#line 1 "main.cpp" /** * @title Template */ #include #include #include #include #include #include template inline bool chmin(T &lhs, const U &rhs) { if (lhs > rhs) { lhs = rhs; return true; } return false; } template inline bool chmax(T &lhs, const U &rhs) { if (lhs < rhs) { lhs = rhs; return true; } return false; } struct range { using itr = int64_t; struct iterator { itr i; constexpr iterator(itr i_) noexcept : i(i_) { } constexpr void operator ++ () noexcept { ++i; } constexpr itr operator * () const noexcept { return i; } constexpr bool operator != (iterator x) const noexcept { return i != x.i; } }; const iterator l, r; constexpr range(itr l_, itr r_) noexcept : l(l_), r(std::max(l_, r_)) { } constexpr iterator begin() const noexcept { return l; } constexpr iterator end() const noexcept { return r; } }; struct revrange { using itr = int64_t; struct iterator { itr i; constexpr iterator(itr i_) noexcept : i(i_) { } constexpr void operator ++ () noexcept { --i; } constexpr itr operator * () const noexcept { return i; } constexpr bool operator != (iterator x) const noexcept { return i != x.i; } }; const iterator l, r; constexpr revrange(itr l_, itr r_) noexcept : l(l_ - 1), r(std::max(l_, r_) - 1) { } constexpr iterator begin() const noexcept { return r; } constexpr iterator end() const noexcept { return l; } }; #line 2 "/Users/kodamankod/Desktop/Programming/Library/graph/network.cpp" #include #include #line 8 "/Users/kodamankod/Desktop/Programming/Library/graph/network.cpp" #include template class network { public: using vertex_type = typename Edge::vertex_type; using edge_type = Edge; using size_type = size_t; class index_helper { private: const size_type M_size; public: explicit index_helper(const size_type size): M_size(size) { } vertex_type operator [] (const size_type index) const { return to_vertex(index); } vertex_type to_vertex(const size_type index) const { return index + M_size; } size_type to_index(const vertex_type vert) const { return vert - M_size; } }; protected: std::vector> M_graph; public: network() = default; template typename std::enable_if::type add_vertex() { vertex_type res = M_graph.size(); M_graph.push_back({ }); return res; } template typename std::enable_if::type add_vertex() { M_graph.push_back({ }); } template typename std::enable_if::type add_vertices(const size_type size) { size_type cur = M_graph.size(); M_graph.resize(cur + size); return index_helper(cur); } template typename std::enable_if::type add_vertices(const size_type size) { size_type cur = M_graph.size(); M_graph.resize(cur + size); } void add_edge(const edge_type &edge) { M_graph[edge.source].push_back(edge); } template void emplace_edge(const vertex_type src, Args&&... args) { M_graph[src].emplace_back(src, std::forward(args)...); } std::vector &operator [] (const vertex_type vert) { return M_graph[vert]; } std::vector &at(const vertex_type vert) { return M_graph.at(vert); } const std::vector &operator [] (const vertex_type vert) const { return M_graph[vert]; } const std::vector &at(const vertex_type vert) const { return M_graph.at(vert); } const std::vector> &get() const { return M_graph; } size_type size() const { return M_graph.size(); } bool empty() const { return M_graph.empty(); } void clear() { M_graph.clear(); M_graph.shrink_to_fit(); } }; class base_edge { public: using vertex_type = uint32_t; const vertex_type source, dest; explicit base_edge(const vertex_type source, const vertex_type dest): source(source), dest(dest) { } base_edge reverse() { return base_edge(dest, source); } }; template class flow_edge: public base_edge { public: using vertex_type = typename base_edge::vertex_type; using flow_type = Flow; flow_type flow; const flow_type capacity; explicit