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#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "my_template.hpp" #include "graph/maximum_matching_size.hpp" #include "flow/bipartite.hpp" void test_bipartite() { FOR(N, 1, 50) { FOR(M, RNG(0, N * (N - 1) / 2 + 1)) { Graph<bool, 0> G(N); FOR(M) { int a = RNG(0, N); int b = RNG(0, N); if (a % 2 == b % 2) continue; G.add(a, b); } G.build(); BipartiteMatching<decltype(G)> X(G); int a = len(X.matching()); int b = maximum_matching_size(G); assert(a == b); } } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test_bipartite(); solve(); return 0; }
#line 1 "test/1_mytest/tutte.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #line 1 "my_template.hpp" #if defined(LOCAL) #include <my_template_compiled.hpp> #else // https://codeforces.com/blog/entry/96344 #pragma GCC optimize("Ofast,unroll-loops") // いまの CF だとこれ入れると動かない? // #pragma GCC target("avx2,popcnt") #include <bits/stdc++.h> using namespace std; using ll = long long; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'010'000'000; template <> constexpr ll infty<ll> = 2'020'000'000'000'000'000; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000; template <> constexpr double infty<double> = infty<ll>; template <> constexpr long double infty<long double> = infty<ll>; using pi = pair<ll, ll>; using vi = vector<ll>; template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using vvvvvc = vector<vvvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template <typename T> T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template <typename T> T ceil(T x, T y) { return floor(x + y - 1, y); } template <typename T> T bmod(T x, T y) { return x - y * floor(x, y); } template <typename T> pair<T, T> divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template <typename T, typename U> T SUM(const vector<U> &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template <typename T> T POP(deque<T> &que) { T a = que.front(); que.pop_front(); return a; } template <typename T> T POP(pq<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(pqg<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(vc<T> &que) { T a = que.back(); que.pop_back(); return a; } template <typename F> ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template <typename F> double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc<int> s_to_vi(const string &S, char first_char) { vc<int> A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template <typename T, typename U> vector<T> cumsum(vector<U> &A, int off = 1) { int N = A.size(); vector<T> B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template <typename T> vector<int> argsort(const vector<T> &A) { vector<int> ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) { vc<T> B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } template <typename T, typename... Vectors> void concat(vc<T> &first, const Vectors &... others) { vc<T> &res = first; (res.insert(res.end(), others.begin(), others.end()), ...); } #endif #line 3 "test/1_mytest/tutte.test.cpp" #line 2 "random/base.hpp" u64 RNG_64() { static uint64_t x_ = uint64_t(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL; x_ ^= x_ << 7; return x_ ^= x_ >> 9; } u64 RNG(u64 lim) { return RNG_64() % lim; } ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); } #line 