// Validator #include "testlib.h" #include #include #include #include #include #include #include #include #include // MaxFlow (Dinic algorithm) template struct MaxFlow { struct edge { int to; T cap; int rev; }; std::vector> edges; std::vector level; // level[i] = distance between vertex S and i (Default: -1) std::vector iter; // iteration counter, used for Dinic's DFS void bfs(int s) { level.assign(edges.size(), -1); std::queue q; level[s] = 0; q.push(s); while (!q.empty()) { int v = q.front(); q.pop(); for (edge &e : edges[v]) { if (e.cap > 0 and level[e.to] < 0) { level[e.to] = level[v] + 1; q.push(e.to); } } } } T dfs_dinic(int v, int goal, T f) { if (v == goal) return f; for (int &i = iter[v]; i < (int)edges[v].size(); i++) { edge &e = edges[v][i]; if (e.cap > 0 and level[v] < level[e.to]) { T d = dfs_dinic(e.to, goal, std::min(f, e.cap)); if (d > 0) { e.cap -= d; edges[e.to][e.rev].cap += d; return d; } } } return 0; } MaxFlow(int N) { edges.resize(N); } void add_edge(int from, int to, T capacity) { edges[from].push_back(edge{to, capacity, (int)edges[to].size()}); edges[to].push_back(edge{from, (T)0, (int)edges[from].size() - 1}); } // Dinic algorithm // Complexity: O(V^2 E) T Dinic(int s, int t, T req) { T flow = 0; while (req > 0) { bfs(s); if (level[t] < 0) break; iter.assign(edges.size(), 0); T f; while ((f = dfs_dinic(s, t, req)) > 0) flow += f, req -= f; } return flow; } }; // 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); } Tvalue error = std::accumulate(x.begin(), x.end(), Tvalue(0)) - xsum; if (error > EPS or -error > 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-10; // UnionFind Tree (0-indexed), based on size of each disjoint set struct UnionFind { std::vector par, cou; UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); } int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); } bool unite(int x, int y) { x = find(x), y = find(y); if (x == y) return false; if (cou[x] < cou[y]) std::swap(x, y); par[y] = x, cou[x] += cou[y]; return true; } int count(int x) { return cou[find(x)]; } }; using std::cin, std::cout, std::vector; int main(int argc, char **argv) { registerValidation(argc, argv); int N = inf.readInt(2, 50); // N <= 50 inf.readSpace(); int M = inf.readInt(N - 1, 200); // M <= 200 inf.readSpace(); long long K = inf.readInt(1, 100000000); inf.readEoln(); vector A(M), B(M); vector C(M), D(M); std::set> edges; UnionFind uf(N); for (int i = 0; i < M; i++) { A[i] = inf.readInt(1, N); inf.readSpace(); B[i] = inf.readInt(1, N); inf.readSpace(); C[i] = inf.readInt(1, 100000000); inf.readSpace(); D[i] = inf.readInt(1, 100000000); inf.readEoln(); A[i]--, B[i]--; assert(A[i] != B[i]); // Graph has NO self-loop. if (A[i] > B[i]) std::swap(A[i], B[i]); assert(edges.count(std::make_pair(A[i], B[i])) == 0); // Graph has NO multi-edge. edges.emplace(A[i], B[i]); uf.unite(A[i], B[i]); } inf.readEof(); assert(uf.count(0) == N); // Graph must be connected. auto maximize_xi = [&](int ie, const vector &xnow) -> long long { MaxFlow mf(N + 2); mf.add_edge(N, A[ie], 1LL << 60); mf.add_edge(N, B[ie], 1LL << 60); 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); long long ret = mf.Dinic(N, N + 1, 1LL << 62) / 2 - K - std::accumulate(xnow.begin(), xnow.end(), 0LL); return std::min(ret, D[ie]); }; LinearProgrammingOnBasePolyhedron solver(C, maximize_xi, K * (N - 1), 0, true); if (solver.infeasible) { cout << "-1\n"; } else { cout << solver.fun << '\n'; } }