test/verify/yosupo-enumerate-triangles.test.cpp

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• Last update: 2024-04-27 01:27:28+09:00
• Problem: https://judge.yosupo.jp/problem/enumerate_triangles

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)
• Enumerate Triangles(三角形全列挙) (graph/others/enumerate-triangles.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/enumerate_triangles

#include "../../template/template.hpp"

#include "../../graph/others/enumerate-triangles.hpp"

int main() {
    int N, M;
    cin >> N >> M;
    vector< int > xs(N);
    for(auto& x : xs) cin >> x;
    Graph<> g(N);
    g.read(M, 0);
    auto triangle = enumerate_triangles(g);
    const int MOD = 998244353;
    int ret = 0;
    for(auto& p : triangle) {
        int a, b, c;
        tie(a, b, c) = p;
        ret += 1LL * xs[a] * xs[b] % MOD * xs[c] % MOD;
        if(ret >= MOD) ret -= MOD;
    }
    cout << ret << "\n";
}

#line 1 "test/verify/yosupo-enumerate-triangles.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/enumerate_triangles

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-enumerate-triangles.test.cpp"

#line 2 "graph/others/enumerate-triangles.hpp"

#line 2 "graph/graph-template.hpp"

/**
 * @brief Graph Template(グラフテンプレート)
 */
template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  vector<vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

  inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 4 "graph/others/enumerate-triangles.hpp"

/**
 * @brief Enumerate Triangles(三角形全列挙)
 *
 */
template <typename T>
vector<tuple<int, int, int> > enumerate_triangles(const Graph<T> &g) {
  int N = (int)g.size();
  using pi = pair<int, int>;
  vector<pi> vp(N);
  for (int i = 0; i < N; i++) {
    vp[i] = {(int)g[i].size(), i};
  }
  vector<vector<int> > h(N);
  for (int i = 0; i < N; i++) {
    for (auto &j : g[i]) {
      if (vp[i] > vp[j]) {
        h[i].emplace_back(j);
      }
    }
  }
  vector<tuple<int, int, int> > triangle;
  vector<int> used(N);
  for (int x = 0; x < N; x++) {
    for (int z : h[x]) used[z] = true;
    for (int y : h[x]) {
      for (int z : h[y]) {
        if (used[z]) triangle.emplace_back(x, y, z);
      }
    }
    for (int z : h[x]) used[z] = false;
  }

  return triangle;
}
#line 6 "test/verify/yosupo-enumerate-triangles.test.cpp"

int main() {
    int N, M;
    cin >> N >> M;
    vector< int > xs(N);
    for(auto& x : xs) cin >> x;
    Graph<> g(N);
    g.read(M, 0);
    auto triangle = enumerate_triangles(g);
    const int MOD = 998244353;
    int ret = 0;
    for(auto& p : triangle) {
        int a, b, c;
        tie(a, b, c) = p;
        ret += 1LL * xs[a] * xs[b] % MOD * xs[c] % MOD;
        if(ret >= MOD) ret -= MOD;
    }
    cout << ret << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	6 ms	4 MB
g++	large_random_00	AC	28 ms	9 MB
g++	large_random_01	AC	20 ms	9 MB
g++	large_random_02	AC	30 ms	10 MB
g++	max_complete_00	AC	157 ms	205 MB
g++	max_random_00	AC	46 ms	16 MB
g++	max_random_01	AC	46 ms	16 MB
g++	max_random_02	AC	46 ms	16 MB
g++	minimum_00	AC	6 ms	4 MB
g++	small_dense_00	AC	6 ms	4 MB
g++	small_dense_01	AC	20 ms	17 MB
g++	small_dense_02	AC	7 ms	4 MB
g++	small_sparse_00	AC	6 ms	4 MB
g++	small_sparse_01	AC	6 ms	4 MB
g++	small_sparse_02	AC	6 ms	4 MB
g++	star_00	AC	35 ms	15 MB
g++	star_01	AC	34 ms	15 MB
clang++	example_00	AC	6 ms	4 MB
clang++	large_random_00	AC	27 ms	9 MB
clang++	large_random_01	AC	20 ms	9 MB
clang++	large_random_02	AC	30 ms	10 MB
clang++	max_complete_00	AC	156 ms	205 MB
clang++	max_random_00	AC	46 ms	16 MB
clang++	max_random_01	AC	46 ms	16 MB
clang++	max_random_02	AC	46 ms	16 MB
clang++	minimum_00	AC	6 ms	4 MB
clang++	small_dense_00	AC	6 ms	4 MB
clang++	small_dense_01	AC	21 ms	18 MB
clang++	small_dense_02	AC	7 ms	4 MB
clang++	small_sparse_00	AC	6 ms	4 MB
clang++	small_sparse_01	AC	6 ms	4 MB
clang++	small_sparse_02	AC	6 ms	4 MB
clang++	star_00	AC	34 ms	15 MB
clang++	star_01	AC	35 ms	15 MB

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