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test/1_mytest/all_cycle_common_vertex.test.cpp
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- Last update: 2026-02-05 01:08:24+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
- ds/fastset.hpp
- ds/hashmap.hpp
- graph/all_cycle_common_vertex.hpp
- graph/base.hpp
- graph/find_cycle.hpp
- graph/strongly_connected_component.hpp
- graph/toposort.hpp
- my_template.hpp
- random/base.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
// #include "other/io.hpp"
#include "graph/base.hpp"
#include "graph/all_cycle_common_vertex.hpp"
#include "random/base.hpp"
vc<int> naive(Graph<int, 1> G) {
int N = G.N;
vc<int> ANS;
auto dag = [&](vc<int> V) -> bool {
Graph<int, 1> H = G.rearrange(V);
return V.empty() || (!toposort(H).empty());
};
vc<int> V;
FOR(i, N) V.eb(i);
if (dag(V)) return {};
FOR(v, N) {
V.erase(find(all(V), v));
if (dag(V)) ANS.eb(v);
V.eb(v);
}
return ANS;
}
void test() {
FOR(1 << 18) {
int N = RNG(1, 4);
Graph<int, 1> G(N);
int prob = RNG(0, 100);
FOR(a, N) FOR(b, N) {
if (a == b) continue;
if (RNG(0, 100) < prob) G.add(a, b);
}
G.build();
auto ANS1 = all_cycle_common_vertex(G, 0);
auto ANS2 = naive(G);
sort(all(ANS1));
sort(all(ANS2));
// G.debug();
// SHOW(ANS1, ANS2);
assert(ANS1 == ANS2);
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test();
solve();
}#line 1 "test/1_mytest/all_cycle_common_vertex.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#if defined(__GNUC__)
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#endif
#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> = numeric_limits<double>::infinity();
template <>
constexpr long double infty<long double> =
numeric_limits<long double>::infinity();
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 pq_max = priority_queue<T>;
template <class T>
using pq_min = 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 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(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(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 UINT>
struct all_bit {
struct iter {
UINT s;
iter(UINT s) : s(s) {}
int operator*() const { return lowbit(s); }
iter &operator++() {
s &= s - 1;
return *this;
}
bool operator!=(const iter) const { return s != 0; }
};
UINT s;
all_bit(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
struct iter {
UINT s, t;
bool ed;
iter(UINT s) : s(s), t(s), ed(0) {}
UINT operator*() const { return s ^ t; }
iter &operator++() {
(t == 0 ? ed = 1 : t = (t - 1) & s);
return *this;
}
bool operator!=(const iter) const { return !ed; }
};
UINT s;
all_subset(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
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};
}
constexpr ll TEN[] = {
1LL,
10LL,
100LL,
1000LL,
10000LL,
100000LL,
1000000LL,
10000000LL,
100000000LL,
1000000000LL,
10000000000LL,
100000000000LL,
1000000000000LL,
10000000000000LL,
100000000000000LL,
1000000000000000LL,
10000000000000000LL,
100000000000000000LL,
1000000000000000000LL,
};
template <typename T, typename U>
T SUM(const U &A) {
return std::accumulate(A.begin(), A.end(), T{});
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
template <class C, class T>
inline long long LB(const C &c, const T &x) {
return lower_bound(c.begin(), c.end(), x) - c.begin();
}
template <class C, class T>
inline long long UB(const C &c, const T &x) {
return upper_bound(c.begin(), c.end(), x) - c.begin();
}
#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 <class T, class Container, class Compare>
T POP(priority_queue<T, Container, Compare> &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 (llabs(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) {
T c = max<T>(a, b);
bool changed = (c != a);
a = c;
return changed;
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
T c = min<T>(a, b);
bool changed = (c != a);
a = c;
return changed;
}
// ? 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>
vc<T> cumsum(const vc<U> &A, int off = 1) {
int N = A.size();
vc<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>
vc<int> argsort(const vc<T> &A) {
vc<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 4 "test/1_mytest/all_cycle_common_vertex.test.cpp"
// #include "other/io.hpp"
#line 2 "ds/hashmap.hpp"
// u64 -> Val
template <typename Val>
struct HashMap {
// n は入れたいものの個数で ok
HashMap(u32 n = 0) { build(n); }
void build(u32 n) {
u32 k = 8;
while (k < n * 2) k *= 2;
cap = k / 2, mask = k - 1;
key.resize(k), val.resize(k), used.assign(k, 0);
}
// size を保ったまま. size=0 にするときは build すること.
