#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); } }; 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/dinic.cpp" #include #line 5 "/Users/kodamankod/Desktop/Programming/Library/graph/dinic.cpp" #line 2 "/Users/kodamankod/Desktop/Programming/Library/other/fix_point.cpp" #line 4 "/Users/kodamankod/Desktop/Programming/Library/other/fix_point.cpp" template struct fix_point: private Func { explicit constexpr fix_point(Func &&func): Func(std::forward(func)) { } template constexpr decltype(auto) operator () (Args &&... args) const { return Func::operator()(*this, std::forward(args)...); } }; template constexpr decltype(auto) make_fix_point(Func &&func) { return fix_point(std::forward(func)); } /** * @title Lambda Recursion */ #line 8 "/Users/kodamankod/Desktop/Programming/Library/graph/dinic.cpp" template class dinic { 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; height_type level; 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_bfs(const vertex_type source) { for (auto &node: M_graph) { node.level = M_graph.size() + 1; } M_graph[source].level = 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(edge) > 0) { if (M_graph[edge.dest].level == M_graph.size() + 1) { M_graph[edge.dest].level = M_graph[vert].level + 1; queue.push(edge.dest); } } } } } std::vector M_graph; public: dinic() = default; explicit dinic(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 auto dfs = make_fix_point([&](const auto dfs, const vertex_type vert, const flow_type flow) -> flow_type { if (vert == sink) return flow; auto &node = M_graph[vert]; for (; node.iter < node.edges.size(); ++node.iter) { auto &edge = M_cur_edge(node); if (M_remain(edge) > 0 && node.level < M_graph[edge.dest].level) { const auto push = dfs(edge.dest, std::min(flow, M_remain(edge))); if (push > 0) { edge.flow += push; M_rev_edge(edge).flow -= push; return push; } } } return 0; }); flow_type max_capacity = 0; for (auto &node: M_graph) { for (auto &edge: node.edges) { if (!edge.is_rev) edge.flow = 0; else edge.flow = edge.capacity; max_capacity = std::max(max_capacity, edge.capacity); } } flow_type flow = 0; while (true) { M_bfs(source); if (M_graph[sink].level == M_graph.size() + 1) { return flow; } for (auto &node: M_graph) { node.iter = 0; } flow_type push; while ((push = dfs(source, max_capacity)) > 0) { flow += push; } } return flow; } template typename std::enable_if>::type max_flow(const vertex_type source, const vertex_type sink) { const auto flow = max_flow(source, sink); 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 Dinic */ #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() { size_t 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 u32 sumA = std::accumulate(A.cbegin(), A.cend(), u32(0)); const u32 sumB = std::accumulate(B.cbegin(), B.cend(), u32(0)); if (sumA != sumB) { std::cout << ":(\n"; return 0; } size_t K; std::cin >> K; std::vector> ans(H, std::vector(W, '.')); for (auto none: range(0, K)) { size_t x, y; std::cin >> x >> y; --x; --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], A[i]); } for (auto j: range(0, W)) { graph.emplace_edge(right[j], T, B[j]); } for (auto i: range(0, H)) { for (auto j: range(0, W)) { if (ans[i][j] != 'x') { graph.emplace_edge(left[i], right[j], 1); } } } const auto [flow, result] = dinic(graph).max_flow(S, T); if (flow != sumA) { std::cout << ":(\n"; return 0; } std::cout << "Yay!\n"; for (auto i: range(0, H)) { for (const auto &e: result[left[i]]) { if (e.flow > 0) { ans[i][right.to_index(e.dest)] = 'o'; } } } for (const auto &vec: ans) { for (auto x: vec) { std::cout << x; } std::cout << '\n'; } return 0; }