#define PROBLEM "https://yukicoder.me/problems/no/1678" #include #include #include #include #include #include template struct PrimalDualonDAG { PrimalDualonDAG(int n) : n(n), G(n), h(n), dist(n), prevv(n), preve(n), indeg(n, 0) {} int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from && from < n); assert(0 <= to && to < n); assert(0 <= cap); // assert(0 <= cost); int m = pos.size(), from_id = G[from].size(), to_id = G[to].size(); pos.emplace_back(from, G[from].size()); G[from].emplace_back(to, cap, cost, to_id); G[to].emplace_back(from, 0, -cost, from_id); if (cap > 0) indeg[to]++; return m; } std::tuple get_edge(int i) { assert(0 <= i && i < (int)pos.size()); auto e = G[pos[i].first][pos[i].second]; auto re = G[e.to][e.rev]; return {pos[i].first, e.to, e.cap + re.cap, re.cap, e.cost}; } std::vector> edges() { std::vector> res; for (size_t i = 0; i < pos.size(); i++) res.emplace_back(get_edge(i)); return res; } Cost min_cost_flow(int s, int t, Cap flow) { auto res = slope(s, t, flow).back(); return res.first == flow ? res.second : -1; } std::pair min_cost_max_flow(int s, int t) { return slope(s, t, std::numeric_limits::max()).back(); } std::vector> slope(int s, int t) { return slope(s, t, std::numeric_limits::max()); } private: struct edge { int to; Cap cap; Cost cost; int rev; edge(int to, Cap cap, Cost cost, int rev) : to(to), cap(cap), cost(cost), rev(rev) {} }; const Cost inf = std::numeric_limits::max(); int n; std::vector> G; std::vector> pos; std::vector h, dist; std::vector prevv, preve, indeg, order; bool topological_sort() { std::queue que; for (int i = 0; i < n; i++) { if (indeg[i] == 0) { que.emplace(i); } } while (!que.empty()) { int v = que.front(); que.pop(); order.emplace_back(v); for (const auto& e : G[v]) { if (e.cap > 0 && --indeg[e.to] == 0) { que.emplace(e.to); } } } return *std::max_element(indeg.begin(), indeg.end()) == 0; } void calc_potential(int s) { fill(h.begin(), h.end(), inf); h[s] = 0; for (int& v : order) { if (h[v] == inf) continue; for (const auto& e : G[v]) { if (e.cap > 0) { h[e.to] = std::min(h[e.to], h[v] + e.cost); } } } } void dijkstra(int s) { struct P { Cost c; int v; P(Cost c, int v) : c(c), v(v) {} bool operator<(const P& rhs) const { return c > rhs.c; } }; std::priority_queue

pq; fill(dist.begin(), dist.end(), inf); dist[s] = 0; pq.emplace(dist[s], s); while (!pq.empty()) { auto p = pq.top(); pq.pop(); int v = p.v; if (dist[v] < p.c) continue; for (size_t i = 0; i < G[v].size(); i++) { auto& e = G[v][i]; if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) { dist[e.to] = dist[v] + e.cost + h[v] - h[e.to]; prevv[e.to] = v; preve[e.to] = i; pq.emplace(dist[e.to], e.to); } } } } std::vector> slope(int s, int t, Cap flow_limit) { assert(0 <= s && s < n); assert(0 <= t && t < n); assert(s != t); assert(topological_sort()); calc_potential(s); Cap flow = 0; Cost cost = 0, prev_cost_pre_flow = -1; std::vector> res; res.emplace_back(flow, cost); while (flow < flow_limit) { dijkstra(s); if (dist[t] == inf) break; for (int v = 0; v < n; v++) h[v] += dist[v]; Cap d = flow_limit - flow; for (int v = t; v != s; v = prevv[v]) d = std::min(d, G[prevv[v]][preve[v]].cap); for (int v = t; v != s; v = prevv[v]) { auto& e = G[prevv[v]][preve[v]]; e.cap -= d; G[v][e.rev].cap += d; } flow += d; cost += d * h[t]; if (prev_cost_pre_flow == d) res.pop_back(); res.emplace_back(flow, cost); prev_cost_pre_flow = d; } return res; } }; int main() { std::cin.tie(0); std::ios::sync_with_stdio(false); int N, K; std::cin >> N >> K; PrimalDualonDAG PD(2 * N + 1); int s = N, t = 2 * N; for (int i = 0; i < N; i++) { int A, M; std::cin >> A >> M; PD.add_edge(N + i, i, K, A); PD.add_edge(i, N + i + 1, K, -A); PD.add_edge(N + i, N + i + 1, K, 0); for (; M--;) { int B; std::cin >> B; PD.add_edge(--B, i, 1, 0); } } long long ans = -PD.min_cost_flow(s, t, K); std::cout << ans << '\n'; }