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:warning: test/yosupo/enumerate_cliques.test.cpp

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Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/enumerate_cliques
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include "src/Math/ModInt.hpp"
#include "src/Graph/CliqueProblem.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<998244353>;
 int N, M;
 cin >> N >> M;
 vector<Mint> x(N);
 for (int i= 0; i < N; ++i) cin >> x[i];
 CliqueProblem graph(N);
 while (M--) {
  int u, v;
  cin >> u >> v;
  graph.add_edge(u, v);
 }
 Mint ans= 0;
 graph.enumerate_cliques([&](const auto& clique) {
  Mint prod= 1;
  for (auto i: clique) prod*= x[i];
  ans+= prod;
 });
 cout << ans << '\n';
 return 0;
}
#line 1 "test/yosupo/enumerate_cliques.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/enumerate_cliques
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#line 2 "src/Math/mod_inv.hpp"
#include <utility>
#include <type_traits>
#include <cassert>
template <class Uint> constexpr inline Uint mod_inv(Uint a, Uint mod) {
 std::make_signed_t<Uint> x= 1, y= 0, z= 0;
 for (Uint q= 0, b= mod, c= 0; b;) z= x, x= y, y= z - y * (q= a / b), c= a, a= b, b= c - b * q;
 return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
#line 2 "src/Internal/Remainder.hpp"
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
struct MP_Na {  // mod < 2^32
 u32 mod;
 constexpr MP_Na(): mod(0) {}
 constexpr MP_Na(u32 m): mod(m) {}
 constexpr inline u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
 constexpr inline u32 set(u32 n) const { return n; }
 constexpr inline u32 get(u32 n) const { return n; }
 constexpr inline u32 norm(u32 n) const { return n; }
 constexpr inline u32 plus(u64 l, u32 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u32 diff(u64 l, u32 r) const { return l-= r, l >> 63 ? l + mod : l; }
};
template <class u_t, class du_t, u8 B> struct MP_Mo {  // mod < 2^32, mod < 2^62
 u_t mod;
 constexpr MP_Mo(): mod(0), iv(0), r2(0) {}
 constexpr MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
 constexpr inline u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
 constexpr inline u_t set(u_t n) const { return mul(n, r2); }
 constexpr inline u_t get(u_t n) const { return n= reduce(n), n >= mod ? n - mod : n; }
 constexpr inline u_t norm(u_t n) const { return n >= mod ? n - mod : n; }
 constexpr inline u_t plus(u_t l, u_t r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u_t diff(u_t l, u_t r) const { return l-= r, l >> (B - 1) ? l + (mod << 1) : l; }
private:
 u_t iv, r2;
 static constexpr u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
 constexpr inline u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
using MP_Mo32= MP_Mo<u32, u64, 32>;
using MP_Mo64= MP_Mo<u64, u128, 64>;
struct MP_Br {  // 2^20 < mod <= 2^41
 u64 mod;
 constexpr MP_Br(): mod(0), x(0) {}
 constexpr MP_Br(u64 m): mod(m), x((u128(1) << 84) / m) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
 static constexpr inline u64 set(u64 n) { return n; }
 constexpr inline u64 get(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 norm(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 plus(u64 l, u64 r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u64 diff(u64 l, u64 r) const { return l-= r, l >> 63 ? l + (mod << 1) : l; }
private:
 u64 x;
 constexpr inline u128 quo(const u128 &n) const { return (n * x) >> 84; }
 constexpr inline u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
template <class du_t, u8 B> struct MP_D2B1 {  // mod < 2^63, mod < 2^64
 u64 mod;
 constexpr MP_D2B1(): mod(0), s(0), d(0), v(0) {}
 constexpr MP_D2B1(u64 m): mod(m), s(__builtin_clzll(m)), d(m << s), v(u128(-1) / d) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