flow_edge(const base_edge &edge, const flow_type capacity): base_edge(edge), flow(0), capacity(capacity) { } explicit flow_edge(const base_edge &edge, const flow_type flow, const flow_type capacity): base_edge(edge), flow(flow), capacity(capacity) { } explicit flow_edge(const vertex_type source, const vertex_type dest, const flow_type capacity): base_edge(source, dest), flow(0), capacity(capacity) { } explicit flow_edge(const vertex_type source, const vertex_type dest, const flow_type flow, const flow_type capacity): base_edge(source, dest), flow(flow), capacity(capacity) { } flow_edge reverse() const { return flow_edge(static_cast(*this).reverse(), capacity - flow, capacity); } }; template class flow_cost_edge: public flow_edge { public: using vertex_type = typename flow_edge::vertex_type; using flow_type = typename flow_edge::flow_type; using cost_type = Cost; const cost_type cost; explicit flow_cost_edge(const flow_edge &edge, const cost_type cost): flow_edge(edge), cost(cost) { } explicit flow_cost_edge(const vertex_type source, const vertex_type dest, const flow_type capacity, const cost_type cost): flow_edge(source, dest, capacity), cost(cost) { } explicit flow_cost_edge(const vertex_type source, const vertex_type dest, const flow_type flow, const flow_type capacity, const cost_type cost): flow_edge(source, dest, flow, capacity), cost(cost) { } flow_cost_edge reverse() const { return flow_cost_edge(static_cast>(*this).reverse(), -cost); } }; /** * @title Network */ #line 2 "/Users/kodamankod/Desktop/Programming/Library/graph/push_relabel.cpp" #include #line 5 "/Users/kodamankod/Desktop/Programming/Library/graph/push_relabel.cpp" #line 7 "/Users/kodamankod/Desktop/Programming/Library/graph/push_relabel.cpp" namespace push_relabel_detail { class stack_helper { private: const size_t M_size; std::vector M_stack; public: explicit stack_helper(const size_t size): M_size(size), M_stack(size * 2) { clear(); } size_t top(const size_t height) const { return M_stack[M_size + height]; } bool empty(const size_t height) const { return M_stack[M_size + height] == M_size + height; } void pop(const size_t height) { M_stack[M_size + height] = M_stack[M_stack[M_size + height]]; } void push(const size_t height, const size_t node) { M_stack[node] = M_stack[M_size + height]; M_stack[M_size + height] = node; } void clear() { std::iota(M_stack.begin() + M_size, M_stack.end(), M_size); } }; class list_helper { private: const size_t M_size; std::vector> M_list; public: explicit list_helper(const size_t size): M_size(size), M_list(size * 2) { clear(); } bool empty(const size_t height) { return M_list[M_size + height].second == M_size + height; } bool more_than_one(const size_t height) { return M_list[M_size + height].first != M_list[M_size + height].second; } void insert(const size_t height, const size_t node) { M_list[node].first = M_list[M_size + height].first; M_list[node].second = M_size + height; M_list[M_list[M_size + height].first].second = node; M_list[M_size + height].first = node; } void erase(const size_t node) { M_list[M_list[node].first].second = M_list[node].second; M_list[M_list[node].second].first = M_list[node].first; } void clear() { for (size_t index = M_size; index < M_size * 2; ++index) { M_list[index].first = M_list[index].second = index; } } void clear(const size_t height) { const size_t index = M_size + height; M_list[index].first = M_list[index].second = index; } template void apply_all(const size_t height, Func &&func) { size_t index = M_list[M_size + height].second; while (index < M_size) { func(index); index = M_list[index].second; } } }; }; template class push_relabel { public: using network_type = Network; using vertex_type = typename Network::vertex_type; using