inline void clear() { for (int i = N; i < N + H; ++i) dat[i].prev = dat[i].next = i; } }; template struct PushRelabel { struct edge { int to; flow_t cap; int rev; bool isrev; int idx; }; int V, height, relabels; std::vector ex; std::vector potential, cur_edge; List all_ver; Stack act_ver; std::vector > graph; PushRelabel(int V) : V(V), height(-1), relabels(0), ex(V, flow_t(0)), potential(V, 0), cur_edge(V), all_ver(V, V), act_ver(V, V), graph(V) {} void add_edge(int from, int to, flow_t cap, int idx = -1) { graph[from].emplace_back( (edge){to, cap, (int)graph[to].size(), false, idx}); graph[to].emplace_back( (edge){from, 0, (int)graph[from].size() - 1, true, idx}); } int calc_active(int t) { height = -1; for (int i = 0; i < V; i++) { if (potential[i] < V) { cur_edge[i] = 0; height = std::max(height, potential[i]); all_ver.insert(potential[i], i); if (ex[i] > 0 && i != t) act_ver.push(potential[i], i); } else { potential[i] = V + 1; } } return height; } void bfs(int t) { for (int i = 0; i < V; i++) { potential[i] = std::max(potential[i], V); } potential[t] = 0; std::queue que; que.emplace(t); while (!que.empty()) { int p = que.front(); que.pop(); for (auto& e : graph[p]) { if (potential[e.to] == V && graph[e.to][e.rev].cap > 0) { potential[e.to] = potential[p] + 1; que.emplace(e.to); } } } } int init(int s, int t) { potential[s] = V + 1; bfs(t); for (auto& e : graph[s]) { if (potential[e.to] < V) { graph[e.to][e.rev].cap = e.cap; ex[s] -= e.cap; ex[e.to] += e.cap; } e.cap = 0; } return calc_active(t); } bool push(int u, int t, edge& e) { flow_t f = std::min(e.cap, ex[u]); int v = e.to; e.cap -= f, ex[u] -= f; graph[v][e.rev].cap += f, ex[v] += f; if (ex[v] == f && v != t) act_ver.push(potential[v], v); return ex[u] == 0; } int discharge(int u, int t) { for (int& i = cur_edge[u]; i < (int)graph[u].size(); i++) { auto& e = graph[u][i]; if (potential[u] == potential[e.to] + 1 && e.cap > 0) { if (push(u, t, e)) return potential[u]; } } return relabel(u); } int global_relabel(int t) { bfs(t); all_ver.clear(), act_ver.clear(); return calc_active(t); } void gap_relabel(const int u) { for (int i = potential[u]; i <= height; ++i) { for (int id = all_ver.dat[V + i].next; id < V; id = all_ver.dat[id].next) { potential[id] = V + 1; } all_ver.dat[V + i].prev = all_ver.dat[V + i].next = V + i; } } int relabel(const int u) { ++relabels; int prv = potential[u], cur = V; for (int i = 0; i < (int)graph[u].size(); ++i) { const edge& e = graph[u][i]; if (cur > potential[e.to] + 1 && e.cap > 0) { cur_edge[u] = i; cur = potential[e.to] + 1; } } if (all_ver.more_one(prv)) { all_ver.erase(u); if ((potential[u] = cur) == V) return potential[u] = V + 1, prv; act_ver.push(cur, u); all_ver.insert(cur, u); height = std::max(height, cur); } else { gap_relabel(u); return height = prv - 1; } return cur; } flow_t max_flow(int s, int t) { int level = init(s, t); while (level >= 0) { if (act_ver.empty(level)) { --level; continue; } int u = act_ver.top(level); act_ver.pop(level); level = discharge(u, t); if (relabels * 2 >= V) { level = global_relabel(t); relabels = 0; } } return ex[t]; } }; int main() { int N, M, S, T; cin >> N >> M >> S >> T; PushRelabel< int64 > g(N); for (int i = 0; i < M; i++) { int a, b, c; cin >> a >> b >> c; --a, --b; g.add_edge(a, b, c); } cout << g.max_flow(S - 1, T - 1) << endl; }