test/yosupo/enumerate_triangles.test.cpp

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Last update: 2024-01-08 13:32:33+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 "../../math/modint.hpp"
#include "../../graph/enumerate_triangles.hpp"

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, s, t) for (int i = (int)(s); i < (int)(t); ++i)
#define revrep(i, t, s) for (int i = (int)(t)-1; i >= (int)(s); --i)
#define all(x) begin(x), end(x)
template <typename T> bool chmax(T& a, const T& b) { return a < b ? (a = b, 1) : 0; }
template <typename T> bool chmin(T& a, const T& b) { return a > b ? (a = b, 1) : 0; }

using mint = Modint<998244353>;

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

    int N, M;
    cin >> N >> M;
    vector<mint> x(N);
    for (auto& v : x) cin >> v;
    vector<vector<int>> G(N);
    rep(i,0,M) {
        int u, v;
        cin >> u >> v;
        G[u].push_back(v);
        G[v].push_back(u);
    }
    mint ans = 0;
    for (auto [a, b, c] : enumerate_triangles(G)) {
        ans += x[a]*x[b]*x[c];
    }
    cout << ans << endl;
}

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

#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 3 "graph/enumerate_triangles.hpp"
#include <vector>

std::vector<std::tuple<int, int, int>> enumerate_triangles(
    const std::vector<std::vector<int>>& G) {
    const int n = G.size();
    std::vector<int> deg(n);
    std::ranges::transform(G, deg.begin(), [&](auto& g) { return g.size(); });
    std::vector<std::vector<int>> G2(n);
    std::vector<std::pair<int, int>> edges;
    for (int i = 0; i < n; ++i) {
        for (int j : G[i]) {
            if (std::make_pair(deg[i], i) < std::make_pair(deg[j], j)) {
                G2[i].push_back(j);
                edges.push_back({i, j});
            }
        }
    }
    std::vector<std::tuple<int, int, int>> ret;
    std::vector<bool> used(n);
    for (auto& [a, b] : edges) {
        for (int c : G2[a]) used[c] = true;
        for (int c : G2[b]) {
            if (used[c]) {
                ret.push_back({a, b, c});
            }
        }
        for (int c : G2[a]) used[c] = false;
    }
    return ret;
}
#line 5 "test/yosupo/enumerate_triangles.test.cpp"

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, s, t) for (int i = (int)(s); i < (int)(t); ++i)
#define revrep(i, t, s) for (int i = (int)(t)-1; i >= (int)(s); --i)
#define all(x) begin(x), end(x)
template <typename T> bool chmax(T& a, const T& b) { return a < b ? (a = b, 1) : 0; }
template <typename T> bool chmin(T& a, const T& b) { return a > b ? (a = b, 1) : 0; }

using mint = Modint<998244353>;

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

    int N, M;
    cin >> N >> M;
    vector<mint> x(N);
    for (auto& v : x) cin >> v;
    vector<vector<int>> G(N);
    rep(i,0,M) {
        int u, v;
        cin >> u >> v;
        G[u].push_back(v);
        G[v].push_back(u);
    }
    mint ans = 0;
    for (auto [a, b, c] : enumerate_triangles(G)) {
        ans += x[a]*x[b]*x[c];
    }
    cout << ans << endl;
}