2 "mod/modint61.hpp" struct modint61 { static constexpr u64 mod = (1ULL << 61) - 1; u64 val; constexpr modint61() : val(0ULL) {} constexpr modint61(u32 x) : val(x) {} constexpr modint61(u64 x) : val(x % mod) {} constexpr modint61(int x) : val((x < 0) ? (x + static_cast<ll>(mod)) : x) {} constexpr modint61(ll x) : val(((x %= static_cast<ll>(mod)) < 0) ? (x + static_cast<ll>(mod)) : x) {} static constexpr u64 get_mod() { return mod; } modint61 &operator+=(const modint61 &a) { val = ((val += a.val) >= mod) ? (val - mod) : val; return *this; } modint61 &operator-=(const modint61 &a) { val = ((val -= a.val) >= mod) ? (val + mod) : val; return *this; } modint61 &operator*=(const modint61 &a) { const unsigned __int128 y = static_cast<unsigned __int128>(val) * a.val; val = (y >> 61) + (y & mod); val = (val >= mod) ? (val - mod) : val; return *this; } modint61 operator-() const { return modint61(val ? mod - val : u64(0)); } modint61 &operator/=(const modint61 &a) { return (*this *= a.inverse()); } modint61 operator+(const modint61 &p) const { return modint61(*this) += p; } modint61 operator-(const modint61 &p) const { return modint61(*this) -= p; } modint61 operator*(const modint61 &p) const { return modint61(*this) *= p; } modint61 operator/(const modint61 &p) const { return modint61(*this) /= p; } bool operator<(const modint61 &other) const { return val < other.val; } bool operator==(const modint61 &p) const { return val == p.val; } bool operator!=(const modint61 &p) const { return val != p.val; } modint61 inverse() const { ll a = val, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b), swap(u -= t * v, v); } return modint61(u); } modint61 pow(ll n) const { assert(n >= 0); modint61 ret(1), mul(val); while (n > 0) { if (n & 1) ret *= mul; mul *= mul, n >>= 1; } return ret; } }; #ifdef FASTIO void rd(modint61 &x) { fastio::rd(x.val); assert(0 <= x.val && x.val < modint61::mod); } void wt(modint61 x) { fastio::wt(x.val); } #endif #line 1 "linalg/matrix_rank.hpp" template <typename T> int matrix_rank(vc<vc<T>> a, int n = -1, int m = -1) { if (n == 0) return 0; if (n == -1) { n = len(a), m = len(a[0]); } assert(n == len(a) && m == len(a[0])); int rk = 0; FOR(j, m) { if (rk == n) break; if (a[rk][j] == 0) { FOR(i, rk + 1, n) if (a[i][j] != T(0)) { swap(a[rk], a[i]); break; } } if (a[rk][j] == 0) continue; T c = T(1) / a[rk][j]; FOR(k, j, m) a[rk][k] *= c; FOR(i, rk + 1, n) { T c = a[i][j]; FOR3(k, j, m) { a[i][k] -= a[rk][k] * c; } } ++rk; } return rk; } #line 4 "graph/maximum_matching_size.hpp" template <typename GT> int maximum_matching_size(GT& G) { static_assert(!GT::is_directed); using mint = modint61; int N = G.N; vv(mint, tutte, N, N); for (auto&& e: G.edges) { mint x = RNG(mint::get_mod()); int i = e.frm, j = e.to; tutte[i][j] += x; tutte[j][i] -= x; } return matrix_rank(tutte, N, N) / 2; } #line 2 "graph/base.hpp" template <typename T> struct Edge { int frm, to; T cost; int id; }; template <typename T = int, bool directed = false> struct Graph { static constexpr bool is_directed = directed; int N, M; using cost_type = T; using edge_type = Edge<T>; vector<edge_type> edges; vector<int> indptr; vector<edge_type> csr_edges; vc<int> vc_deg, vc_indeg, vc_outdeg; bool prepared; class OutgoingEdges { public: OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {} const