/** * author: nok0 * created: 2020.10.29 19:10:49 **/ #ifdef LOCAL #define _GLIBCXX_DEBUG #endif #include using namespace std; #pragma region Macros #define FOR(i, l, r) for(int i = (l); i < (r); ++i) #define REP(i, n) FOR(i, 0, n) #define REPS(i, n) FOR(i, 1, n + 1) #define RFOR(i, l, r) for(int i = (l); i >= (r); --i) #define RREP(i, n) RFOR(i, n - 1, 0) #define RREPS(i, n) RFOR(i, n, 1) #define pb push_back #define eb emplace_back #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() template using V = vector; template using VV = V>; using ll = long long; using ld = long double; using pii = pair; using pll = pair; #define VEC(type, name, size) \ V name(size); \ INPUT(name) #define VVEC(type, name, h, w) \ VV name(h, V(w)); \ INPUT(name) #define INT(...) \ int __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ INPUT(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ INPUT(__VA_ARGS__) #define DOUBLE(...) \ DOUBLE __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LD(...) \ LD __VA_ARGS__; \ INPUT(__VA_ARGS__) void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(long double &a) { cin >> a; } void scan(char a[]) { scanf("%s", a); } void scan(string &a) { cin >> a; } template void scan(V &); template void scan(pair &); template void scan(V &a) { for(auto &i : a) scan(i); } template void scan(pair &p) { scan(p.first); scan(p.second); } template void scan(T &a) { cin >> a; } void INPUT() {} template void INPUT(Head &head, Tail &... tail) { scan(head); INPUT(tail...); } template inline void print(T x) { cout << x << '\n'; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, vector &v) { for(T &in : v) is >> in; return is; } template ostream &operator<<(ostream &os, const V &v) { REP(i, SZ(v)) { if(i) os << " "; os << v[i]; } return os; } //debug template void view(const V &v) { cerr << "{ "; for(const auto &e : v) { cerr << e << ", "; } cerr << "\b\b }"; } template void view(const VV &vv) { cerr << "{\n"; for(const auto &v : vv) { cerr << "\t"; view(v); cerr << "\n"; } cerr << "}"; } template void view(const V> &v) { cerr << "{\n"; for(const auto &c : v) cerr << "\t(" << c.first << ", " << c.second << ")\n"; cerr << "}"; } template void view(const map &m) { cerr << "{\n"; for(auto &t : m) cerr << "\t[" << t.first << "] : " << t.second << "\n"; cerr << "}"; } template void view(const pair &p) { cerr << "(" << p.first << ", " << p.second << ")"; } template void view(const set &s) { cerr << "{ "; for(auto &t : s) { view(t); cerr << ", "; } cerr << "\b\b }"; } template void view(T e) { cerr << e; } #ifdef LOCAL void debug_out() {} template void debug_out(Head H, Tail... T) { view(H); cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ cerr << "\b\b]\n"; \ } while(0) #else #define debug(...) (void(0)) #endif template V press(V &x) { V res = x; sort(all(res)); res.erase(unique(all(res)), res.end()); REP(i, SZ(x)) { x[i] = lower_bound(all(res), x[i]) - res.begin(); } return res; } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if(a < b) { a = b; return true; } return false; } inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; } inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; } inline void err(bool b = true) { if(b) { cout << -1 << '\n'; exit(0); } } template inline void fin(bool b = true, T e = 0) { if(b) { cout << e << '\n'; exit(0); } } template T divup(T x, T y) { return (x + (y - 1)) / y; } template T pow(T a, long long n, T e = 1) { T ret = e; while(n) { if(n & 1) ret *= a; a *= a; n >>= 1; } return ret; } struct iofast { iofast() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); } } iofast_; const int inf = 1e9; const ll INF = 1e18; #pragma endregion enum Objective { MINIMIZE = 1, MAXIMIZE = -1, }; enum class Status { OPTIMAL, INFEASIBLE, }; template struct MinCostFlow { private: using V_id = uint32_t; using E_id = uint32_t; struct Edge { friend struct MinCostFlow; private: V_id src, dst; Flow flow, cap; Cost cost; E_id rev; public: Edge() = default; Edge(const V_id src, const V_id dst, const Flow cap, const Cost cost, const E_id rev) : src(src), dst(dst), flow(0), cap(cap), cost(cost), rev(rev) {} [[nodiscard]] Flow residual_cap() const { return cap - flow; } }; public: struct EdgePtr { friend struct MinCostFlow; private: const MinCostFlow *instance; const V_id v; const E_id e; EdgePtr(const MinCostFlow *instance, const V_id v, const E_id e) : instance(instance), v(v), e(e) {} [[nodiscard]] const Edge &edge() const { return instance->g[v][e]; } [[nodiscard]] const Edge &rev() const { const Edge &e = edge(); return instance->g[e.dst][e.rev]; } public: [[nodiscard]] V_id src() const { return rev().dst; } [[nodiscard]] V_id dst() const { return edge().dst; } [[nodiscard]] Flow flow() const { return edge().flow; } [[nodiscard]] Flow lower() const { return -rev().cap; } [[nodiscard]] Flow upper() const { return edge().cap; } [[nodiscard]] Cost cost() const { return edge().cost; } [[nodiscard]] Cost gain() const { return -edge().cost; } }; private: V_id n; std::vector> g; std::vector b; public: MinCostFlow() : n(0) {} V_id add_vertex() { ++n; g.resize(n); b.resize(n); return n - 1; } std::vector add_vertices(const size_t size) { std::vector ret; for(V_id i = 0; i < size; ++i) ret.emplace_back(n + i); n += size; g.resize(n); b.resize(n); return ret; } EdgePtr add_edge(const V_id src, const V_id dst, const Flow lower, const Flow upper, const Cost cost) { const E_id e = g[src].size(), re = src == dst ? e + 1 : g[dst].size(); assert(lower <= upper); g[src].emplace_back(Edge{src, dst, upper, cost * objective, re}); g[dst].emplace_back(Edge{dst, src, -lower, -cost * objective, e}); return EdgePtr{this, src, e}; } void add_supply(const V_id v, const Flow amount) { b[v] += amount; } void add_demand(const V_id v, const Flow amount) { b[v] -= amount; } private: static Cost constexpr unreachable = std::numeric_limits::max(); Cost farthest; std::vector potential; std::vector dist; std::vector parent; std::priority_queue, std::vector>, std::greater<>> pq; std::vector excess_vs, deficit_vs; Edge &rev(const Edge &e) { return g[e.dst][e.rev]; } void push(Edge &e, const Flow amount) { e.flow += amount; g[e.dst][e.rev].flow -= amount; } Cost residual_cost(const V_id src, const V_id dst, const Edge &e) { return e.cost + potential[src] - potential[dst]; } bool dual(const Flow delta) { dist.assign(n, unreachable); parent.assign(n, nullptr); excess_vs.erase(std::remove_if(std::begin(excess_vs), std::end(excess_vs), [&](const V_id v) { return b[v] < delta; }), std::end(excess_vs)); deficit_vs.erase(std::remove_if(std::begin(deficit_vs), std::end(deficit_vs), [&](const V_id v) { return b[v] > -delta; }), std::end(deficit_vs)); for(const auto v : excess_vs) pq.emplace(dist[v] = 0, v); farthest = 0; std::size_t deficit_count = 0; while(!pq.empty()) { const auto [d, u] = pq.top(); pq.pop(); if(dist[u] < d) continue; farthest = d; if(b[u] <= -delta) ++deficit_count; if(deficit_count >= deficit_vs.size()) break; for(auto &e : g[u]) { if(e.residual_cap() < delta) continue; const auto v = e.dst; const auto new_dist = d + residual_cost(u, v, e); if(new_dist >= dist[v]) continue; pq.emplace(dist[v] = new_dist, v); parent[v] = &e; } } pq = decltype(pq)(); for(V_id v = 0; v < n; ++v) { potential[v] += std::min(dist[v], farthest); } return deficit_count > 0; } void primal(const Flow delta) { for(const auto t : deficit_vs) { if(dist[t] > farthest) continue; Flow f = -b[t]; V_id v; for(v = t; parent[v] != nullptr && f >= delta; v = parent[v]->src) { f = std::min(f, parent[v]->residual_cap()); } f = std::min(f, b[v]); if(f < delta) continue; for(v = t; parent[v] != nullptr;) { auto &e = *parent[v]; push(e, f); const size_t u = parent[v]->src; parent[v] = nullptr; v = u; } b[t] += f; b[v] -= f; } } void saturate_negative(const Flow delta) { excess_vs.clear(); deficit_vs.clear(); for(auto &es : g) for(auto &e : es) { const Flow rcap = e.residual_cap(); const Cost rcost = residual_cost(e.src, e.dst, e); if(rcost < 0 && rcap >= delta) { push(e, rcap); b[e.src] -= rcap; b[e.dst] += rcap; } } for(V_id v = 0; v < n; ++v) if(b[v] != 0) { (b[v] > 0 ? excess_vs : deficit_vs).emplace_back(v); } } public: std::pair solve() { potential.resize(n); for(auto &es : g) for(auto &e : es) { const Flow rcap = e.residual_cap(); if(rcap < 0) { push(e, rcap); b[e.src] -= rcap; b[e.dst] += rcap; } } Flow inf_flow = 1; for(const auto &es : g) for(const auto &e : es) inf_flow = std::max(inf_flow, e.residual_cap()); Flow delta = 1; while(delta <= inf_flow) delta *= SCALING_FACTOR; for(delta /= SCALING_FACTOR; delta; delta /= SCALING_FACTOR) { saturate_negative(delta); while(dual(delta)) primal(delta); } Cost value = 0; for(const auto &es : g) for(const auto &e : es) { value += e.flow * e.cost; } value /= 2; if(excess_vs.empty() && deficit_vs.empty()) { return {Status::OPTIMAL, value / objective}; } else { return {Status::INFEASIBLE, value / objective}; } } }; template using MaxGainFlow = MinCostFlow; int u, v; ll c, d; int main() { INT(n, m); MinCostFlow MCF; MCF.add_vertices(n); MCF.add_supply(0, 2); MCF.add_demand(n - 1, 2); auto add = [&](int u, int v) { auto w = MCF.add_vertex(); MCF.add_edge(u, w, 0, 2, c); MCF.add_edge(w, v, 0, 1, 0); MCF.add_edge(w, v, 0, 1, d - c); }; REP(i, m) { cin >> u >> v >> c >> d; u--, v--; add(u, v); add(v, u); } auto p = MCF.solve(); print(p.second); }