 constexpr inline u64 set(u64 n) const { return n; }
 constexpr inline u64 get(u64 n) const { return n; }
 constexpr inline u64 norm(u64 n) const { return n; }
 constexpr inline u64 plus(du_t l, u64 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u64 diff(du_t l, u64 r) const { return l-= r, l >> B ? l + mod : l; }
private:
 u8 s;
 u64 d, v;
 constexpr inline u64 rem(const u128 &u) const {
  u128 q= (u >> 64) * v + u;
  u64 r= u64(u) - (q >> 64) * d - d;
  if (r > u64(q)) r+= d;
  if (r >= d) r-= d;
  return r;
 }
};
using MP_D2B1_1= MP_D2B1<u64, 63>;
using MP_D2B1_2= MP_D2B1<u128, 127>;
template <class u_t, class MP> constexpr u_t pow(u_t x, u64 k, const MP &md) {
 for (u_t ret= md.set(1);; x= md.mul(x, x))
  if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
}
#line 3 "src/Internal/modint_traits.hpp"
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
#line 6 "src/Math/ModInt.hpp"
namespace math_internal {
template <class MP, u64 MOD> struct SB: s_b {
protected:
 static constexpr MP md= MP(MOD);
};
template <class U, class B> struct MInt: public B {
 using Uint= U;
 static constexpr inline auto mod() { return B::md.mod; }
 constexpr MInt(): x(0) {}
 template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> constexpr MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
 constexpr MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
 constexpr MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
 constexpr MInt name const { \
  MInt ret; \
  return ret.x= op, ret; \
 }
 FUNC(operator+(const MInt & r), B::md.plus(x, r.x))
 FUNC(operator-(const MInt & r), B::md.diff(x, r.x))
 FUNC(operator*(const MInt & r), B::md.mul(x, r.x))
 FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
 constexpr MInt operator/(const MInt &r) const { return *this * r.inv(); }
 constexpr MInt &operator+=(const MInt &r) { return *this= *this + r; }
 constexpr MInt &operator-=(const MInt &r) { return *this= *this - r; }
 constexpr MInt &operator*=(const MInt &r) { return *this= *this * r; }
 constexpr MInt &operator/=(const MInt &r) { return *this= *this / r; }
 constexpr bool operator==(const MInt &r) const { return B::md.norm(x) == B::md.norm(r.x); }
 constexpr bool operator!=(const MInt &r) const { return !(*this == r); }
 constexpr bool operator<(const MInt &r) const { return B::md.norm(x) < B::md.norm(r.x); }
 constexpr inline MInt inv() const { return mod_inv<U>(val(), B::md.mod); }
 constexpr inline Uint val() const { return B::md.get(x); }
 friend ostream &operator<<(ostream &os, const MInt &r) { return os << r.val(); }
 friend istream &operator>>(istream &is, MInt &r) {
  i64 v;
  return is >> v, r= MInt(v), is;
 }
private:
 Uint x;
};
template <u64 MOD> using MP_B= conditional_t < (MOD < (1 << 30)) & MOD, MP_Mo32, conditional_t < MOD < (1ull << 32), MP_Na, conditional_t<(MOD < (1ull << 62)) & MOD, MP_Mo64, conditional_t<MOD<(1ull << 41), MP_Br, conditional_t<MOD<(1ull << 63), MP_D2B1_1, MP_D2B1_2>>>>>;
template <u64 MOD> using ModInt= MInt < conditional_t<MOD<(1 << 30), u32, u64>, SB<MP_B<MOD>, MOD>>;
}
using math_internal::ModInt;
#line 2 "src/Graph/CliqueProblem.hpp"
#include <vector>
#include <algorithm>
class CliqueProblem {
 using u128= __uint128_t;
 using u64= unsigned long long;
 using u16= unsigned short;
 const u16 n, m;
 struct id_num {
  u16 id, num;
 };
 std::vector<u128> adj_;
 std::vector<u16> calc(bool complement) const {
  std::vector<u128> buf, adj(adj_);
  std::vector<u16> deg(n), clique, cur;
  if (complement)
   for (int u= n; u--;)
    for (int v= u; v--;) adj[u * m + (v >> 7)]^= u128(1) << (v & 127), adj[v * m + (u >> 7)]^= u128(1) << (u & 127);
  auto dfs= [&](auto dfs, std::vector<id_num> &rem) -> void {
   if (clique.size() < cur.size()) clique= cur;
