// https://atcoder.jp/contests/practice2/submissions/16936680 #line 1 "main.cpp" #include #include #include #include #include #include #include #include #line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/chmin_chmax.cpp" template constexpr bool chmin(T &lhs, const U &rhs) { if (lhs > rhs) { lhs = rhs; return true; } return false; } template constexpr bool chmax(T &lhs, const U &rhs) { if (lhs < rhs) { lhs = rhs; return true; } return false; } /** * @title Chmin/Chmax */ #line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp" #line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp" class range { public: class iterator { private: int64_t M_position; public: constexpr iterator(int64_t position) noexcept: M_position(position) { } constexpr void operator ++ () noexcept { ++M_position; } constexpr bool operator != (iterator other) const noexcept { return M_position != other.M_position; } constexpr int64_t operator * () const noexcept { return M_position; } }; class reverse_iterator { private: int64_t M_position; public: constexpr reverse_iterator(int64_t position) noexcept: M_position(position) { } constexpr void operator ++ () noexcept { --M_position; } constexpr bool operator != (reverse_iterator other) const noexcept { return M_position != other.M_position; } constexpr int64_t operator * () const noexcept { return M_position; } }; private: const iterator M_first, M_last; public: constexpr range(int64_t first, int64_t last) noexcept: M_first(first), M_last(std::max(first, last)) { } constexpr iterator begin() const noexcept { return M_first; } constexpr iterator end() const noexcept { return M_last; } constexpr reverse_iterator rbegin() const noexcept { return reverse_iterator(*M_last - 1); } constexpr reverse_iterator rend() const noexcept { return reverse_iterator(*M_first - 1); } }; /** * @title Range */ #line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/rev.cpp" #include #include #line 6 "/Users/kodamankod/Desktop/cpp_programming/Library/other/rev.cpp" template class rev_impl { public: using iterator = decltype(std::rbegin(std::declval())); private: const iterator M_begin; const iterator M_end; public: constexpr rev_impl(T &&cont) noexcept: M_begin(std::rbegin(cont)), M_end(std::rend(cont)) { } constexpr iterator begin() const noexcept { return M_begin; } constexpr iterator end() const noexcept { return M_end; } }; template constexpr decltype(auto) rev(T &&cont) { return rev_impl(std::forward(cont)); } /** * @title Reverser */ #line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network_simplex.cpp" #line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/adjust_index.cpp" #include #line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/other/adjust_index.cpp" class adjust_index { private: const size_t M_stuff, M_size; public: explicit adjust_index(const size_t stuff, const size_t size): M_stuff(stuff), M_size(size) { } size_t operator [] (const size_t index) const { assert(index < M_size); return M_stuff + index; } size_t to_index(const size_t fixed) const { assert(fixed >= M_stuff); assert(fixed < M_size + M_stuff); return fixed - M_stuff; } size_t size() const { return M_size; } }; /** * @title Index Adjustment */ #line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network_simplex.cpp" #line 6 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network_simplex.cpp" #include #line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network_simplex.cpp" #include #include #line 11 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network_simplex.cpp" #include #include #include #line 15 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network_simplex.cpp" template class network_simplex { public: using flow_type = Flow; using cost_type = Cost; using size_type = size_t; using node_id = size_t; using