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#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "my_template.hpp" #include "random/random_graph.hpp" #include "graph/count/count_C3_C4.hpp" #include "graph/find_C4.hpp" void test() { FOR(N, 20) { FOR(50) { Graph<int, 0> G(N); for (auto& [a, b]: random_graph<false>(N, true)) G.add(a, b); G.build(); vv(int, adj, N, N); for (auto& e: G.edges) adj[e.frm][e.to] += 1, adj[e.to][e.frm] += 1; auto [a, b, c, d] = find_C4(G); ll cnt = count_C3_C4(G).se; if (cnt == 0) { assert(a == -1); } else { assert(adj[a][b] && adj[b][c] && adj[c][d] && adj[d][a]); } } } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test(); solve(); return 0; }
#line 1 "test/1_mytest/find_C4.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_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(ll x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(u64 x) { return (__builtin_parity(x) & 1 ? -1 : 1); } // (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 kth_bit(int k) { return T(1) << k; } template <typename T> bool has_kth_bit(T x, int k) { return x >> k & 1; } 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/find_C4.test.cpp" #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 "random/base.hpp" u64 RNG_64() { static u64 x_ = u64(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 "random/shuffle.hpp" template <typename T> void shuffle(vc<T>& A) { FOR(i, len(A)) { int j = RNG(0, i + 1); if (i != j) swap(A[i], A[j]); } } #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 "random/random_graph.hpp" void random_relabel(int N, vc<pair<int, int>>& G) { shuffle(G); vc<int> A(N); FOR(i, N) A[i] = i; shuffle(A); for (auto& [a, b]: G) a = A[a], b = A[b]; } template <int DIRECTED> vc<pair<int, int>> random_graph(int n, bool simple) { vc<pair<int, int>> G, cand; FOR(a, n) FOR(b, n) { if (simple && a == b) continue; if (!DIRECTED && a > b) continue; cand.eb(a, b); } int m = RNG(0, len(cand) + 1); set<int> ss; FOR(m) { while (1) { int i = RNG(0, len(cand)); if (simple && ss.count(i)) continue; ss.insert(i); auto [a, b] = cand[i]; G.eb(a, b); break; } } random_relabel(n, G); return G; } vc<pair<int, int>> random_tree(int n) { vc<pair<int, int>> G; FOR(i, 1, n) { G.eb(RNG(0, i), i); } random_relabel(n, G); return G; } // EDGE = true: 各辺が唯一のサイクル(関節点でサイクルまたは辺) // EDGE = false: 各頂点が唯一のサイクル(橋でサイクルまたは辺) vc<pair<int, int>> random_cactus(int N, bool EDGE) { if (!EDGE) { // n 頂点を 1 または 3 以上に分割 vvc<int> A; int n = RNG(1, N + 1); vc<int> S(n, 1); int rest = N - n; while (rest > 0) { int k = RNG(0, n); if (S[k] == 1) { if (rest == 1) { S.eb(1), rest = 0; } else { S[k] += 2, rest -= 2; } } else { S[k]++, rest--; } } n = len(S); int p = 0; FOR(i, n) { vc<int> C; FOR(v, p, p + S[i]) C.eb(v); A.eb(C); p += S[i]; } int m = len(A); auto H = random_tree(m); vc<pair<int, int>> G; FOR(i, m) { vc<int>& V = A[i]; if (len(V) == 1) continue; FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); } } for (auto& [c1, c2]: H) { int a = A[c1][RNG(0, len(A[c1]))]; int b = A[c2][RNG(0, len(A[c2]))]; G.eb(a, b); } random_relabel(N, G); return G; } assert(EDGE); if (N == 1) return {}; int n = RNG(1, N); vc<int> S(n, 2); int rest = N - 1 - n; while (rest > 0) { int k = RNG(0, n); S[k]++, --rest; } vvc<int> A; int p = 0; FOR(i, n) { vc<int> C; FOR(v, p, p + S[i]) C.eb(v); A.eb(C); p += S[i]; } assert(p == N + n - 1); UnionFind uf(p); auto H = random_tree(n); for (auto& [c1, c2]: H) { int a = A[c1][RNG(0, len(A[c1]))]; int b = A[c2][RNG(0, len(A[c2]))]; uf.merge(a, b); } vc<int> new_idx(p); int x = 0; FOR(i, p) if (uf[i] == i) new_idx[i] = x++; assert(x == N); FOR(i, p) new_idx[i] = new_idx[uf[i]]; vc<pair<int, int>> G; FOR(i, n) { vc<int>& V = A[i]; for (auto& v: V) v = new_idx[v]; if (len(V) == 2) { G.eb(V[0], V[1]); } else { FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); } } } random_relabel(N, G); return G; } #line 2 "graph/count/count_C3_C4.hpp" // 各点に対してその点を含む C3, C4 を数える // simple graph を仮定 template <typename GT> pair<vi, vi> count_C3_C4_pointwise(GT &G) { static_assert(!GT::is_directed); int N = G.N; auto deg = G.deg_array(); auto I = argsort(deg); reverse(all(I)); vc<int> rk(N); FOR(i, N) rk[I[i]] = i; // 遷移先を降順に並べる vvc<int> TO(N); for (auto &&e: G.edges) { int a = rk[e.frm], b = rk[e.to]; TO[a].eb(b), TO[b].eb(a); } FOR(v, N) { sort(all(TO[v])), reverse(all(TO[v])); } vc<int> A(N); vi C3(N), C4(N); FOR(a, N) { for (auto &b: TO[a]) TO[b].pop_back(); for (auto &b: TO[a]) { for (auto &c: TO[b]) { C4[a] += A[c], C4[c] += A[c], A[c] += 1; } } for (auto &b: TO[a]) { C3[a] += A[b], C3[b] += A[b] + A[b]; for (auto &c: TO[b]) { C4[b] += A[c] - 1; } } for (auto &b: TO[a]) { for (auto &c: TO[b]) { A[c] = 0; } } } for (auto &x: C3) x /= 2; C3 = rearrange(C3, rk), C4 = rearrange(C4, rk); return {C3, C4}; } // (2e5,5e5) で 500 ms // https://codeforces.com/gym/104053/problem/K template <typename GT> pair<ll, ll> count_C3_C4(GT &G) { static_assert(!GT::is_directed); int N = G.N; ll x3 = 0, x4 = 0; auto deg = G.deg_array(); auto I = argsort(deg); reverse(all(I)); vc<int> rk(N); FOR(i, N) rk[I[i]] = i; // 遷移先を降順に並べる vvc<int> TO(N); for (auto &&e: G.edges) { int a = rk[e.frm], b = rk[e.to]; if (a != b) TO[a].eb(b), TO[b].eb(a); } FOR(v, N) { sort(all(TO[v])); reverse(all(TO[v])); } vc<int> A(N); FOR(a, N) { for (auto &&b: TO[a]) TO[b].pop_back(); for (auto &&b: TO[a]) { for (auto &&c: TO[b]) { x4 += A[c]++; } } for (auto &&b: TO[a]) { x3 += A[b]; } for (auto &&b: TO[a]) { for (auto &&c: TO[b]) { A[c] = 0; } } } x3 /= 2; return {x3, x4}; } #line 2 "graph/find_C4.hpp" // 無向グラフから C4 をひとつ見つける // https://codeforces.com/problemset/problem/1468/M template <typename GT> tuple<int, int, int, int> find_C4(GT& G) { static_assert(!GT::is_directed); int N = G.N; auto deg = G.deg_array(); auto I = argsort(deg); reverse(all(I)); vc<int> rk(N); FOR(i, N) rk[I[i]] = i; // 遷移先を降順に並べる vvc<int> TO(N); for (auto&& e: G.edges) { int a = rk[e.frm], b = rk[e.to]; TO[a].eb(b); TO[b].eb(a); } FOR(v, N) { sort(all(TO[v])); reverse(all(TO[v])); } vc<int> par(N, -1); FOR(a, N) { for (auto&& b: TO[a]) TO[b].pop_back(); for (auto&& b: TO[a]) { for (auto&& c: TO[b]) { if (par[c] != -1) { return {I[a], I[b], I[c], I[par[c]]}; } par[c] = b; } } for (auto&& b: TO[a]) { for (auto&& c: TO[b]) { par[c] = -1; } } } return {-1, -1, -1, -1}; } #line 7 "test/1_mytest/find_C4.test.cpp" void test() { FOR(N, 20) { FOR(50) { Graph<int, 0> G(N); for (auto& [a, b]: random_graph<false>(N, true)) G.add(a, b); G.build(); vv(int, adj, N, N); for (auto& e: G.edges) adj[e.frm][e.to] += 1, adj[e.to][e.frm] += 1; auto [a, b, c, d] = find_C4(G); ll cnt = count_C3_C4(G).se; if (cnt == 0) { assert(a == -1); } else { assert(adj[a][b] && adj[b][c] && adj[c][d] && adj[d][a]); } } } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test(); solve(); return 0; }