test/verify/aoj-2306.test.cpp

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• Last update: 2024-04-27 01:27:28+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2306

Depends on

• Enumerate Cliques(クリーク全列挙) (graph/others/enumerate-cliques.hpp)
• Square-Matrix(正方行列) (math/matrix/square-matrix.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2306

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

#include "../../math/matrix/square-matrix.hpp"
#include "../../graph/others/enumerate-cliques.hpp"

int main() {
  int N, M;
  cin >> N >> M;
  SquareMatrix< bool, 100 > g;
  SquareMatrix< int, 100 > h;
  for(int i = 0; i < M; i++) {
    int x, y, z;
    cin >> x >> y >> z;
    --x, --y;
    g[x][y] = true;
    g[y][x] = true;
    h[x][y] = z;
    h[y][x] = z;
  }
  auto cliques = enumerate_cliques(g);
  int ret = 0;
  for(auto &clique : cliques) {
    if(clique.size() == 1) continue;
    int add = 0;
    for(auto &i : clique) {
      int uku = 1 << 30;
      for(auto &j : clique) {
        if(i != j) uku = min(uku, h[i][j]);
      }
      add += uku;
    }
    ret = max(ret, add);
  }
  cout << ret << "\n";
}

#line 1 "test/verify/aoj-2306.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2306

#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/aoj-2306.test.cpp"

#line 1 "math/matrix/square-matrix.hpp"
/**
 * @brief Square-Matrix(正方行列)
 */
template <class T, size_t N>
struct SquareMatrix {
  array<array<T, N>, N> A;

  SquareMatrix() : A{{}} {}

  size_t size() const { return N; }

  inline const array<T, N> &operator[](int k) const { return (A.at(k)); }

  inline array<T, N> &operator[](int k) { return (A.at(k)); }

  static SquareMatrix add_identity() { return SquareMatrix(); }

  static SquareMatrix mul_identity() {
    SquareMatrix mat;
    for (size_t i = 0; i < N; i++) mat[i][i] = 1;
    return mat;
  }

  SquareMatrix &operator+=(const SquareMatrix &B) {
    for (size_t i = 0; i < N; i++) {
      for (size_t j = 0; j < N; j++) {
        (*this)[i][j] += B[i][j];
      }
    }
    return *this;
  }

  SquareMatrix &operator-=(const SquareMatrix &B) {
    for (size_t i = 0; i < N; i++) {
      for (size_t j = 0; j < N; j++) {
        (*this)[i][j] -= B[i][j];
      }
    }
    return *this;
  }

  SquareMatrix &operator*=(const SquareMatrix &B) {
    array<array<T, N>, N> C;
    for (size_t i = 0; i < N; i++) {
      for (size_t j = 0; j < N; j++) {
        for (size_t k = 0; k < N; k++) {
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
        }
      }
    }
    A.swap(C);
    return (*this);
  }

  SquareMatrix &operator^=(uint64_t k) {
    SquareMatrix B = SquareMatrix::mul_identity();
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return *this;
  }

  SquareMatrix operator+(const SquareMatrix &B) const {
    return SquareMatrix(*this) += B;
  }

  SquareMatrix operator-(const SquareMatrix &B) const {
    return SquareMatrix(*this) -= B;
  }

  SquareMatrix operator*(const SquareMatrix &B) const {
    return SquareMatrix(*this) *= B;
  }

  SquareMatrix operator^(uint64_t k) const { return SquareMatrix(*this) ^= k; }

  friend ostream &operator<<(ostream &os, SquareMatrix &p) {
    for (int i = 0; i < N; i++) {
      os << "[";
      for (int j = 0; j < N; j++) {
        os << p[i][j] << (j + 1 == N ? "]\n" : ",");
      }
    }
    return os;
  }
};
#line 1 "graph/others/enumerate-cliques.hpp"
/**
 * @brief Enumerate Cliques(クリーク全列挙)
 * @see https://www.slideshare.net/wata_orz/ss-12131479
 *
 */
template <typename Matrix>
vector<vector<int> > enumerate_cliques(Matrix &g) {
  int N = (int)g.size(), M = 0;
  vector<int> deg(N);
  vector<vector<int> > edge(N, vector<int>(N));
  for (int i = 0; i < N; i++) {
    for (auto p : g[i]) deg[i] += p;
    M += deg[i];
  }
  int lim = (int)sqrt(M);

  vector<vector<int> > cliques;

  auto add_clique = [&](const vector<int> &rem, bool last) {
    vector<int> neighbor((int)rem.size() - last);
    for (int i = 0; i < (int)neighbor.size(); i++) {
      for (int j = 0; j < (int)neighbor.size(); j++) {
        if (i != j && !g[rem[i]][rem[j]]) neighbor[i] |= 1 << j;
      }
    }
    for (int i = 1 - last; i < (1 << neighbor.size()); i++) {
      bool ok = true;
      for (int j = 0; j < (int)neighbor.size(); j++) {
        if ((i >> j) & 1) {
          if (i & neighbor[j]) {
            ok = false;
            break;
          }
        }
      }
      if (ok) {
        vector<int> clique;
        if (last) clique.emplace_back(rem.back());
        for (int j = 0; j < (int)neighbor.size(); j++) {
          if ((i >> j) & 1) clique.emplace_back(rem[j]);
        }
        cliques.emplace_back(clique);
      }
    }
  };