edge_id = size_t; static_assert(std::is_signed::value, "flow-type must be signed integer"); static_assert(std::is_integral::value, "flow-type must be signed integer"); static_assert(std::is_signed::value, "cost-type must be signed integer"); static_assert(std::is_integral::value, "cost-type must be signed integer"); struct return_type { public: const bool feasible; const std::vector potentials; const std::vector> edges; explicit return_type( const bool feasible, const std::vector potentials, const std::vector> edges ): feasible(feasible), potentials(potentials), edges(edges) { } template T calculate() const { T res = 0; for (const auto &e: edges) { res += (T) e.first * e.second; } return res; } }; private: class edge_type { public: const node_id src, dst; flow_type flow; const flow_type capacity; const cost_type cost; explicit edge_type( const node_id src, const node_id dst, const flow_type flow, const flow_type capacity, const cost_type cost ): src(src), dst(dst), flow(flow), capacity(capacity), cost(cost) { } }; class node_type { public: flow_type balance; cost_type potential; std::set tree_edges; size_type depth; edge_id parent_edge; explicit node_type(const flow_type balance = 0): balance(balance), potential(0), tree_edges(), depth(0), parent_edge(-1) { } }; std::vector edges; std::vector nodes; static edge_id rev_id(const edge_id eid) { return (eid ^ 1); } template static bool minimize(T ¤t, const T &new_cost) { if (current > new_cost) { current = new_cost; return true; } return false; } flow_type residual_capacity(const edge_id eid) const { return edges[eid].capacity - edges[eid].flow; } cost_type reduced_cost(const edge_id eid) const { return edges[eid].cost + nodes[edges[eid].src].potential - nodes[edges[eid].dst].potential; } bool send_flow(const edge_id eid, const flow_type flow) { edges[eid].flow += flow; edges[rev_id(eid)].flow -= flow; return edges[eid].flow == edges[eid].capacity; } void precompute() { cost_type inf_cost = 1; for (const auto &e: edges) { if (e.cost > 0) inf_cost += e.cost; } const auto root = add_node(); for (node_id nid = 0; nid != root; ++nid) { const auto flow = nodes[nid].balance; if (flow < 0) { const auto eid = add_edge(root, nid, (flow_type) 0, -flow, inf_cost) << 1; send_flow(eid, -flow); nodes[root].tree_edges.insert(eid); nodes[nid].tree_edges.insert(rev_id(eid)); } else { const auto eid = add_edge(nid, root, (flow_type) 0, flow + 1, inf_cost) << 1; send_flow(eid, flow); nodes[nid].tree_edges.insert(eid); nodes[root].tree_edges.insert(rev_id(eid)); } } evert(root); } void evert(const node_id root) { std::stack stack; stack.push(root); while (!stack.empty()) { const auto nid = stack.top(); stack.pop(); for (const auto eid: nodes[nid].tree_edges) { if (eid != nodes[nid].parent_edge) { const auto dst = edges[eid].dst; nodes[dst].potential = nodes[nid].potential + edges[eid].cost; nodes[dst].depth = nodes[nid].depth + 1; nodes[dst].parent_edge = rev_id(eid); stack.push(dst); } } } } edge_id select_edge() { static const size_type block_size = (size_type) std::sqrt(edges.size()); static size_type edge_scan = 0; static const auto advance = [&] { if (++edge_scan == edges.size()) edge_scan = 0; }; size_type step = 0; while (step < edges.size()) { cost_type optimal_cost = 0; edge_id select = -1; for (size_type minor = 0; minor != block_size; ++minor) { if (step == edges.size()) break; const edge_id eid = edge_scan; advance(); ++step; if (residual_capacity(eid) > 0) { if (minimize(optimal_cost, reduced_cost(eid))) select = eid; } } if (~select) return select; } return (edge_id) -1; } void pivot(const edge_id eid) { flow_type send = residual_capacity(eid); auto src_side = edges[eid].src; auto dst_side = edges[eid].dst; while (src_side != dst_side) { if (nodes[src_side].depth > nodes[dst_side].depth) { const