test/library_checker/graph/enumerate_triangles.test.cpp

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Last update: 2024-11-03 21:58:22+09:00
Problem: https://judge.yosupo.jp/problem/enumerate_triangles

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/enumerate_triangles"
#include <bits/stdc++.h>
using namespace std;

#include "../../../lib/graph/enumerate_triangles.hpp"
#include "../../../lib/math/modint.hpp"

using mint = ModInt<998244353>;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m; cin >> n >> m;
    vector<mint> x(n);
    for(int i = 0; i < n; i++){
        cin >> x[i];
    }
    vector<vector<int>> G(n);
    for(int i = 0; i < m; i++) {
        int u, v; cin >> u >> v;
        G[u].push_back(v);
        G[v].push_back(u);
    }

    mint ans = 0;
    for(auto &s : enumerateTriangles(G)){
        mint mul = 1;
        for(auto &i : s){
            mul *= x[i];
        }
        ans += mul;
    }
    cout << ans << '\n';
}

#line 1 "test/library_checker/graph/enumerate_triangles.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/enumerate_triangles"
#include <bits/stdc++.h>
using namespace std;

#line 2 "lib/graph/enumerate_triangles.hpp"

/**
 * @brief Enumerate Triangles
 * @see https://www.slideshare.net/slideshow/trianguler/38443802
 */

vector<array<int, 3>> enumerateTriangles(vector<vector<int>> &G){
    int n = G.size();
    vector<vector<int>> DAG(n);
    for(int i = 0; i < n; i++){
        for(auto &j : G[i]){
            pair<int, int> p = {(int) G[i].size(), i}, q = {(int) G[j].size(), j};
            if(p < q){
                DAG[i].push_back(j);
            }
        }
    }

    vector<array<int, 3>> res;
    vector<int> edge(n);
    for(int i = 0; i < n; i++){
        for(auto j : DAG[i]){
            for(auto k : DAG[i]){
                edge[k]++;
            }
            for(auto k : DAG[j]){
                if(edge[k]){
                    res.push_back({i, j, k});
                }
            }
            for(auto k : DAG[i]){
                edge[k]--;
            }
        }
    }
    return res;
}
#line 2 "lib/math/modint.hpp"

#line 5 "lib/math/modint.hpp"

/**
 * @brief ModInt
 * @docs docs/math/modint.md
 */

template <long long Modulus>
struct ModInt{
    long long val;
    static constexpr int mod() { return Modulus; }
    constexpr ModInt(const long long _val = 0) noexcept : val(_val) {
        normalize();
    }
    void normalize(){
        val = (val % Modulus + Modulus) % Modulus;
    }
    inline ModInt &operator+=(const ModInt &rhs) noexcept {
        if(val += rhs.val, val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt &operator-=(const ModInt &rhs) noexcept {
        if(val -= rhs.val, val < 0) val += Modulus;
        return *this;
    }
    inline ModInt &operator*=(const ModInt &rhs) noexcept {
        val = val * rhs.val % Modulus;
        return *this;
    }
    inline ModInt &operator/=(const ModInt &rhs) noexcept {
        val = val * inv(rhs.val).val % Modulus;
        return *this;
    }
    inline ModInt &operator++() noexcept {
        if(++val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt operator++(int) noexcept {
        ModInt t = val;
        if(++val >= Modulus) val -= Modulus;
        return t;
    }
    inline ModInt &operator--() noexcept {
        if(--val < 0) val += Modulus;
        return *this;
    }
    inline ModInt operator--(int) noexcept {
        ModInt t = val;
        if(--val < 0) val += Modulus;
        return t;
    }
    inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; }
    inline ModInt inv(void) const { return inv(val); }
    ModInt pow(long long n) const {
        assert(0 <= n);
        ModInt x = *this, r = 1;
        while(n){
            if(n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    ModInt inv(const long long n) const {
        long long a = n, b = Modulus, u = 1, v = 0;
        while(b){
            long long t = a / b;
            a -= t * b; std::swap(a, b);
            u -= t * v; std::swap(u, v);
        }
        u %= Modulus;
        if(u < 0) u += Modulus;
        return u;
    }
    friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; }
    friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; }
    friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; }
    friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; }
    friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; }
    friend inline std::istream &operator>>(std::istream &is, ModInt &x) noexcept {
        is >> x.val;
        x.normalize();
        return is;
    }
    friend inline std::ostream &operator<<(std::ostream &os, const ModInt &x) noexcept { return os << x.val; }
};
#line 7 "test/library_checker/graph/enumerate_triangles.test.cpp"

using mint = ModInt<998244353>;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m; cin >> n >> m;
    vector<mint> x(n);
    for(int i = 0; i < n; i++){
        cin >> x[i];
    }
    vector<vector<int>> G(n);
    for(int i = 0; i < m; i++) {
        int u, v; cin >> u >> v;
        G[u].push_back(v);
        G[v].push_back(u);
    }

    mint ans = 0;
    for(auto &s : enumerateTriangles(G)){
        mint mul = 1;
        for(auto &i : s){
            mul *= x[i];
        }
        ans += mul;
    }
    cout << ans << '\n';
}