void clear() {
used.assign(len(used), 0);
cap = (mask + 1) / 2;
}
int size() { return len(used) / 2 - cap; }
int index(const u64& k) {
int i = 0;
for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {}
return i;
}
Val& operator[](const u64& k) {
if (cap == 0) extend();
int i = index(k);
if (!used[i]) { used[i] = 1, key[i] = k, val[i] = Val{}, --cap; }
return val[i];
}
Val get(const u64& k, Val default_value) {
int i = index(k);
return (used[i] ? val[i] : default_value);
}
bool count(const u64& k) {
int i = index(k);
return used[i] && key[i] == k;
}
// f(key, val)
template <typename F>
void enumerate_all(F f) {
FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
}
private:
u32 cap, mask;
vc<u64> key;
vc<Val> val;
vc<bool> used;
u64 hash(u64 x) {
static const u64 FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
x += FIXED_RANDOM;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return (x ^ (x >> 31)) & mask;
}
void extend() {
vc<pair<u64, Val>> dat;
dat.reserve(len(used) / 2 - cap);
FOR(i, len(used)) {
if (used[i]) dat.eb(key[i], val[i]);
}
build(2 * len(dat));
for (auto& [a, b]: dat) (*this)[a] = b;
}
};
#line 3 "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() {
#ifdef LOCAL
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
}
#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;
}
HashMap<int> MP_FOR_EID;
int get_eid(u64 a, u64 b) {
if (len(MP_FOR_EID) == 0) {
MP_FOR_EID.build(N - 1);
for (auto& e: edges) {
u64 a = e.frm, b = e.to;
u64 k = to_eid_key(a, b);
MP_FOR_EID[k] = e.id;
}
}
return MP_FOR_EID.get(to_eid_key(a, b), -1);
}
u64 to_eid_key(u64 a, u64 b) {
if (!directed && a > b) swap(a, b);
return N * a + b;
}
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 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 2 "ds/fastset.hpp"
// 64-ary tree
// space: (N/63) * u64
struct FastSet {
static constexpr u32 B = 64;
int n, log;
vvc<u64> seg;
FastSet() {}
FastSet(int n) { build(n); }
int size() { return n; }
template <typename F>
FastSet(int n, F f) {
build(n, f);
}
void build(int m) {
seg.clear();
n = m;
do {
seg.push_back(vc<u64>((m + B - 1) / B));
m = (m + B - 1) / B;
} while (m > 1);
log = len(seg);
}
template <typename F>
void build(int n, F f) {
build(n);
FOR(i, n) { seg[0][i / B] |= u64(f(i)) << (i % B); }
FOR(h, log - 1) {
FOR(i, len(seg[h])) {
seg[h + 1][i / B] |= u64(bool(seg[h][i])) << (i % B);
}
}
}
bool operator[](int i) const { return seg[0][i / B] >> (i % B) & 1; }
void insert(int i) {
assert(0 <= i && i < n);
for (int h = 0; h < log; h++) {
seg[h][i / B] |= u64(1) << (i % B), i /= B;
}
}
void add(int i) { insert(i); }
void erase(int i) {
assert(0 <= i && i < n);
u64 x = 0;
for (int h = 0; h < log; h++) {
seg[h][i / B] &= ~(u64(1) << (i % B));
seg[h][i / B] |= x << (i % B);
x = bool(seg[h][i / B]);
i /= B;
}
}
void remove(int i) { erase(i); }
// min[x,n) or n
int next(int i) {
assert(i <= n);
chmax(i, 0);
for (int h = 0; h < log; h++) {
if (i / B == seg[h].size()) break;
u64 d = seg[h][i / B] >> (i % B);
if (!d) {
i = i / B + 1;
continue;
}
i += lowbit(d);
for (int g = h - 1; g >= 0; g--) {