edge_type* begin() const { if (l == r) { return 0; } return &G->csr_edges[l]; } const edge_type* end() const { if (l == r) { return 0; } return &G->csr_edges[r]; } private: const Graph* G; int l, r; }; bool is_prepared() { return prepared; } Graph() : N(0), M(0), prepared(0) {} Graph(int N) : N(N), M(0), prepared(0) {} void build(int n) { N = n, M = 0; prepared = 0; edges.clear(); indptr.clear(); csr_edges.clear(); vc_deg.clear(); vc_indeg.clear(); vc_outdeg.clear(); } void add(int frm, int to, T cost = 1, int i = -1) { assert(!prepared); assert(0 <= frm && 0 <= to && to < N); if (i == -1) i = M; auto e = edge_type({frm, to, cost, i}); edges.eb(e); ++M; } #ifdef FASTIO // wt, off void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); } void read_graph(int M, bool wt = false, int off = 1) { for (int m = 0; m < M; ++m) { INT(a, b); a -= off, b -= off; if (!wt) { add(a, b); } else { T c; read(c); add(a, b, c); } } build(); } #endif void build() { assert(!prepared); prepared = true; indptr.assign(N + 1, 0); for (auto&& e: edges) { indptr[e.frm + 1]++; if (!directed) indptr[e.to + 1]++; } for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; } auto counter = indptr; csr_edges.resize(indptr.back() + 1); for (auto&& e: edges) { csr_edges[counter[e.frm]++] = e; if (!directed) csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id}); } } OutgoingEdges operator[](int v) const { assert(prepared); return {this, indptr[v], indptr[v + 1]}; } vc<int> deg_array() { if (vc_deg.empty()) calc_deg(); return vc_deg; } pair<vc<int>, vc<int>> deg_array_inout() { if (vc_indeg.empty()) calc_deg_inout(); return {vc_indeg, vc_outdeg}; } int deg(int v) { if (vc_deg.empty()) calc_deg(); return vc_deg[v]; } int in_deg(int v) { if (vc_indeg.empty()) calc_deg_inout(); return vc_indeg[v]; } int out_deg(int v) { if (vc_outdeg.empty()) calc_deg_inout(); return vc_outdeg[v]; } #ifdef FASTIO void debug() { print("Graph"); if (!prepared) { print("frm to cost id"); for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id); } else { print("indptr", indptr); print("frm to cost id"); FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id); } } #endif vc<int> new_idx; vc<bool> used_e; // G における頂点 V[i] が、新しいグラフで i になるようにする // {G, es} // sum(deg(v)) の計算量になっていて、 // 新しいグラフの n+m より大きい可能性があるので注意 Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) { if (len(new_idx) != N) new_idx.assign(N, -1); int n = len(V); FOR(i, n) new_idx[V[i]] = i; Graph<T, directed> G(n); vc<int> history; FOR(i, n) { for (auto&& e: (*this)[V[i]]) { if (len(used_e) <= e.id) used_e.resize(e.id + 1); if (used_e[e.id]) continue; int a = e.frm, b = e.to; if (new_idx[a] != -1 && new_idx[b] != -1) { history.eb(e.id); used_e[e.id] = 1; int eid = (keep_eid ? e.id : -1); G.add(new_idx[a], new_idx[b], e.cost, eid); } } } FOR(i, n) new_idx[V[i]] = -1; for (auto&& eid: history) used_e[eid] = 0; G.build(); return G; } Graph<T, true> to_directed_tree(int root = -1) { if (root == -1) root = 0; assert(!is_directed && prepared && M == N - 1); Graph<T, true> G1(N); vc<int> par(N, -1); auto dfs = [&](auto& dfs, int v) -> void { for (auto& e: (*this)[v]) { if (e.to == par[v]) continue; par[e.to] = v, dfs(dfs, e.to); } }; dfs(dfs, root); for (auto& e: edges) { int a = e.frm, b = e.to; if (par[a] == b) swap(a, b); assert(par[b] == a); G1.add(a, b, e.cost); } G1.build(); return G1; } private: void calc_deg() { assert(vc_deg.empty()); vc_deg.resize(N); for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++; } void calc_deg_inout() { assert(vc_indeg.empty()); vc_indeg.resize(N); vc_outdeg.resize(N); for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; } } }; #line 2 "graph/bipartite_vertex_coloring.hpp" #line 2 "ds/unionfind/unionfind.hpp" struct UnionFind { int n, n_comp; vc<int> dat; // par or (-size) UnionFind(int n = 0) { build(n); } void build(int m) { n = m, n_comp = m; dat.assign(n, -1); } void reset() { build(n); } int operator[](int x) { while (dat[x] >= 0) { int pp = dat[dat[x]]; if (pp < 0) { return dat[x]; } x = dat[x] = pp; } return x; } ll size(int x) { x = (*this)[x]; return -dat[x]; } bool merge(int x, int y) { x = (*this)[x], y = (*this)[y]; if (x == y) return false; if (-dat[x] < -dat[y]) swap(x, y); dat[x] += dat[y], dat[y] = x, n_comp--; return true; } vc<int> get_all() { vc<int> A(n); FOR(i, n) A[i] = (*this)[i]; return A; } }; #line 5 "graph/bipartite_vertex_coloring.hpp" // 二部グラフでなかった場合には empty template <typename GT> vc<int> bipartite_vertex_coloring(GT& G) { assert(!GT::is_directed); assert(G.is_prepared()); int n = G.N; UnionFind uf(2 * n); for (auto&& e: G.edges) { int u = e.frm, v = e.to; uf.merge(u + n, v), uf.merge(u, v + n); } vc<int> color(2 * n, -1); FOR(v, n) if (uf[v] == v && color[uf[v]] < 0) { color[uf[v]] = 0; color[uf[v + n]] = 1; } FOR(v, n) color[v] = color[uf[v]]; color.resize(n); FOR(v, n) if (uf[v] == uf[v + n]) return {}; return color; } #line 3 "graph/strongly_connected_component.hpp" template <typename GT> pair<int, vc<int>> strongly_connected_component(GT& G) { static_assert(GT::is_directed); assert(G.is_prepared()); int N = G.N; int C = 0; vc<int> comp(N), low(N), ord(N, -1), path; int now = 0; auto dfs = [&](auto& dfs, int v) -> void { low[v] = ord[v] = now++; path.eb(v); for (auto&& [frm, to, cost, id]: G[v]) { if (ord[to] == -1) { dfs(dfs, to), chmin(low[v], low[to]); } else { chmin(low[v], ord[to]); } } if (low[v] == ord[v]) { while (1) { int u = POP(path); ord[u] = N, comp[u] = C; if (u == v) break; } ++C; } }; FOR(v, N) { if (ord[v] == -1) dfs(dfs, v); } FOR(v, N) comp[v] = C - 1 - comp[v]; return {C, comp}; } template <typename GT> Graph<int, 1> scc_dag(GT& G, int C, vc<int>& comp) { Graph<int, 1> DAG(C); vvc<int> edges(C); for (auto&& e: G.edges) { int x = comp[e.frm], y = comp[e.to]; if (x == y) continue; edges[x].eb(y); } FOR(c, C) { UNIQUE(edges[c]); for (auto&& to: edges[c]) DAG.add(c, to); } DAG.build(); return DAG; } #line 4 "flow/bipartite.hpp" template <typename GT> struct BipartiteMatching { int N; GT& G; vc<int> color; vc<int> dist, match; vc<int> vis; BipartiteMatching(GT& G) : N(G.N), G(G), dist(G.N, -1), match(G.N, -1) { color = bipartite_vertex_coloring(G); if (N > 0) assert(!color.empty()); while (1) { bfs(); vis.assign(N, false); int flow = 0; FOR(v, N) if (!color[v] && match[v] == -1 && dfs(v))++ flow; if (!flow) break; } } BipartiteMatching(GT& G, vc<int> color) : N(G.N), G(G), color(color), dist(G.N, -1), match(G.N, -1) { while (1) { bfs(); vis.assign(N, false); int flow = 0; FOR(v, N) if (!color[v] && match[v] == -1 && dfs(v))++ flow; if (!flow) break; } } void