#include using namespace std; #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #pragma GCC target("avx2") // 数値型 using ll = long long; using ull = unsigned long long; using ld = long double; using P = pair; using Pll = pair; using Pli = pair; using Pil = pair; // vector関連 using vi = vector; using vvi = vector; using vvvi = vector; using vll = vector; using vvll = vector; using vvvll = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; // priority_queue template using pq = priority_queue; template using pqg = priority_queue, greater>; #define rep(i, n) for(int i = 0; i < (int)(n); i++) #define FOR(i, a, b) for(int i = a; i < (int)(b); i++) #define all(a) (a).begin(),(a).end() #define rall(a) (a).rbegin(),(a).rend() #define MIN(vec) *min_element(vec) #define MAX(vec) *max_element(vec) #define next_perm(vec) next_permutation((vec).begin(), (vec).end()) #define UNIQUE(vec) vec.erase(unique(vec.begin(), vec.end()), vec.end()) #define el "\n" #define Yes cout << "Yes" << el #define No cout << "No" << el #define YES cout << "YES" << el #define NO cout << "NO" << el #define EPS 1e-8 #define Equal(a, b) (fabs((a)-(b)) < EPS) #define dbg(x) cerr << #x << "=" << x << el // 定数 const string abc = "abcdefghijklmnopqrstuvwxyz"; const string ABC = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; constexpr int INF = 1001001001; constexpr ll LINF = 1001001001001001001ll; constexpr int DX[] = {1, 0, -1, 0}; constexpr int DY[] = {0, 1, 0, -1}; constexpr int DX8[] = {1, 0, -1, 0, 1, 1, -1, -1}; constexpr int DY8[] = {0, 1, 0, -1, 1, -1, 1, -1}; template ostream &operator<< (ostream &os, pair p) { os << "{" << p.first << "," << p.second << "}"; return os; } template ostream &operator<< (ostream &os, vc &vec) { int sz = vec.size(); rep(i, sz){ os << vec[i] << (i==sz-1?"":" "); } return os; } template istream &operator>> (istream &is, pair &p) { is >> p.first >> p.second; return is; } template istream &operator>> (istream &is, vc &vec) { int sz = vec.size(); rep(i, sz) { is >> vec[i]; } return is; } /// @brief aとbの最大値をaに格納。更新があったかbool値を返す /// @tparam T1 /// @tparam T2 /// @param a /// @param b /// @return bool template inline bool chmax(T1 &a, T2 b){ bool ret = a inline bool chmin(T1 &a, T2 b){ bool ret = a>b; if(ret) {a = b;} return ret; } inline void YesNo(bool flag){ if(flag) {Yes;} else {No;} return; } inline void YESNO(bool flag){ if(flag) {YES;} else {NO;} return; } inline bool outof(ll x, ll xlim){ return (x<0 || x>=xlim); } template inline T sqnorm(T x, T y){ return x*x+y*y; } /// @brief char->int /// @param c /// @return int inline int ctoi(char c){ return c-'0'; } /// @brief xを素因数分解 /// @param x /// @return vector, 素因数の昇順に {p, cnt} vector prime_fact(ll x){ vector ret; for(ll i=2; i*i<=x; i++){ if(x%i == 0){ ret.emplace_back(i, 0); while(x%i == 0){ ret.back().second++; x /= i; } } } if(x != 1) ret.emplace_back(x, 1); return ret; } /// @brief xの約数列挙 /// @param x /// @return vll, 約数の昇順 vll divisor_enum(ll x){ vector ret; for(ll i=1; i*i<=x; i++){ if(x%i == 0){ ret.push_back(x/i); ret.push_back(i); } } sort(all(ret)); UNIQUE(ret); return ret; } /// @brief 繰り返し二乗法。 /// @tparam T /// @param x /// @param k /// @param op /// @param e /// @return template T pow_t(T x, ll k, T (*op)(T, T), T (*e)()){ T ret = e(); while(k){ if(k&1) ret = op(ret, x); x = op(x, x); k >>= 1; } return ret; } ll powll(ll x, ll k){ return pow_t(x, k, [](ll a, ll b) -> ll{return a*b;}, []() -> ll{return 1;}); } inline int pop_cnt(ll x) { return __builtin_popcountll(x); } inline int top_bit(ll x) { return (x==0?-1:63-__builtin_clzll(x));} void main2(); int main(){ ios::sync_with_stdio(false); std::cin.tie(nullptr); main2(); } template< typename flow_t > struct PushRelabel { const flow_t INF; struct edge { int to; flow_t cap; int rev; bool isrev; int idx; }; vector< vector< edge > > graph; vector< flow_t > ex; int relabels, high; vector< int > cnt, h; vector< vector< int > > hs; PushRelabel(int V) : graph(V), INF(numeric_limits< flow_t >::max()), hs(V + 1), high(0) {} 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}); } void update_height(int idx, int nxt_height) { ++relabels; if(h[idx] != graph.size() + 1) { --cnt[h[idx]]; } h[idx] = nxt_height; if(h[idx] != graph.size() + 1) { high = nxt_height; ++cnt[nxt_height]; if(ex[idx] > 0) hs[nxt_height].emplace_back(idx); } } void global_relabel(int idx) { for(int i = 0; i <= high; i++) hs[i].clear(); relabels = 0; high = 0; h.assign(graph.size(), graph.size() + 1); cnt.assign(graph.size(), 0); queue< int > que; que.emplace(idx); h[idx] = 0; while(que.size()) { int p = que.front(); que.pop(); for(auto &e : graph[p]) { if(h[e.to] == graph.size() + 1 && graph[e.to][e.rev].cap > 0) { que.emplace(e.to); high = h[p] + 1; update_height(e.to, high); } } } } void push(int idx, edge &e) { if(h[e.to] == graph.size() + 1) return; if(ex[e.to] == 0) { hs[h[e.to]].emplace_back(e.to); } flow_t df = min(ex[idx], e.cap); e.cap -= df; graph[e.to][e.rev].cap += df; ex[idx] -= df; ex[e.to] += df; } void discharge(int idx) { int next_height = (int) graph.size() + 1; for(auto &&e : graph[idx]) { if(e.cap > 0) { if(h[idx] == h[e.to] + 1) { push(idx, e); if(ex[idx] <= 0) return; } else { next_height = min(next_height, h[e.to] + 1); } } } if(cnt[h[idx]] > 1) { update_height(idx, next_height); } else { for(; high >= h[idx]; hs[high--].clear()) { for(int j : hs[high]) update_height(j, graph.size() + 1); } } } flow_t max_flow(int s, int t) { ex.assign(graph.size(), 0); ex[s] = INF; ex[t] = -INF; global_relabel(t); for(auto &e : graph[s]) push(s, e); for(; high >= 0; high--) { while(!hs[high].empty()) { int idx = hs[high].back(); hs[high].pop_back(); discharge(idx); if(relabels >= graph.size() * 4) global_relabel(t); } } return ex[t] + INF; } void output() { for(int i = 0; i < graph.size(); i++) { for(auto &e : graph[i]) { if(e.isrev) continue; auto &rev_e = graph[e.to][e.rev]; cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/" << e.cap + rev_e.cap << ")" << endl; } } } }; // https://ei1333.github.io/luzhiled/snippets/graph/push-relabel.html void main2(){ int n, m, s, t; cin >> n >> m >> s >> t; PushRelabel mf(n); rep(i, m) { int u, v, c; cin >> u >> v >> c; mf.add_edge(u-1, v-1, c); } cout << mf.max_flow(s-1, t-1) << el; }