#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif struct Problem { int N1, N2, N3; vector edges; int s() const { return N1 + N2 + N3; } int t() const { return s() + 1; } pint get_v(int vid) const { if (vid < N1) return {0, vid}; if (vid < N1 + N2) return {1, vid - N1}; if (vid < N1 + N2 + N3) return {2, vid - N1 - N2}; exit(1); } int convert_to(int did, int i) const { if (did == 0) return i; if (did == 1) return i + N1; if (did == 2) return i + N1 + N2; exit(1); } }; Problem truncate(const Problem &p) { vector dels(3, vector()); dels.at(0).assign(p.N1, 0); dels.at(1).assign(p.N2, 0); dels.at(2).assign(p.N3, 0); for (auto [u, v] : p.edges) { if (u > v) swap(u, v); const auto [du, iu] = p.get_v(u); if (v == p.s() or v == p.t()) { if (v == p.s()) { // ++dels.at(du).front(); // --dels.at(du).at(iu); } else { // ++dels.at(du).at(iu); } } else { const auto [dv, iv] = p.get_v(v); if (du == dv) { ++dels.at(du).at(min(iu, iv)); --dels.at(du).at(max(iu, iv)); } } } for (auto &v : dels) { FOR(i, 1, v.size()) v.at(i) += v.at(i - 1); } vector> alives(3); REP(d, 3) { REP(i, dels.at(d).size()) { if (!dels.at(d).at(i)) alives.at(d).push_back(i); } } Problem ret; ret.N1 = alives.at(0).size(); ret.N2 = alives.at(1).size(); ret.N3 = alives.at(2).size(); for (auto [u, v] : p.edges) { if (u > v) swap(u, v); if (v == p.s() or v == p.t()) { const auto [du, iu] = p.get_v(u); int ju = arglb(alives.at(du), iu); if (v == p.s()) ret.edges.emplace_back(ret.convert_to(du, ju), ret.s()); if (v == p.t()) ret.edges.emplace_back(ret.convert_to(du, ju), ret.t()); } else { const auto [du, iu] = p.get_v(u); const auto [dv, iv] = p.get_v(v); int ju = arglb(alives.at(du), iu); int jv = arglb(alives.at(dv), iv); if (du == dv and ju == jv) continue; ret.edges.emplace_back(ret.convert_to(du, ju), ret.convert_to(dv, jv)); } } ret.edges = sort_unique(ret.edges); return ret; } struct Rect { int xl, xr; int yl, yr; lint area() const { lint xw = max(0, xr - xl); lint yw = max(0, yr - yl); return xw * yw; } Rect bottom_left(int x, int y) { return Rect{xl, min(xr, x), yl, min(yr, y)}; } Rect top_right(int x, int y) { return Rect{max(xl, x), xr, max(yl, y), yr}; } template friend OStream &operator<<(OStream &os, const Rect &x) { return os << "(" << x.xl << "," << x.xr << "," << x.yl << "," << x.yr << ")"; } }; lint solve(const Problem &p) { vector> switch13(p.N3 + 1), switch23(p.N3 + 1); multiset xubs, yubs; xubs.insert(p.N1 + 1); yubs.insert(p.N2 + 1); int xlb = 0, ylb = 0, zlb = 0, zub = 1 << 26; vector rectv12s; rectv12s.emplace_back(p.N1 + 1, p.N2 + 1); for (auto [u, v] : p.edges) { if (u > v) swap(u, v); const auto [du, iu] = p.get_v(u); if (v == p.s() or v == p.t()) { if (v == p.s()) { if (du == 0) chmax(xlb, iu + 1); if (du == 1) chmax(ylb, iu + 1); if (du == 2) chmax(zlb, iu + 1); } else { if (du == 0) xubs.insert(iu + 1); if (du == 1) yubs.insert(iu + 1); if (du == 2) chmin(zub, iu + 1); } } else { const auto [dv, iv] = p.get_v(v); assert(du != dv); if (du == 0 and dv == 1) { rectv12s.emplace_back(iu + 1, iv + 1); } else if (du == 0 and dv == 2) { switch13.at(iv).push_back(iu + 1); xubs.insert(iu + 1); } else if (du == 1 and dv == 2) { switch23.at(iv).push_back(iu + 1); yubs.insert(iu + 1); } else { // exit(1); } } } dbg(rectv12s); vector rects; rects.push_back(Rect{0, p.N1 + 1, 0, p.N2 + 1}); for (auto [x, y] : sort_unique(rectv12s)) { if (rects.empty()) continue; auto last = rects.back(); rects.pop_back(); while (rects.size() and rects.back().yl >= y) rects.pop_back(); if (rects.size()) { rects.back() = rects.back().bottom_left(x, y); if (!rects.back().area()) rects.pop_back(); } rects.push_back(last.bottom_left(x, y)); if (!rects.back().area()) rects.pop_back(); rects.push_back(last.top_right(x, y)); if (!rects.back().area()) rects.pop_back(); } vector area_sum{0}; vector xrs, yrs; for (auto r : rects) { auto tmp = area_sum.back() + r.area(); area_sum.push_back(tmp); xrs.push_back(r.xr); yrs.push_back(r.yr); } dbg(make_tuple(rects)); dbg(area_sum); auto calc_area_bottomleft = [&](int x, int y) -> lint { int i = min(arglb(xrs, x), arglb(yrs, y)); lint ret = area_sum.at(i); if (i < int(rects.size())) ret += rects.at(i).bottom_left(x, y).area(); return ret; }; lint ret = 0; REP(z, p.N3 + 1) { int xub = *xubs.cbegin(); int yub = *yubs.cbegin(); if (z >= zlb and z <= zub and xlb < xub and ylb < yub) { ret += calc_area_bottomleft(xub, yub) + calc_area_bottomleft(xlb, ylb); ret -= calc_area_bottomleft(xub, ylb) + calc_area_bottomleft(xlb, yub); } for (int x : switch13.at(z)) { xubs.erase(xubs.lower_bound(x)); chmax(xlb, x); } for (int y : switch23.at(z)) { yubs.erase(yubs.lower_bound(y)); chmax(ylb, y); } } return ret; } // MaxFlow based and AtCoder Library, single class, no namespace, no private variables, compatible // with C++11 Reference: template struct mf_graph { struct simple_queue_int { 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 int &t) { payload.push_back(t); } int &front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; mf_graph() : _n(0) {} 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; } std::vector level, iter; simple_queue_int que; void _bfs(int s, int t) { 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); } } } Cap _dfs(int v, int s, 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 = _dfs(e.to, s, 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(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); level.assign(_n, 0), iter.assign(_n, 0); que.clear(); Cap flow = 0; while (flow < flow_limit) { _bfs(s, t); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); Cap f = _dfs(t, s, flow_limit - flow); if (!f) break; flow += f; } return flow; } std::vector min_cut(int s) { std::vector visited(_n); simple_queue_int 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; } void dump_graphviz(std::string filename = "maxflow") const { std::ofstream ss(filename + ".DOT"); ss << "digraph{\n"; for (int i = 0; i < _n; i++) { for (const auto &e : g[i]) { if (e.cap > 0) ss << i << "->" << e.to << "[label=" << e.cap << "];\n"; } } ss << "}\n"; ss.close(); return; } int _n; struct _edge { int to, rev; Cap cap; }; std::vector> pos; std::vector> g; }; bool check_infeasible(const Problem &p) { const int gs = p.s(), gt = p.t(); mf_graph mf(gt + 1); REP(i, p.N1 - 1) mf.add_edge(i, i + 1, 1); REP(i, p.N2 - 1) mf.add_edge(p.N1 + i, p.N1 + i + 1, 1); REP(i, p.N3 - 1) mf.add_edge(p.N1 + p.N2 + i, p.N1 + p.N2 + i + 1, 1); if (p.N1) mf.add_edge(gs, 0, 1); if (p.N2) mf.add_edge(gs, p.N1, 1); if (p.N3) mf.add_edge(gs, p.N1 + p.N2, 1); if (p.N1) mf.add_edge(p.N1 - 1, gt, 1); if (p.N2) mf.add_edge(p.N1 + p.N2 - 1, gt, 1); if (p.N3) mf.add_edge(p.N1 + p.N2 + p.N3 - 1, gt, 1); for (auto [u, v] : p.edges) mf.add_edge(u, v, 1), mf.add_edge(v, u, 1); auto f = mf.flow(gs, gt, 4); return f == 4; } int main() { int M; Problem problem; cin >> problem.N1 >> problem.N2 >> problem.N3 >> M; while (M--) { int u, v; cin >> u >> v; --u, --v; if (u > v) swap(u, v); problem.edges.emplace_back(u, v); } if (check_infeasible(problem)) { puts("0"); } problem = truncate(problem); cout << solve(problem) << endl; }