#include #include #include #include #include #include #include #include #include // LinearProgrammingOnBasePolyhedron : Maximize/minimize linear function on base polyhedron, using Edmonds' algorithm // // maximize/minimize cx s.t. (x on some base polyhedron) // Reference: , Sec. 2.4, Algorithm 2.2-2.3 // "Submodular Functions, Matroids, and Certain Polyhedra" [Edmonds+, 1970] template struct LinearProgrammingOnBasePolyhedron { using Tfunc = std::function &)>; static Tvalue EPS; int N; std::vector c; Tfunc maximize_xi; Tvalue xsum; bool minimize; Tvalue fun; std::vector x; bool infeasible; void _init(const std::vector &c_, Tfunc q_, Tvalue xsum_, Tvalue xlowerlimit, bool minimize_) { N = c_.size(); c = c_; maximize_xi = q_; xsum = xsum_; minimize = minimize_; fun = 0; x.assign(N, xlowerlimit); infeasible = false; } void _solve() { std::vector> c2i(N); for (int i = 0; i < N; i++) c2i[i] = std::make_pair(c[i], i); std::sort(c2i.begin(), c2i.end()); if (!minimize) std::reverse(c2i.begin(), c2i.end()); for (const auto &p : c2i) { const int i = p.second; x[i] = maximize_xi(i, x); } if (std::abs(std::accumulate(x.begin(), x.end(), Tvalue(0)) - xsum) > EPS) { infeasible = true; } else { for (int i = 0; i < N; i++) fun += x[i] * c[i]; } } LinearProgrammingOnBasePolyhedron(const std::vector &c_, Tfunc q_, Tvalue xsum_, Tvalue xlowerlimit, bool minimize_) { _init(c_, q_, xsum_, xlowerlimit, minimize_); _solve(); } }; template <> long long LinearProgrammingOnBasePolyhedron::EPS = 0; template <> long double LinearProgrammingOnBasePolyhedron::EPS = 1e-12; using std::cin, std::cout, std::vector; int main() { using Num = long long; int N, M; long long K; cin >> N >> M >> K; vector A(M), B(M); vector C(M), D(M); for (int i = 0; i < M; i++) { cin >> A[i] >> B[i] >> C[i] >> D[i]; A[i]--, B[i]--; } auto maximize_xi = [&](int ie, const vector &xnow) -> Num { atcoder::mf_graph mf(N + 2); mf.add_edge(N, A[ie], 2 * K * N); mf.add_edge(N, B[ie], 2 * K * N); for (int je = 0; je < M; je++) { mf.add_edge(A[je], B[je], xnow[je]); mf.add_edge(B[je], A[je], xnow[je]); mf.add_edge(N, A[je], xnow[je]); mf.add_edge(N, B[je], xnow[je]); } for (int iv = 0; iv < N; iv++) mf.add_edge(iv, N + 1, 2 * K); Num ret = mf.flow(N, N + 1) / 2 - K - std::accumulate(xnow.begin(), xnow.end(), (Num)0); return std::min(ret, D[ie]); }; LinearProgrammingOnBasePolyhedron solver(C, maximize_xi, K * (N - 1), 0, true); if (solver.infeasible) { cout << "-1\n"; } else { cout << (long long)solver.fun << '\n'; } }