i *= B;
i += lowbit(seg[g][i / B]);
}
return i;
}
return n;
}
// max [0,x], or -1
int prev(int i) {
assert(i >= -1);
if (i >= n) i = n - 1;
for (int h = 0; h < log; h++) {
if (i == -1) break;
u64 d = seg[h][i / B] << (63 - i % B);
if (!d) {
i = i / B - 1;
continue;
}
i -= __builtin_clzll(d);
for (int g = h - 1; g >= 0; g--) {
i *= B;
i += topbit(seg[g][i / B]);
}
return i;
}
return -1;
}
bool any(int l, int r) { return next(l) < r; }
// [l, r)
template <typename F>
void enumerate(int l, int r, F f) {
for (int x = next(l); x < r; x = next(x + 1)) f(x);
}
void reset() {
enumerate(0, n, [&](int i) -> void { erase(i); });
}
string to_string() {
string s(n, '?');
for (int i = 0; i < n; ++i) s[i] = ((*this)[i] ? '1' : '0');
return s;
}
};
#line 3 "graph/toposort.hpp"
// 辞書順最小の toposort を返す
template <typename GT>
vc<int> toposort(GT& G) {
static_assert(GT::is_directed);
assert(G.is_prepared());
const int N = G.N;
auto [indeg, outdeg] = G.deg_array_inout();
FastSet que(N);
vc<int> V;
FOR(v, N) if (indeg[v] == 0) que.insert(v);
while (1) {
int v = que.next(0);
if (v == N) break;
que.erase(v), V.eb(v);
for (auto&& e: G[v]) {
if (--indeg[e.to] == 0) que.insert(e.to);
}
}
return (len(V) < N ? vc<int>{} : V);
}
// inv_perm=true: inv perm が辞書最小（各インデックスの現れる場所の列が最小）
template <typename GT>
vc<int> lex_min_toposort(GT& G, bool inv_perm = false) {
static_assert(GT::is_directed);
assert(G.is_prepared());
const int N = G.N;
if (inv_perm) {
GT H(N);
for (auto& e: G.edges) H.add(N - 1 - e.to, N - 1 - e.frm);
H.build();
auto V = lex_min_toposort(H, false);
reverse(all(V));
for (auto& x: V) x = N - 1 - x;
return V;
}
auto [indeg, outdeg] = G.deg_array_inout();
FastSet que(N);
vc<int> V;
FOR(v, N) if (indeg[v] == 0) que.insert(v);
while (1) {
int v = que.next(0);
if (v == N) break;
que.erase(v), V.eb(v);
for (auto&& e: G[v]) {
if (--indeg[e.to] == 0) que.insert(e.to);
}
}
return (len(V) < N ? vc<int>{} : V);
}
#line 2 "graph/find_cycle.hpp"
// {vs, es} or empty. minimal.
template <typename GT>
pair<vc<int>, vc<int>> find_cycle_directed(GT& G) {
static_assert(GT::is_directed);
assert(G.is_prepared());
int N = G.N;
vc<int> used(N);
vc<pair<int, int>> par(N);
vector<int> es, vs;
auto dfs = [&](auto self, int v) -> void {
used[v] = 1;
for (auto&& e: G[v]) {
if (len(es)) return;
if (!used[e.to]) {
par[e.to] = {v, e.id};
self(self, e.to);
}
elif (used[e.to] == 1) {
es = {e.id};
int cur = v;
while (cur != e.to) {
es.eb(par[cur].se);
cur = par[cur].fi;
}
reverse(all(es));
return;
}
}
used[v] = 2;
};
FOR(v, N) if (!used[v]) dfs(dfs, v);
if (es.empty()) return {vs, es};
// minimal cycle
vc<int> nxt(N, -1);
for (auto&& eid: es) nxt[G.edges[eid].frm] = eid;
for (auto&& e: G.edges) {
int a = e.frm, b = e.to;
if (nxt[a] == -1 || nxt[b] == -1) continue;
if (G.edges[nxt[a]].to == e.to) continue;
while (a != b) {
int t = G.edges[nxt[a]].to;
nxt[a] = -1;
a = t;
}
nxt[e.frm] = e.id;
}
es.clear();
FOR(v, N) {
if (nxt[v] == -1) continue;
int x = v;
while (1) {
vs.eb(x);
es.eb(nxt[x]);
x = G.edges[nxt[x]].to;
if (x == v) break;
}
break;
}
return {vs, es};
}
// {vs, es} or empty. minimal.