bfs() { dist.assign(N, -1); queue<int> que; FOR(v, N) if (!color[v] && match[v] == -1) que.emplace(v), dist[v] = 0; while (!que.empty()) { int v = que.front(); que.pop(); for (auto&& e: G[v]) { dist[e.to] = 0; int w = match[e.to]; if (w != -1 && dist[w] == -1) dist[w] = dist[v] + 1, que.emplace(w); } } } bool dfs(int v) { vis[v] = 1; for (auto&& e: G[v]) { int w = match[e.to]; if (w == -1 || (!vis[w] && dist[w] == dist[v] + 1 && dfs(w))) { match[e.to] = v, match[v] = e.to; return true; } } return false; } vc<pair<int, int>> matching() { vc<pair<int, int>> res; FOR(v, N) if (v < match[v]) res.eb(v, match[v]); return res; } vc<int> vertex_cover() { vc<int> res; FOR(v, N) if (color[v] ^ (dist[v] == -1)) { res.eb(v); } return res; } vc<int> independent_set() { vc<int> res; FOR(v, N) if (!(color[v] ^ (dist[v] == -1))) { res.eb(v); } return res; } vc<int> edge_cover() { vc<bool> done(N); vc<int> res; for (auto&& e: G.edges) { if (done[e.frm] || done[e.to]) continue; if (match[e.frm] == e.to) { res.eb(e.id); done[e.frm] = done[e.to] = 1; } } for (auto&& e: G.edges) { if (!done[e.frm]) { res.eb(e.id); done[e.frm] = 1; } if (!done[e.to]) { res.eb(e.id); done[e.to] = 1; } } sort(all(res)); return res; } /* Dulmage–Mendelsohn decomposition https://en.wikipedia.org/wiki/Dulmage%E2%80%93Mendelsohn_decomposition http://www.misojiro.t.u-tokyo.ac.jp/~murota/lect-ouyousurigaku/dm050410.pdf https://hitonanode.github.io/cplib-cpp/graph/dulmage_mendelsohn_decomposition.hpp.html - 最大マッチングとしてありうる iff 同じ W を持つ - 辺 uv が必ず使われる:同じ W を持つ辺が唯一 - color=0 から 1 への辺:W[l] <= W[r] - color=0 の点が必ず使われる:W=1,2,...,K - color=1 の点が必ず使われる:W=0,1,...,K-1 */ pair<int, vc<int>> DM_decomposition() { // 非飽和点からの探索 vc<int> W(N, -1); vc<int> que; auto add = [&](int v, int x) -> void { if (W[v] == -1) { W[v] = x; que.eb(v); } }; FOR(v, N) if (match[v] == -1 && color[v] == 0) add(v, 0); FOR(v, N) if (match[v] == -1 && color[v] == 1) add(v, infty<int>); while (len(que)) { auto v = POP(que); if (match[v] != -1) add(match[v], W[v]); if (color[v] == 0 && W[v] == 0) { for (auto&& e: G[v]) { add(e.to, W[v]); } } if (color[v] == 1 && W[v] == infty<int>) { for (auto&& e: G[v]) { add(e.to, W[v]); } } } // 残った点からなるグラフを作って強連結成分分解 vc<int> V; FOR(v, N) if (W[v] == -1) V.eb(v); int n = len(V); Graph<bool, 1> DG(n); FOR(i, n) { int v = V[i]; if (match[v] != -1) { int j = LB(V, match[v]); DG.add(i, j); } if (color[v] == 0) { for (auto&& e: G[v]) { if (W[e.to] != -1 || e.to == match[v]) continue; int j = LB(V, e.to); DG.add(i, j); } } } DG.build(); auto [K, comp] = strongly_connected_component(DG); K += 1; // 答 FOR(i, n) { W[V[i]] = 1 + comp[i]; } FOR(v, N) if (W[v] == infty<int>) W[v] = K; return {K, W}; } #ifdef FASTIO void debug() { print("match", match); print("min vertex covor", vertex_cover()); print("max indep set", independent_set()); print("min edge cover", edge_cover()); } #endif }; #line 6 "test/1_mytest/tutte.test.cpp" void test_bipartite() { FOR(N, 1, 50) { FOR(M, RNG(0, N * (N - 1) / 2 + 1)) { Graph<bool, 0> G(N); FOR(M) { int a = RNG(0, N); int b = RNG(0, N); if (a % 2 == b % 2) continue; G.add(a, b); } G.build(); BipartiteMatching<decltype(G)> X(G); int a = len(X.matching()); int b = maximum_matching_size(G); assert(a == b); } } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test_bipartite(); solve(); return 0; }