tests/Enumerate_Cliques.test.cpp

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Last update: 2025-11-28 13:07:52+07:00
Problem: https://judge.yosupo.jp/problem/enumerate_cliques

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/enumerate_cliques"

#include "../misc/macros.h"
#include "../math/ModInt.h"
#include "../graph/Cliques.h"

using Fp = modint<998244353>;

void solve() {
  int n, m;
  cin >> n >> m;
  vector<Fp> x(n);
  for (int i = 0; i < n; ++i) cin >> x[i];
  vector<bs> g(n, bs(n));
  for (int i = 0; i < m; ++i) {
    int u, v;
    cin >> u >> v;
    g[u][v] = g[v][u] = 1;
  }
  Fp ans = 0;
  EnumClique(g, [&](const bs& clique) {
    if(!clique.any()) return;
    Fp prod = 1;
    for(int i = clique.find_first(); i < n; i = clique.find_next(i)) prod *= x[i];
    ans += prod; }, ~bs(n), bs(n), bs(n));
  cout << ans << '\n';
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin.exceptions(cin.failbit);
  int tc = 1;
  //   cin >> tc;
  for (int i = 1; i <= tc; ++i) {
    solve();
  }
}

#line 1 "tests/Enumerate_Cliques.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/enumerate_cliques"

#line 1 "misc/macros.h"
// #pragma GCC optimize("Ofast,unroll-loops")       // unroll long, simple loops
// #pragma GCC target("avx2,fma")                   // vectorizing code
// #pragma GCC target("lzcnt,popcnt,abm,bmi,bmi2")  // for fast bitset operation

#include <bits/extc++.h>
#include <tr2/dynamic_bitset>

using namespace std;
using namespace __gnu_pbds;  // ordered_set, gp_hash_table
// using namespace __gnu_cxx; // rope

// for templates to work
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#define pb push_back
#define eb emplace_back
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using pii = pair<i32, i32>;
using vi = vector<i32>;

// fast map
const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash {  // customize hash function for gp_hash_table
  int operator()(int x) const { return x ^ RANDOM; }
};
gp_hash_table<int, int, chash> table;

/* ordered set
    find_by_order(k): returns an iterator to the k-th element (0-based)
    order_of_key(k): returns the number of elements in the set that are strictly less than k
*/
template <class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

/*  rope
    rope <int> cur = v.substr(l, r - l + 1);
    v.erase(l, r - l + 1);
    v.insert(v.mutable_begin(), cur);
*/
#line 2 "math/ModInt.h"

template <int mod>
struct modint {
  using M = modint;
  static_assert(mod > 0 && mod <= 2147483647);
  static constexpr int modulo = mod;
  static constexpr u32 r1 = []() {
    u32 r1 = mod;
    for (int i = 0; i < 5; ++i) r1 *= 2 - mod * r1;
    return -r1;
  }();
  static constexpr u32 r2 = -u64(mod) % mod;
  static u32 reduce(u64 x) {
    u32 y = u32(x) * r1, r = (x + u64(y) * mod) >> 32;
    return r >= mod ? r - mod : r;
  }
  u32 x;
  modint() : x(0) {}
  modint(i64 x) : x(reduce(u64(x % mod + mod) * r2)) {}
  M& operator+=(const M& a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  M& operator-=(const M& a) {
    if ((x += mod - a.x) >= mod) x -= mod;
    return *this;
  }
  M& operator*=(const M& a) {
    x = reduce(u64(x) * a.x);
    return *this;
  }
  M& operator/=(const M& a) { return *this *= a.inv(); }
  M operator-() const { return M(0) - *this; }
  M operator+(const M& a) const { return M(*this) += a; }
  M operator-(const M& a) const { return M(*this) -= a; }
  M operator*(const M& a) const { return M(*this) *= a; }
  M operator/(const M& a) const { return M(*this) /= a; }
  bool operator==(const M& a) const { return x == a.x; }
  bool operator!=(const M& a) const { return x != a.x; }
  M pow(u64 k) const {
    M res(1), b = *this;
    while (k) {
      if (k & 1) res *= b;
      b *= b, k >>= 1;
    }
    return res;
  }
  M inv() const { return pow(mod - 2); }
  friend ostream& operator<<(ostream& os, const M& a) {
    return os << reduce(a.x);
  }
  friend istream& operator>>(istream& is, M& a) {
    i64 v;
    is >> v;
    a = M(v);
    return is;
  }
};

u64 modmul(u64 x, u64 y, u64 m) { return u128(x) * y % m; }
u64 modpow(u64 x, u64 k, u64 m) {
  u64 res = 1;
  while (k) {
    if (k & 1) res = modmul(res, x, m);
    x = modmul(x, x, m);
    k >>= 1;
  }
  return res;
}
#line 1 "graph/Cliques.h"
using bs = tr2::dynamic_bitset<uint64_t>;

// Usage: bs P(n), X(n), R(n); P.set(); EnumClique(g, [&](bs& c){...}, P, X, R);
template <class F>
void EnumClique(vector<bs>& g, F f, bs P, bs X, bs R) {
  f(R); 
  if (P.none() && X.none()) return;
  // if only need to find all maximal cliques
  // auto q = (P | X).find_first();
  // auto cands = P & ~g[q]; // then trav through cands
  for (auto i = P.find_first(); i < sz(P); i = P.find_next(i)) {
    R[i] = 1;
    EnumClique(g, f, P & g[i], X & g[i], R);
    R[i] = 0, P[i] = 0, X[i] = 1;
  }
}

// Usage: bs P(n), R(n), sol; u64 ans=0; P.set(); MaxClique(g, P, R, sol, ans);
void MaxClique(vector<bs>& g, bs P, bs R, bs& sol, u32& res) {
  if (R.count() + P.count() <= res) return;
  if (P.none()) { res = R.count(), sol = R; return; }
  auto q = P.find_first(), max_k = u64(0);
  for (auto i = q; i < sz(P); i = P.find_next(i)) {
    auto k = (P & g[i]).count();
    if (k > max_k) max_k = k, q = i;
  }
  bs cands = P & ~g[q];
  for (auto i = cands.find_first(); i < sz(cands); i = cands.find_next(i)) {
    R[i] = 1, MaxClique(g, P & g[i], R, sol, res);
    R[i] = P[i] = 0;
  }
}
#line 6 "tests/Enumerate_Cliques.test.cpp"

using Fp = modint<998244353>;

void solve() {
  int n, m;
  cin >> n >> m;
  vector<Fp> x(n);
  for (int i = 0; i < n; ++i) cin >> x[i];
  vector<bs> g(n, bs(n));
  for (int i = 0; i < m; ++i) {
    int u, v;
    cin >> u >> v;
    g[u][v] = g[v][u] = 1;
  }
  Fp ans = 0;
  EnumClique(g, [&](const bs& clique) {
    if(!clique.any()) return;
    Fp prod = 1;
    for(int i = clique.find_first(); i < n; i = clique.find_next(i)) prod *= x[i];
    ans += prod; }, ~bs(n), bs(n), bs(n));
  cout << ans << '\n';
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin.exceptions(cin.failbit);
  int tc = 1;
  //   cin >> tc;
  for (int i = 1; i <= tc; ++i) {
    solve();
  }
}