template <typename GT>
pair<vc<int>, vc<int>> find_cycle_undirected(GT& G) {
assert(!GT::is_directed);
assert(G.is_prepared());
const int N = G.N;
const int M = G.M;
vc<int> dep(N, -1);
vc<bool> used_e(M);
vc<int> par(N, -1); // edge idx
auto dfs = [&](auto& dfs, int v, int d) -> void {
dep[v] = d;
for (auto&& e: G[v]) {
if (dep[e.to] != -1) continue;
used_e[e.id] = 1;
par[e.to] = e.id;
dfs(dfs, e.to, d + 1);
}
};
vc<int> vs, es;
FOR(v, N) {
if (dep[v] == -1) dfs(dfs, v, 0);
}
int mi_len = infty<int>;
int back_e = -1;
for (auto& e: G.edges) {
if (used_e[e.id]) continue;
int d = abs(dep[e.frm] - dep[e.to]);
if (chmin(mi_len, d)) back_e = e.id;
}
if (back_e == -1) return {vs, es};
int a = G.edges[back_e].frm, b = G.edges[back_e].to;
if (dep[a] > dep[b]) swap(a, b);
es.eb(back_e), vs.eb(a);
while (1) {
int x = vs.back();
auto& e = G.edges[es.back()];
int y = e.frm + e.to - x;
if (y == a) break;
vs.eb(y);
es.eb(par[y]);
}
return {vs, es};
}
#line 4 "graph/all_cycle_common_vertex.hpp"
// v を通るサイクルが存在し, v を消すと DAG になるような v を昇順全列挙する
// v を消すと 非DAG -> DAG
// loop はないものとしたかも
// https://codeforces.com/contest/982/problem/F
template <typename GT>
vc<int> all_cycle_common_vertex(GT& G, bool strongly_connected) {
static_assert(GT::is_directed);
int N = G.N;
if (!strongly_connected) {
auto [nc, comp] = strongly_connected_component(G);
vc<int> sz(nc);
FOR(v, N) sz[comp[v]]++;
int k = -1;
FOR(i, nc) {
if (sz[i] >= 2) {
if (k != -1) return {};
k = i;
}
}
if (k == -1) return {}; // DAG
vc<int> V;
FOR(v, N) if (comp[v] == k) V.eb(v);
Graph<int, 1> H = G.rearrange(V);
vc<int> ANS = all_cycle_common_vertex(H, true);
for (int& x : ANS) x = V[x];
return ANS;
}
assert(strongly_connected);
if (N == 1) return {}; // DAG
// main cycle
vc<int> C = find_cycle_directed(G).fi;
int n = len(C);
vc<int> idx(N, -1);
FOR(i, n) idx[C[i]] = i;
vc<int> other;
FOR(i, N) if (idx[i] == -1) other.eb(i);
if (len(other)) {
Graph<int, 1> H = G.rearrange(other);
if (toposort(H).empty()) return {}; // two vertex disjoint cycle
}
vc<int> F(N + 1);
auto arc = [&](int s, int t) -> void {
if (s < t) {
F[s + 1]++, F[t]--;
} else {
F[s + 1]++, F[n]--;
F[0]++, F[t]--;
}
};
vc<int> dp(N, -2);
FOR(s, n) {
auto eval = [&](int i) -> int {
if (i < 0) return i;
return (s < i ? i - s : i + n - s);
};
auto dfs = [&](auto& dfs, int v) -> int {
if (idx[v] != -1) return idx[v];
if (dp[v] != -2) return dp[v];
int ans = -1;
for (auto& e : G[v]) {
int i = dfs(dfs, e.to);
if (eval(ans) < eval(i)) ans = i;
}
return dp[v] = ans;
};
int i = -1;
for (auto& e : G[C[s]]) {
int j = dfs(dfs, e.to);
if (eval(i) < eval(j)) i = j;
}
if (i != -1) arc(s, i);
}
FOR(i, n) F[i + 1] += F[i];
F.pop_back();
vc<int> ANS;
FOR(i, n) if (F[i] == 0) ANS.eb(C[i]);
if (ANS.empty()) return {};
vc<int> V;
FOR(v, N) if (v != ANS[0]) V.eb(v);
{
Graph<int, 1> H = G.rearrange(V);
if (toposort(H).empty()) return {};
}
return ANS;
}
#line 8 "test/1_mytest/all_cycle_common_vertex.test.cpp"
#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 10 "test/1_mytest/all_cycle_common_vertex.test.cpp"
vc<int> naive(Graph<int, 1> G) {
int N = G.N;
vc<int> ANS;
auto dag = [&](vc<int> V) -> bool {
Graph<int, 1> H = G.rearrange(V);
return V.empty() || (!toposort(H).empty());
};
vc<int> V;
FOR(i, N) V.eb(i);
if (dag(V)) return {};
FOR(v, N) {
V.erase(find(all(V), v));
if (dag(V)) ANS.eb(v);
V.eb(v);
}
return ANS;
}
void test() {
FOR(1 << 18) {
int N = RNG(1, 4);
Graph<int, 1> G(N);
int prob = RNG(0, 100);
FOR(a, N) FOR(b, N) {
if (a == b) continue;
if (RNG(0, 100) < prob) G.add(a, b);
}
G.build();
auto ANS1 = all_cycle_common_vertex(G, 0);
auto ANS2 = naive(G);
sort(all(ANS1));
sort(all(ANS2));
// G.debug();
// SHOW(ANS1, ANS2);
assert(ANS1 == ANS2);
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test();
solve();
}