#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_CYAN = "\033[1;36m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif // https://hitonanode.github.io/cplib-cpp/flow/maxflow_pushrelabel.hpp #include #include #include #include // Maxflow (push-relabel, highest-label) // Complexity: O(N^2 M^(1/2)) template struct mf_pushrelabel { struct pque_ { std::vector> even_, odd_; int se, so; void init(int n) { even_.resize(n), odd_.resize(n), se = so = 0; }; void clear() { se = so = 0; } bool empty() const { return se + so == 0; } void push(int i, int h) { (h & 1 ? odd_[so++] : even_[se++]) = {i, h}; } int highest() const { int a = se ? even_[se - 1].second : -1, b = so ? odd_[so - 1].second : -1; return a > b ? a : b; } int pop() { if (!se or (so and odd_[so - 1].second > even_[se - 1].second)) return odd_[--so].first; return even_[--se].first; } } pque; int _n; struct _edge { int to, rev; Cap cap; }; std::vector> g; std::vector> pos; mf_pushrelabel(int n) : _n(n), g(n) { static_assert(GlobalRelabelFreq >= 0, "Global relabel parameter must be nonnegative."); } int add_edge(int from, int to, Cap cap) { assert(0 <= from and from < _n); assert(0 <= to and to < _n); assert(0 <= cap); int m = int(pos.size()); pos.emplace_back(from, int(g[from].size())); int from_id = g[from].size(), to_id = g[to].size() + (from == to); g[from].push_back({to, to_id, cap}); g[to].push_back({from, from_id, Cap(0)}); return m; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) const { int m = int(pos.size()); assert(0 <= i and i < m); auto e = g[pos[i].first][pos[i].second], re = g[e.to][e.rev]; return edge{pos[i].first, e.to, e.cap + re.cap, re.cap}; } std::vector edges() const { std::vector ret(pos.size()); for (int i = 0; i < int(pos.size()); i++) ret[i] = get_edge(i); return ret; } std::vector dist; std::vector dcnt; std::vector excess; int gap; void global_relabeling(int t) { dist.assign(_n, _n), dist[t] = 0; static std::vector q; if (q.empty()) q.resize(_n); q[0] = t; int qb = 0, qe = 1; pque.clear(); if (UseGapRelabeling) gap = 1, dcnt.assign(_n + 1, 0); while (qb < qe) { int now = q[qb++]; if (UseGapRelabeling) gap = dist[now] + 1, dcnt[dist[now]]++; if (excess[now] > 0) pque.push(now, dist[now]); for (const auto &e : g[now]) { if (g[e.to][e.rev].cap and dist[e.to] == _n) { dist[e.to] = dist[now] + 1; while (int(q.size()) <= qe) q.push_back(0); q[qe++] = e.to; } } } } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits::max(), true); } Cap flow(int s, int t, Cap flow_limit, bool retrieve = true) { assert(0 <= s and s < _n); assert(0 <= t and t < _n); assert(s != t); excess.resize(_n, 0); excess[s] += flow_limit, excess[t] -= flow_limit; dist.assign(_n, 0); dist[s] = _n; if (UseGapRelabeling) gap = 1, dcnt.assign(_n + 1, 0), dcnt[0] = _n - 1; pque.init(_n); for (auto &e : g[s]) _push(s, e); _run(t); Cap ret = excess[t] + flow_limit; excess[s] += excess[t], excess[t] = 0; if (retrieve) { global_relabeling(s); _run(s); assert(excess == std::vector(_n, 0)); } return ret; } void _run(int t) { if (GlobalRelabelFreq) global_relabeling(t); int tick = pos.size() * GlobalRelabelFreq; while (!pque.empty()) { int i = pque.pop(); if (UseGapRelabeling and dist[i] > gap) continue; int dnxt = _n * 2 - 1; for (auto &e : g[i]) { if (!e.cap) continue; if (dist[e.to] == dist[i] - 1) { _push(i, e); if (excess[i] == 0) break; } else { if (dist[e.to] + 1 < dnxt) dnxt = dist[e.to] + 1; } } if (excess[i] > 0) { if (UseGapRelabeling) { if (dnxt != dist[i] and dcnt[dist[i]] == 1 and dist[i] < gap) gap = dist[i]; if (dnxt == gap) gap++; while (pque.highest() > gap) pque.pop(); if (dnxt > gap) dnxt = _n; if (dist[i] != dnxt) dcnt[dist[i]]--, dcnt[dnxt]++; } dist[i] = dnxt; if (!UseGapRelabeling or dist[i] < gap) pque.push(i, dist[i]); } if (GlobalRelabelFreq and --tick == 0) { tick = pos.size() * GlobalRelabelFreq, global_relabeling(t); } } return; } void _push(int i, _edge &e) { Cap delta = e.cap < excess[i] ? e.cap : excess[i]; excess[i] -= delta, e.cap -= delta; excess[e.to] += delta, g[e.to][e.rev].cap += delta; if (excess[e.to] > 0 and excess[e.to] <= delta) { if (!UseGapRelabeling or dist[e.to] <= gap) pque.push(e.to, dist[e.to]); } } }; int main() { int N, M, S, T; cin >> N >> M >> S >> T; mf_pushrelabel mf(N); REP(_, M) { int u, v, c; cin >> u >> v >> c; --u, --v; mf.add_edge(u, v, c); } --S, --T; cout << mf.flow(S, T) << '\n'; }