#define PROBLEM "https://yukicoder.me/problems/no/1984" #include #ifdef LOCAL #include #else #define debug(...) void(0) #endif using namespace std; typedef long long ll; #define all(x) begin(x), end(x) constexpr int INF = (1 << 30) - 1; constexpr long long IINF = (1LL << 60) - 1; constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; template istream& operator>>(istream& is, vector& v) { for (auto& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { auto sep = ""; for (const auto& x : v) os << exchange(sep, " ") << x; return os; } template bool chmin(T& x, U&& y) { return y < x and (x = forward(y), true); } template bool chmax(T& x, U&& y) { return x < y and (x = forward(y), true); } template void mkuni(vector& v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template int lwb(const vector& v, const T& x) { return lower_bound(begin(v), end(v), x) - begin(v); } namespace atcoder { namespace internal { template struct simple_queue { std::vector payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder namespace atcoder { template struct mf_graph { public: mf_graph() : _n(0) {} explicit mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); int from_id = int(g[from].size()); int to_id = int(g[to].size()); if (from == to) to_id++; g[from].push_back(_edge{to, to_id, cap}); g[to].push_back(_edge{from, from_id, 0}); return m; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap}; } std::vector edges() { int m = int(pos.size()); std::vector result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); std::vector level(_n), iter(_n); internal::simple_queue que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(g[v].size()); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) return res; } level[v] = _n; return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } return flow; } std::vector min_cut(int s) { std::vector visited(_n); internal::simple_queue que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector> pos; std::vector> g; }; } // namespace atcoder template struct ProjectSelectionProblem { ProjectSelectionProblem() = default; explicit ProjectSelectionProblem(int n) : n(n), costs(n, std::vector(2, 0)) {} void add_cost_0(int x, T cost) { assert(0 <= x and x < n); assert(cost >= 0); add_cost(x, {cost, 0}); } void add_cost_1(int x, T cost) { assert(0 <= x and x < n); assert(cost >= 0); add_cost(x, {0, cost}); } void add_profit_0(int x, T profit) { assert(0 <= x and x < n); assert(profit >= 0); add_cost(x, {-profit, 0}); } void add_profit_1(int x, T profit) { assert(0 <= x and x < n); assert(profit >= 0); add_cost(x, {0, -profit}); } void add_cost_01(int x, int y, T cost) { assert(0 <= x and x < n); assert(0 <= y and y < n); assert(cost >= 0); add_edge(x, y, cost); } void add_cost_10(int x, int y, T cost) { add_cost_01(y, x, cost); } void add_profit_00(int x, int y, T profit) { assert(0 <= x and x < n); assert(0 <= y and y < n); assert(profit >= 0); add_cost(x, y, {-profit, 0, 0, 0}); } void add_profit_11(int x, int y, T profit) { assert(0 <= x and x < n); assert(0 <= y and y < n); assert(profit >= 0); add_cost(x, y, {0, 0, 0, -profit}); } // void add_cost_for_3(int x, int y, int z, std::array, 2>, 2> cost) { // add_cost(x, y, z, cost); // } void add_profit_all_0(const std::vector& v, T profit) { assert(profit >= 0); if (v.size() == 0) base_cost -= profit; else if (v.size() == 1) add_profit_0(v[0], profit); else if (v.size() == 2) add_profit_00(v[0], v[1], profit); else { base_cost -= profit; int nxt = n + aux++; add_edge(source, nxt, profit); for (const int& x : v) add_edge(nxt, x, profit); } } void add_profit_all_1(const std::vector& v, T profit) { assert(profit >= 0); if (v.size() == 0) base_cost -= profit; else if (v.size() == 1) add_profit_1(v[0], profit); else if (v.size() == 2) add_profit_11(v[0], v[1], profit); else { base_cost -= profit; int nxt = n + aux++; add_edge(nxt, sink, profit); for (const int& x : v) add_edge(x, nxt, profit); } } std::pair> min_cost() { for (int i = 0; i < n; i++) { auto& tmp = costs[i]; if (tmp[0] <= tmp[1]) { base_cost += tmp[0]; add_edge(source, i, tmp[1] - tmp[0]); } else { base_cost += tmp[1]; add_edge(i, sink, tmp[0] - tmp[1]); } } atcoder::mf_graph g(n + aux + 2); int s = n + aux, t = s + 1; for (auto [u, v, w] : es) { u = (u == source ? s : u == sink ? t : u); v = (v == source ? s : v == sink ? t : v); g.add_edge(u, v, w); } auto sum = base_cost + g.flow(s, t); auto x = g.min_cut(s); x.resize(n); for (int i = 0; i < n; i++) x[i] = not x[i]; return {sum, x}; } std::pair> max_profit() { auto res = min_cost(); res.first *= -1; return res; } private: int n, aux = 0, source = -1, sink = -2; T base_cost = 0; std::vector> costs; std::vector> es; void add_edge(int x, int y, T cost) { assert(x == source or x == sink or (0 <= x and x < n + aux)); assert(y == source or y == sink or (0 <= y and y < n + aux)); if (cost == 0) return; es.emplace_back(x, y, cost); } void add_cost(int x, std::array cost) { for (int i = 0; i < 2; i++) costs[x][i] += cost[i]; } void add_cost(int x, int y, std::array, 2> cost) { assert(cost[0][1] + cost[1][0] >= cost[0][0] + cost[1][1]); base_cost += cost[0][0]; add_cost(x, {0, cost[1][0] - cost[0][0]}); add_cost(y, {0, cost[1][1] - cost[1][0]}); add_cost_01(x, y, (cost[0][1] - cost[0][0]) - (cost[1][1] - cost[1][0])); } // void add_cost(int x, int y, std::array, 2>, 2> cost) {} }; const long long inf = 1LL << 40; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int N, M, K, P; std::cin >> N >> M >> K >> P; std::vector E(N), F(M), V(K); for (int& val : E) cin >> val; for (int& val : F) cin >> val; for (int& val : V) cin >> val; ProjectSelectionProblem PSP(N + M + K); for (int i = 0; i < N; i++) { int L; cin >> L; for (; L--;) { int A; cin >> A; A--; PSP.add_cost_10(i, N + M + A, inf); } PSP.add_profit_1(i, E[i]); } for (int i = 0; i < M; i++) PSP.add_profit_0(N + i, F[i]); for (int i = 0; i < K; i++) PSP.add_cost_1(N + M + i, V[i]); for (; P--;) { int I, J; cin >> I >> J; I--, J--; PSP.add_cost_10(I, N + J, inf); } auto [C, res] = PSP.max_profit(); std::cout << C << '\n'; std::vector motions; for (int i = N + M; i < N + M + K; i++) { if (res[i]) { std::cout << "Preparation " << i - (N + M) + 1 << '\n'; } } for (int i = 0; i < N; i++) { if (res[i]) { std::cout << "Goal " << i + 1 << '\n'; } } for (int i = N; i < N + M; i++) { if (not res[i]) { std::cout << "Action " << i - N + 1 << '\n'; } } return 0; }