test/yosupo/enumerate_cliques.test.cpp

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Last update: 2024-01-08 13:32:33+09:00
Problem: https://judge.yosupo.jp/problem/enumerate_cliques

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Code

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

#include "../../math/modint.hpp"
#include "../../graph/enumerate_cliques.hpp"

#include <bits/stdc++.h>
using namespace std;

using mint = Modint<998244353>;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int N, M;
    cin >> N >> M;
    vector<mint> x(N);
    for (auto& y : x) cin >> y;
    vector<vector<bool>> G(N, vector<bool>(N));
    for (int i = 0; i < M; ++i) {
        int u, v;
        cin >> u >> v;
        G[u][v] = G[v][u] = true;
    }
    mint ans = 0;
    for (auto& clique : enumerate_cliques(G)) {
        mint res = 1;
        for (int i : clique) {
            res *= x[i];
        }
        ans += res;
    }
    cout << ans << endl;
}

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

#line 2 "math/modint.hpp"
#include <algorithm>
#include <iostream>

/**
 * @brief Mod int
 */
template <int m>
class Modint {
    using mint = Modint;
    static_assert(m > 0, "Modulus must be positive");

   public:
    static constexpr int mod() { return m; }

    constexpr Modint(long long y = 0) : x(y >= 0 ? y % m : (y % m + m) % m) {}

    constexpr int val() const { return x; }

    constexpr mint& operator+=(const mint& r) {
        if ((x += r.x) >= m) x -= m;
        return *this;
    }
    constexpr mint& operator-=(const mint& r) {
        if ((x += m - r.x) >= m) x -= m;
        return *this;
    }
    constexpr mint& operator*=(const mint& r) {
        x = static_cast<int>(1LL * x * r.x % m);
        return *this;
    }
    constexpr mint& operator/=(const mint& r) { return *this *= r.inv(); }

    constexpr bool operator==(const mint& r) const { return x == r.x; }

    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint(-x); }

    constexpr friend mint operator+(const mint& l, const mint& r) {
        return mint(l) += r;
    }
    constexpr friend mint operator-(const mint& l, const mint& r) {
        return mint(l) -= r;
    }
    constexpr friend mint operator*(const mint& l, const mint& r) {
        return mint(l) *= r;
    }
    constexpr friend mint operator/(const mint& l, const mint& r) {
        return mint(l) /= r;
    }

    constexpr mint inv() const {
        int a = x, b = m, u = 1, v = 0;
        while (b > 0) {
            int t = a / b;
            std::swap(a -= t * b, b);
            std::swap(u -= t * v, v);
        }
        return mint(u);
    }

    constexpr mint pow(long long n) const {
        mint ret(1), mul(x);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend std::ostream& operator<<(std::ostream& os, const mint& r) {
        return os << r.x;
    }

    friend std::istream& operator>>(std::istream& is, mint& r) {
        long long t;
        is >> t;
        r = mint(t);
        return is;
    }

   private:
    int x;
};
#line 2 "graph/enumerate_cliques.hpp"
#include <cmath>
#include <vector>

std::vector<std::vector<int>> enumerate_cliques(
    const std::vector<std::vector<bool>>& G) {
    int N = G.size(), M = 0;
    std::vector<int> deg(N);
    for (int i = 0; i < N; ++i) {
        for (int j = 0; j < N; ++j) {
            if (G[i][j]) {
                ++deg[i];
                ++M;
            }
        }
    }
    M /= 2;
    int B = std::sqrt(2 * M);
    std::vector<std::vector<int>> cliques;

    auto check = [&](const std::vector<int>& vs, bool use_first) {
        int n = vs.size();
        for (int S = 1; S < 1 << n; ++S) {
            if (use_first && !(S & 1)) continue;
            bool ok = true;
            for (int i = 0; i < n - 1; ++i) {
                if (!(S >> i & 1)) continue;
                for (int j = i + 1; j < n; ++j) {
                    if ((S >> j & 1) && !G[vs[i]][vs[j]]) {
                        ok = false;
                        break;
                    }
                }
                if (!ok) break;
            }
            if (ok) {
                cliques.emplace_back();
                for (int i = 0; i < n; ++i) {
                    if (S >> i & 1) {
                        cliques.back().push_back(vs[i]);
                    }
                }
            }
        }
    };

    std::vector<bool> checked(N);
    std::vector<int> big;
    for (int i = 0; i < N; ++i) {
        if (deg[i] >= B) {
            big.push_back(i);
            continue;
        }
        std::vector<int> vs;
        vs.push_back(i);
        for (int j = 0; j < N; ++j) {
            if (G[i][j] && !checked[j]) {
                vs.push_back(j);
            }
        }
        check(vs, true);
        checked[i] = true;
    }
    check(big, false);
    return cliques;
}
#line 5 "test/yosupo/enumerate_cliques.test.cpp"

#include <bits/stdc++.h>
using namespace std;

using mint = Modint<998244353>;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int N, M;
    cin >> N >> M;
    vector<mint> x(N);
    for (auto& y : x) cin >> y;
    vector<vector<bool>> G(N, vector<bool>(N));
    for (int i = 0; i < M; ++i) {
        int u, v;
        cin >> u >> v;
        G[u][v] = G[v][u] = true;
    }
    mint ans = 0;
    for (auto& clique : enumerate_cliques(G)) {
        mint res = 1;
        for (int i : clique) {
            res *= x[i];
        }
        ans += res;
    }
    cout << ans << endl;
}