auto down_edge = rev_id(nodes[src_side].parent_edge); minimize(send, residual_capacity(down_edge)); src_side = edges[down_edge].src; } else { const auto up_edge = nodes[dst_side].parent_edge; minimize(send, residual_capacity(up_edge)); dst_side = edges[up_edge].dst; } } const auto lca = src_side; edge_id remove = -1; enum leaving_arc { SRC, DST, ENT }; leaving_arc state = ENT; src_side = edges[eid].src; while (src_side != lca) { const auto down_edge = rev_id(nodes[src_side].parent_edge); if (send_flow(down_edge, send)) { if (~remove == 0) { remove = down_edge; state = SRC; } } src_side = edges[down_edge].src; } if (send_flow(eid, send)) { remove = eid; state = ENT; } dst_side = edges[eid].dst; while (dst_side != lca) { const auto up_edge = nodes[dst_side].parent_edge; if (send_flow(up_edge, send)) { remove = up_edge; state = DST; } dst_side = edges[up_edge].dst; } if (state == ENT) return; nodes[edges[eid].src].tree_edges.insert(eid); nodes[edges[eid].dst].tree_edges.insert(rev_id(eid)); nodes[edges[remove].src].tree_edges.erase(remove); nodes[edges[remove].dst].tree_edges.erase(rev_id(remove)); evert(state == SRC ? edges[eid].dst : edges[eid].src); } public: explicit network_simplex() = default; explicit network_simplex(const size_type size) { add_nodes(size); } node_id add_node(const flow_type balance = 0) { const node_id res = nodes.size(); nodes.emplace_back(balance); return res; } adjust_index add_nodes(const size_type size) { const size_type cur = nodes.size(); nodes.resize(cur + size); return adjust_index(cur, size); } void add_supply(const node_id node, const flow_type supply) { assert(node < nodes.size()); nodes[node].balance += supply; } void add_demand(const node_id node, const flow_type demand) { assert(node < nodes.size()); nodes[node].balance -= demand; } edge_id add_edge( const node_id src, const node_id dst, const flow_type lower_bound, const flow_type upper_bound, const cost_type cost ) { assert(src < nodes.size()); assert(dst < nodes.size()); assert(lower_bound <= upper_bound); const edge_id res = edges.size() >> 1; edges.emplace_back(src, dst, lower_bound, upper_bound, cost); edges.emplace_back(dst, src, -lower_bound, -lower_bound, -cost); if (lower_bound != (flow_type) 0) { add_demand(src, lower_bound); add_supply(dst, lower_bound); } return res; } return_type solve() { precompute(); edge_id select = select_edge(); while (~select) { pivot(select); select = select_edge(); } bool feasible = true; const auto split = edges.size() - 2 * (nodes.size() - 1); for (edge_id eid = split; eid != edges.size(); ++eid) { if (edges[eid].flow > 0) { feasible = false; break; } } std::vector pt(nodes.size() - 1); for (node_id nid = 0; nid != nodes.size() - 1; ++nid) { pt[nid] = nodes[nid].potential; } std::vector> es; es.reserve(split >> 1); for (edge_id eid = 0; eid != split; eid += 2) { es.emplace_back(edges[eid].flow, edges[eid].cost); } return return_type(feasible, pt, es); } }; /** * @title Network Simplex */ #line 18 "main.cpp" using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; constexpr i32 inf32 = (i32(1) << 30) - 1; constexpr i64 inf64 = (i64(1) << 62) - 1; int main() { i32 N, M, K, L, bit[31] = {1}; std::cin >> N >> M >> K >> L; network_simplex net; const auto src = net.add_node((N < M)? N: M); const auto sink = net.add_node((N < M)? -N: -M); const auto row = net.add_nodes(N); const auto column = net.add_nodes(M); net.add_edge(src, sink, 0, N + M, 0); for (auto k: range(0, N)) net.add_edge(src, row[k], 0, 1, 0); for (auto k: range(0, M)) net.add_edge(column[k], sink, 0, 1, 0); for (auto k: range(1, 31)) bit[k] = bit[k-1] << 1; for (auto k: range(0, L)) { i32 i, j, c; std::cin >> i >> j >> c; net.add_edge(row[i-1], column[j-1], 0, 1, -bit[c]); } const auto ans = net.solve(); std::cout << -ans.calculate() << '\n'; return 0; }