   std::sort(rem.begin(), rem.end(), [&](id_num l, id_num r) { return deg[l.id] > deg[r.id]; }), buf.assign((n + 1) * m, 0);
   for (auto &v: rem) {
    int b= v.id * m, bb= 0;
    for (v.num= 0;; ++v.num, bb+= m) {
     bool any= 1;
     for (u16 i= 0; i < m; ++i) any&= !(adj[b + i] & buf[bb + i]);
     if (any) break;
    }
    buf[bb + (v.id >> 7)]|= u128(1) << (v.id & 127);
   }
   std::sort(rem.begin(), rem.end(), [&](id_num l, id_num r) { return l.num < r.num; });
   std::vector<id_num> nrem;
   for (nrem.reserve(rem.size()); !rem.empty();) {
    auto p= rem.back();
    if (p.num + cur.size() < clique.size()) break;
    nrem.clear();
    auto a= adj.cbegin() + p.id * m;
    for (auto u: rem)
     if ((a[u.id >> 7] >> (u.id & 127)) & 1) nrem.emplace_back(u);
    std::fill_n(buf.begin(), m, 0);
    for (auto u: nrem) buf[u.id >> 7]|= u128(1) << (u.id & 127);
    for (auto u: nrem) {
     int b= u.id * m, i= 0, cnt= 0;
     for (u128 tmp; i < m; ++i) tmp= buf[i] & adj[b + i], cnt+= __builtin_popcountll(tmp >> 64) + __builtin_popcountll(u64(tmp));
     deg[u.id]= cnt;
    }
    cur.push_back(p.id), dfs(dfs, nrem), cur.pop_back(), rem.pop_back();
   }
  };
  std::vector<id_num> nrem;
  for (u16 u= n, cnt; u--; nrem.push_back(id_num{u, 0}), deg[u]= cnt) {
   int b= u * m, i= cnt= 0;
   for (u128 tmp; i < m; ++i) tmp= adj[b + i], cnt+= __builtin_popcountll(tmp >> 64) + __builtin_popcountll(u64(tmp));
  }
  return dfs(dfs, nrem), clique;
 }
public:
 CliqueProblem(int n): n(n), m((n + 127) >> 7), adj_(n * m) {}
 void add_edge(int u, int v) { adj_[u * m + (v >> 7)]|= u128(1) << (v & 127), adj_[v * m + (u >> 7)]|= u128(1) << (u & 127); }
 std::vector<u16> get_max_clique() const { return calc(false); }
 std::vector<u16> get_max_independent_set() const { return calc(true); }
 std::vector<u16> get_min_vertex_cover() const {
  std::vector<u128> buf(m);
  for (u16 u: calc(true)) buf[u >> 7]|= u128(1) << (u & 127);
  std::vector<u16> ret;
  for (u16 i= 0; i < n; ++i)
   if (!((buf[i >> 7] >> (i & 127)) & 1)) ret.push_back(i);
  return ret;
 }
 template <class F> void enumerate_cliques(const F &out) const {
  std::vector<u128> buf;
  std::vector<u16> deg(n), clique, nbd;
  for (u16 u= n, cnt; u--; deg[u]= cnt) {
   int b= u * m, i= cnt= 0;
   for (u128 tmp; i < m; ++i) tmp= adj_[b + i], cnt+= __builtin_popcountll(tmp >> 64) + __builtin_popcountll(u64(tmp));
  }
  u16 nn;
  auto dfs= [&](auto dfs, u16 k) -> void {
   out(clique);
   for (u16 i= k; i < nn; ++i) {
    u16 v= nbd[i];
    auto b= adj_.cbegin() + v * m;
    bool all= 1;
    for (u16 j= 0; j < m; ++j) all&= (b[j] & buf[j]) == buf[j];
    if (all) clique.push_back(v), buf[v >> 7]|= u128(1) << (v & 127), dfs(dfs, i + 1), clique.pop_back(), buf[v >> 7]^= u128(1) << (v & 127);
   }
  };
  bool unused[n];
  std::fill_n(unused, n, 1);
  for (u16 _= n; _--;) {
   u16 v, min_d= n;
   for (u16 i= n; i--;)
    if (unused[i] && min_d > deg[i]) v= i, min_d= deg[i];
   nbd.clear(), clique= {v}, buf.assign(m, 0), buf[v >> 7]|= u128(1) << (v & 127);
   auto a= adj_.cbegin() + v * m;
   for (int i= 0; i < n; ++i)
    if ((a[i >> 7] >> (i & 127)) & unused[i]) nbd.push_back(i);
   nn= nbd.size(), dfs(dfs, 0), unused[v]= 0;
   for (auto u: nbd) --deg[u];
  }
 }
};
#line 7 "test/yosupo/enumerate_cliques.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<998244353>;
 int N, M;
 cin >> N >> M;
 vector<Mint> x(N);
 for (int i= 0; i < N; ++i) cin >> x[i];
 CliqueProblem graph(N);
 while (M--) {
  int u, v;
  cin >> u >> v;
  graph.add_edge(u, v);
 }
 Mint ans= 0;
 graph.enumerate_cliques([&](const auto& clique) {
  Mint prod= 1;
  for (auto i: clique) prod*= x[i];
  ans+= prod;
 });
 cout << ans << '\n';
 return 0;
}
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