edge_type = typename Network::edge_type; using size_type = typename Network::size_type; using flow_type = typename Network::edge_type::flow_type; using height_type = uint32_t; static_assert(std::is_integral::value, "invalid flow type :: non-integral"); private: class residual_edge: public edge_type { public: const size_type rev; const bool is_rev; explicit residual_edge(const edge_type &edge, const size_type rev, const bool is_rev): edge_type(edge), rev(rev), is_rev(is_rev) { } }; class node_type { public: std::vector edges; flow_type excess; height_type height; size_type iter; node_type() = default; }; flow_type M_remain(const residual_edge &edge) { return edge.capacity - edge.flow; } residual_edge &M_cur_edge(node_type &node) { return node.edges[node.iter]; } residual_edge &M_rev_edge(const residual_edge &edge) { return M_graph[edge.dest].edges[edge.rev]; } void M_push(node_type &node, residual_edge &edge) { const auto flow = std::min(node.excess, M_remain(edge)); edge.flow += flow; node.excess -= flow; M_rev_edge(edge).flow -= flow; M_graph[edge.dest].excess += flow; } void M_relabel(node_type &node) { height_type min = M_graph.size() + 1; for (const auto &edge: node.edges) { if (M_remain(edge) > 0 && min > M_graph[edge.dest].height + 1) { min = M_graph[edge.dest].height + 1; } } node.height = min; } void M_reverse_bfs(const vertex_type source) { for (auto &node: M_graph) { node.height = M_graph.size() + 1; } M_graph[source].height = 0; std::queue queue; queue.push(source); while (!queue.empty()) { const auto vert = queue.front(); queue.pop(); for (const auto &edge: M_graph[vert].edges) { if (M_remain(M_rev_edge(edge)) > 0) { if (M_graph[edge.dest].height == M_graph.size() + 1) { M_graph[edge.dest].height = M_graph[vert].height + 1; queue.push(edge.dest); } } } } } std::vector M_graph; public: push_relabel() = default; explicit push_relabel(const network_type &net) { const auto &graph = net.get(); M_graph.resize(graph.size()); for (size_type src = 0; src < graph.size(); ++src) { for (const auto &edge: graph[src]) { M_graph[src].edges.emplace_back(edge, M_graph[edge.dest].edges.size(), false); M_graph[edge.dest].edges.emplace_back(edge.reverse(), M_graph[src].edges.size() - 1, true); } } } template typename std::enable_if::type max_flow(const vertex_type source, const vertex_type sink, const bool initialize_edges = false) { push_relabel_detail::stack_helper active(M_graph.size()); push_relabel_detail::list_helper level(M_graph.size()); height_type min_gap, max_active; for (auto &node: M_graph) { node.excess = 0; node.iter = 0; for (auto &edge: node.edges) { if (initialize_edges) { if (!edge.is_rev) edge.flow = 0; else edge.flow = edge.capacity; } } } M_reverse_bfs(sink); if (M_graph[source].height == M_graph.size() + 1) { return 0; } for (auto &edge: M_graph[source].edges) { M_graph[source].excess += M_remain(edge); M_push(M_graph[source], edge); } M_graph[source].height = M_graph.size(); min_gap = M_graph.size(); max_active = 0; for (size_type index = 0; index < M_graph.size(); ++index) { const auto &node = M_graph[index]; if (node.height < M_graph.size()) { if (node.excess > 0 && index != sink) { active.push(node.height, index); max_active = std::max(max_active, node.height); } level.insert(node.height, index); } } for (size_type index = 0; index < M_graph.size(); ++index) { if (level.empty(index)) { min_gap = index; break; } } while (max_active > 0) { if (active.empty(max_active)) { --max_active; continue; } const auto vert = active.top(max_active); auto &node = M_graph[vert]; active.pop(max_active); while (true) { auto &edge = M_cur_edge(node); const auto &dest = M_graph[edge.dest]; if (M_remain(edge) > 0 && node.height == dest.height + 1) { if (dest.excess == 0 && edge.dest != sink) { active.push(dest.height, edge.dest); max_active = std::max(max_active, dest.height); } M_push(node, edge); if (node.excess == 0) { break; } } node.iter++; if (node.iter == node.edges.size()) { node.iter = 0; if (level.more_than_one(node.height)) { level.erase(vert); M_relabel(node); if (node.height > min_gap) { node.height = M_graph.size() + 1; break; } if (node.height == min_gap) { min_gap++; } level.insert(node.height, vert); } else { const height_type old_gap = min_gap; min_gap = node.height; for (height_type index = node.height; index < old_gap; ++index) { level.apply_all(index, [&](const vertex_type vert) { M_graph[vert].height = M_graph.size() + 1; }); level.clear(index); } break; } } } max_active = std::min(max_active, min_gap - 1); } return M_graph[sink].excess; } template typename std::enable_if>::type max_flow(const vertex_type source, const vertex_type sink, const bool initialize_edges = false) { const auto flow = max_flow(source, sink, initialize_edges); std::queue active; M_reverse_bfs(source); for (vertex_type index = 0; index < M_graph.size(); ++index) { const auto &node = M_graph[index]; if (node.excess > 0 && node.height < M_graph.size() && index != sink) { active.push(index); } } while (!active.empty()) { auto &node = M_graph[active.front()]; active.pop(); while (node.excess > 0) { auto &edge = M_cur_edge(node); const auto &dest = M_graph[edge.dest]; if (M_remain(edge) > 0 && node.height == dest.height + 1) { if (dest.excess == 0 && edge.dest != source) { active.push(edge.dest); } M_push(node, edge); if (node.excess == 0) { break; } } node.iter++; if (node.iter == node.edges.size()) { node.iter = 0; M_relabel(node); } } } network_type graph; graph.template add_vertices (M_graph.size()); for (size_type index = 0; index < M_graph.size(); ++index) { for (const auto &edge: M_graph[index].edges) { if (!edge.is_rev) { graph.add_edge(static_cast(edge)); } } } return std::make_pair(flow, std::move(graph)); } }; /** * @title Push Relabel */ #line 57 "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 H, W; std::cin >> H >> W; std::vector A(H), B(W); for (auto &x: A) { std::cin >> x; } for (auto &x: B) { std::cin >> x; } const auto tA = A; const auto tB = B; std::vector> ans(H, std::vector(W, '.')); for (auto i: range(0, H)) { std::vector> vec(H); for (auto j: range(0, W)) { if (B[j] > 0) { vec[B[j] - 1].push_back(j); } } for (auto j: revrange(0, H)) { for (auto x: vec[j]) { if (A[i] > 0) { ans[i][x] = 'o'; --A[i]; --B[x]; } } } if (A[i] > 0) { std::cout << ":(\n"; return 0; } } if (*std::max_element(B.cbegin(), B.cend()) > 0) { std::cout << ":(\n"; return 0; } i32 K; std::cin >> K; while (K--) { i32 x, y; std::cin >> x >> y; --x; --y; if (ans[x][y] == 'o') { ++A[x]; ++B[y]; } ans[x][y] = 'x'; } network> graph; const auto S = graph.add_vertex(); const auto T = graph.add_vertex(); const auto left = graph.add_vertices(H); const auto right = graph.add_vertices(W); for (auto i: range(0, H)) { graph.emplace_edge(S, left[i], tA[i] - A[i], tA[i]); } for (auto j: range(0, W)) { graph.emplace_edge(right[j], T, tB[j] - B[j], tB[j]); } for (auto i: range(0, H)) { for (auto j: range(0, W)) { if (ans[i][j] == '.') { graph.emplace_edge(left[i], right[j], 0, 1); } if (ans[i][j] == 'o') { graph.emplace_edge(left[i], right[j], 1, 1); } } } const auto [flow, result] = push_relabel(graph).max_flow(S, T); if (flow < std::accumulate(A.cbegin(), A.cend(), 0)) { std::cout << ":(\n"; return 0; } std::cout << "Yay!\n"; for (auto i: range(0, H)) { for (const auto &e: result[left[i]]) { ans[i][right.to_index(e.dest)] = (e.flow > 0 ? 'o' : '.'); } } for (auto &vec: ans) { for (auto x: vec) { std::cout << x; } std::cout << '\n'; } return 0; }