#line 1 "main.cpp" #define PROBLEM "https://yukicoder.me/problems/no/957" #line 2 "/Users/kodamankod/Desktop/Programming/Library/graph/network.cpp" #include #include #include #include template class network { public: using vertex_type = typename Edge::vertex_type; using edge_type = Edge; using size_type = size_t; protected: std::vector> M_graph; public: network() = default; [[nodiscard]] vertex_type add_vertex() { vertex_type res = M_graph.size(); M_graph.push_back({ }); return res; } [[nodiscard]] std::vector add_vertices(const size_type size) { size_type cur = M_graph.size(); std::vector res(size); std::iota(res.begin(), res.end(), cur); M_graph.resize(cur + size); return res; } void add_edge(const vertex_type src, const edge_type &edge) { M_graph[src].push_back(edge); } template void emplace_edge(const vertex_type src, Args&&... args) { M_graph[src].emplace_back(std::forward(args)...); } 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 = size_t; const vertex_type dest; explicit base_edge(const vertex_type dest): dest(dest) { } }; template class flow_edge: public base_edge { public: using vertex_type = typename base_edge::vertex_type; using flow_type = Flow; const flow_type capacity; flow_type flow; explicit flow_edge(const vertex_type dest, const flow_type capacity): base_edge(dest), capacity(capacity), flow() { } }; 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 vertex_type dest, const flow_type capacity, const cost_type cost): flow_edge(dest, capacity), cost(cost) { } }; /** * @title Network */ #line 2 "/Users/kodamankod/Desktop/Programming/Library/graph/push_relabel.cpp" #line 5 "/Users/kodamankod/Desktop/Programming/Library/graph/push_relabel.cpp" #include #include #line 9 "/Users/kodamankod/Desktop/Programming/Library/graph/push_relabel.cpp" #include 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 = size_t; static_assert(std::is_integral::value, "invalid flow type :: non-integral"); private: class residual_edge { public: const vertex_type dest; flow_type remain; const size_type rev; const bool is_rev; explicit residual_edge(const vertex_type dest, const flow_type remain, const size_type rev, const bool is_rev): dest(dest), remain(remain), 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; }; residual_edge &M_cur_edge(const vertex_type node) { return M_graph[node].edges[M_graph[node].iter]; } residual_edge &M_rev_edge(const residual_edge &edge) { return M_graph[edge.dest].edges[edge.rev]; } void M_push(const vertex_type node, residual_edge &edge) { auto flow = std::min(M_graph[node].excess, edge.remain); edge.remain -= flow; M_rev_edge(edge).remain += flow; M_graph[node].excess -= flow; M_graph[edge.dest].excess += flow; } void M_relabel(const vertex_type node) { height_type min = M_graph.size() + 1; for (const auto &edge: M_graph[node].edges) { if (edge.remain > 0 && min > M_graph[edge.dest].height + 1) { min = M_graph[edge.dest].height + 1; } } M_graph[node].height = min; } 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.dest, edge.capacity, M_graph[edge.dest].edges.size(), false); M_graph[edge.dest].edges.emplace_back(src, 0, M_graph[src].edges.size() - 1, true); } } } flow_type max_flow(const vertex_type source, const vertex_type sink) { 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.height = M_graph.size() + 1; node.iter = 0; for (auto &edge: node.edges) { if (edge.is_rev) edge.remain = 0; else edge.remain = edge.remain + M_rev_edge(edge).remain; } } M_graph[sink].height = 0; std::queue queue; queue.push(sink); while (!queue.empty()) { const auto node = queue.front(); queue.pop(); for (const auto &edge: M_graph[node].edges) { if (M_rev_edge(edge).remain > 0) { if (M_graph[edge.dest].height == M_graph.size() + 1) { M_graph[edge.dest].height = M_graph[node].height + 1; queue.push(edge.dest); } } } } if (M_graph[source].height == M_graph.size() + 1) { return 0; } for (auto &edge: M_graph[source].edges) { M_graph[source].excess += edge.remain; M_push(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 node = active.top(max_active); active.pop(max_active); while (true) { auto &edge = M_cur_edge(node); if (edge.remain > 0 && M_graph[node].height == M_graph[edge.dest].height + 1) { if (M_graph[edge.dest].excess == 0 && edge.dest != sink) { active.push(M_graph[edge.dest].height, edge.dest); max_active = std::max(max_active, M_graph[edge.dest].height); } M_push(node, edge); if (M_graph[node].excess == 0) { break; } } M_graph[node].iter++; if (M_graph[node].iter == M_graph[node].edges.size()) { M_graph[node].iter = 0; if (level.more_than_one(M_graph[node].height)) { level.erase(node); M_relabel(node); if (M_graph[node].height > min_gap) { M_graph[node].height = M_graph.size() + 1; break; } if (M_graph[node].height == min_gap) { ++min_gap; } level.insert(M_graph[node].height, node); } else { for (height_type index = M_graph[node].height; index < min_gap; ++index) { level.apply_all(index, [&](const vertex_type tmp) { M_graph[tmp].height = M_graph.size() + 1; }); level.clear(index); } break; } } } max_active = std::min(max_active, min_gap - 1); } return M_graph[sink].excess; } }; /** * @title Push Relabel */ #line 2 "/Users/kodamankod/Desktop/Programming/Library/other/fast_io.cpp" #line 4 "/Users/kodamankod/Desktop/Programming/Library/other/fast_io.cpp" #include #include #include namespace fast_io { static constexpr size_t buf_size = 1 << 18; static constexpr size_t buf_margin = 1; static constexpr size_t block_size = 10000; static constexpr size_t integer_size = 20; static char inbuf[buf_size + buf_margin] = {}; static char outbuf[buf_size + buf_margin] = {}; static char block_str[block_size * 4 + buf_margin] = {}; static constexpr uint64_t power10[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 10000000000000000000u }; class scanner { private: size_t M_in_pos = 0, M_in_end = buf_size; void M_load() { M_in_end = fread(inbuf, 1, buf_size, stdin); inbuf[M_in_end] = '\0'; } void M_reload() { size_t length = M_in_end - M_in_pos; memmove(inbuf, inbuf + M_in_pos, length); M_in_end = length + fread(inbuf + length, 1, buf_size - length, stdin); inbuf[M_in_end] = '\0'; M_in_pos = 0; } void M_ignore_space() { while (inbuf[M_in_pos] <= ' ') { if (__builtin_expect(++M_in_pos == M_in_end, 0)) M_reload(); } } char M_next() { return inbuf[M_in_pos++]; } char M_next_nonspace() { M_ignore_space(); return inbuf[M_in_pos++]; } public: scanner() { M_load(); } void scan(char &c) { c = M_next_nonspace(); } void scan(std::string &s) { M_ignore_space(); s = ""; do { size_t start = M_in_pos; while (inbuf[M_in_pos] > ' ') ++M_in_pos; s += std::string(inbuf + start, inbuf + M_in_pos); if (inbuf[M_in_pos] != '\0') break; M_reload(); } while (true); } template typename std::enable_if::value, void>::type scan(T &x) { char c = M_next_nonspace(); if (__builtin_expect(M_in_pos + integer_size >= M_in_end, 0)) M_reload(); bool n = false; if (c == '-') n = true, x = 0; else x = c & 15; while ((c = M_next()) >= '0') x = x * 10 + (c & 15); if (n) x = -x; } template void scan(T &x, Args&... args) { scan(x); scan(args...); } template scanner& operator >> (T &x) { scan(x); return *this; } }; class printer { private: size_t M_out_pos = 0; void M_flush() { fwrite(outbuf, 1, M_out_pos, stdout); M_out_pos = 0; } void M_precompute() { for (size_t i = 0; i < block_size; ++i) { size_t j = 4, k = i; while (j--) { block_str[i * 4 + j] = k % 10 + '0'; k /= 10; } } } static constexpr size_t S_integer_digits(uint64_t n) { if (n >= power10[10]) { if (n >= power10[19]) return 20; if (n >= power10[18]) return 19; if (n >= power10[17]) return 18; if (n >= power10[16]) return 17; if (n >= power10[15]) return 16; if (n >= power10[14]) return 15; if (n >= power10[13]) return 14; if (n >= power10[12]) return 13; if (n >= power10[11]) return 12; return 11; } else { if (n >= power10[9]) return 10; if (n >= power10[8]) return 9; if (n >= power10[7]) return 8; if (n >= power10[6]) return 7; if (n >= power10[5]) return 6; if (n >= power10[4]) return 5; if (n >= power10[3]) return 4; if (n >= power10[2]) return 3; if (n >= power10[1]) return 2; return 1; } } public: printer() { M_precompute(); } ~printer() { M_flush(); } void print(char c) { outbuf[M_out_pos++] = c; if (__builtin_expect(M_out_pos == buf_size, 0)) M_flush(); } void print(const char *s) { while (*s != 0) { outbuf[M_out_pos++] = *s++; if (M_out_pos == buf_size) M_flush(); } } void print(const std::string &s) { for (auto c: s) { outbuf[M_out_pos++] = c; if (M_out_pos == buf_size) M_flush(); } } template typename std::enable_if::value, void>::type print(T x) { if (__builtin_expect(M_out_pos + integer_size >= buf_size, 0)) M_flush(); if (x < 0) print('-'), x = -x; size_t digit = S_integer_digits(x); size_t len = digit; while (len >= 4) { len -= 4; memcpy(outbuf + M_out_pos + len, block_str + (x % block_size) * 4, 4); x /= 10000; } memcpy(outbuf + M_out_pos, block_str + x * 4 + 4 - len, len); M_out_pos += digit; } template void print(const T &x, const Args&... args) { print(x); print(' '); print(args...); } template void println(const Args&... args) { print(args...); print('\n'); } template printer& operator << (const T &x) { print(x); return *this; } }; }; /** * @title Fast Input/Output */ #line 7 "main.cpp" #line 10 "main.cpp" fast_io::scanner cin; fast_io::printer cout; int main() { size_t H, W; cin.scan(H, W); network> graph; const auto source = graph.add_vertex(); const auto sink = graph.add_vertex(); const auto row = graph.add_vertices(H); const auto column = graph.add_vertices(W); std::vector accum(H); for (size_t i = 0; i < H; ++i) { for (size_t j = 0; j < W; ++j) { int32_t g; cin.scan(g); accum[i] += g; graph.emplace_edge(row[i], column[j], g); } } int64_t sum = 0; for (size_t i = 0; i < H; ++i) { int64_t r; cin.scan(r); int64_t min = std::min(accum[i], r); sum += r - min; graph.emplace_edge(source, row[i], accum[i] - min); } for (size_t j = 0; j < W; ++j) { int64_t r; cin.scan(r); sum += r; graph.emplace_edge(column[j], sink, r); } cout.println(sum - push_relabel(graph).max_flow(source, sink)); return 0; }