  vector<int> used(N);
  queue<int> que;
  for (int i = 0; i < N; i++) {
    if (deg[i] < lim) {
      used[i] = true;
      que.emplace(i);
    }
  }
  while (!que.empty()) {
    int idx = que.front();
    que.pop();
    vector<int> rem;
    for (int k = 0; k < N; k++) {
      if (g[idx][k]) rem.emplace_back(k);
    }
    rem.emplace_back(idx);
    add_clique(rem, true);
    used[idx] = true;
    for (int k = 0; k < N; k++) {
      if (g[idx][k]) {
        g[idx][k] = false;
        g[k][idx] = false;
        --deg[k];
        if (!used[k] && deg[k] < lim) {
          used[k] = true;
          que.emplace(k);
        }
      }
    }
  }
  vector<int> rem;
  for (int i = 0; i < N; i++) {
    if (!used[i]) rem.emplace_back(i);
  }
  add_clique(rem, false);
  return cliques;
}
#line 7 "test/verify/aoj-2306.test.cpp"

int main() {
  int N, M;
  cin >> N >> M;
  SquareMatrix< bool, 100 > g;
  SquareMatrix< int, 100 > h;
  for(int i = 0; i < M; i++) {
    int x, y, z;
    cin >> x >> y >> z;
    --x, --y;
    g[x][y] = true;
    g[y][x] = true;
    h[x][y] = z;
    h[y][x] = z;
  }
  auto cliques = enumerate_cliques(g);
  int ret = 0;
  for(auto &clique : cliques) {
    if(clique.size() == 1) continue;
    int add = 0;
    for(auto &i : clique) {
      int uku = 1 << 30;
      for(auto &j : clique) {
        if(i != j) uku = min(uku, h[i][j]);
      }
      add += uku;
    }
    ret = max(ret, add);
  }
  cout << ret << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	testcase_00	AC	6 ms	4 MB
g++	testcase_01	AC	6 ms	4 MB
g++	testcase_02	AC	6 ms	4 MB
g++	testcase_03	AC	6 ms	4 MB
g++	testcase_04	AC	6 ms	4 MB
g++	testcase_05	AC	6 ms	4 MB
g++	testcase_06	AC	6 ms	4 MB
g++	testcase_07	AC	6 ms	4 MB
g++	testcase_08	AC	6 ms	4 MB
g++	testcase_09	AC	6 ms	4 MB
g++	testcase_10	AC	6 ms	4 MB
g++	testcase_11	AC	6 ms	4 MB
g++	testcase_12	AC	6 ms	4 MB
g++	testcase_13	AC	6 ms	4 MB
g++	testcase_14	AC	11 ms	5 MB
g++	testcase_15	AC	11 ms	5 MB
g++	testcase_16	AC	11 ms	5 MB
g++	testcase_17	AC	11 ms	5 MB
g++	testcase_18	AC	11 ms	5 MB
g++	testcase_19	AC	11 ms	5 MB
g++	testcase_20	AC	11 ms	5 MB
g++	testcase_21	AC	11 ms	5 MB
g++	testcase_22	AC	11 ms	5 MB
g++	testcase_23	AC	11 ms	5 MB
g++	testcase_24	AC	6 ms	4 MB
g++	testcase_25	AC	6 ms	4 MB
g++	testcase_26	AC	6 ms	4 MB
g++	testcase_27	AC	6 ms	4 MB
g++	testcase_28	AC	6 ms	4 MB
g++	testcase_29	AC	6 ms	4 MB
g++	testcase_30	AC	7 ms	4 MB
g++	testcase_31	AC	6 ms	4 MB
g++	testcase_32	AC	7 ms	4 MB
g++	testcase_33	AC	9 ms	4 MB
g++	testcase_34	AC	6 ms	4 MB
g++	testcase_35	AC	6 ms	4 MB
g++	testcase_36	AC	6 ms	4 MB
g++	testcase_37	AC	6 ms	4 MB
g++	testcase_38	AC	6 ms	4 MB
g++	testcase_39	AC	6 ms	4 MB
g++	testcase_40	AC	6 ms	4 MB
g++	testcase_41	AC	6 ms	4 MB
g++	testcase_42	AC	7 ms	4 MB
g++	testcase_43	AC	9 ms	4 MB
g++	testcase_44	AC	6 ms	4 MB
g++	testcase_45	AC	6 ms	4 MB
g++	testcase_46	AC	6 ms	4 MB
g++	testcase_47	AC	6 ms	4 MB
g++	testcase_48	AC	6 ms	4 MB
g++	testcase_49	AC	6 ms	4 MB
g++	testcase_50	AC	6 ms	4 MB
g++	testcase_51	AC	7 ms	4 MB
g++	testcase_52	AC	7 ms	4 MB
g++	testcase_53	AC	8 ms	4 MB
g++	testcase_54	AC	7 ms	4 MB
clang++	testcase_00	AC	6 ms	4 MB
clang++	testcase_01	AC	6 ms	4 MB
clang++	testcase_02	AC	6 ms	4 MB
clang++	testcase_03	AC	6 ms	4 MB
clang++	testcase_04	AC	6 ms	4 MB
clang++	testcase_05	AC	6 ms	4 MB
clang++	testcase_06	AC	6 ms	4 MB
clang++	testcase_07	AC	6 ms	4 MB
clang++	testcase_08	AC	6 ms	4 MB
clang++	testcase_09	AC	6 ms	4 MB
clang++	testcase_10	AC	6 ms	4 MB
clang++	testcase_11	AC	6 ms	4 MB
clang++	testcase_12	AC	6 ms	4 MB
clang++	testcase_13	AC	6 ms	4 MB
clang++	testcase_14	AC	11 ms	5 MB
clang++	testcase_15	AC	11 ms	5 MB
clang++	testcase_16	AC	11 ms	5 MB
clang++	testcase_17	AC	11 ms	5 MB
clang++	testcase_18	AC	11 ms	5 MB
clang++	testcase_19	AC	11 ms	5 MB
clang++	testcase_20	AC	11 ms	5 MB
clang++	testcase_21	AC	11 ms	5 MB
clang++	testcase_22	AC	11 ms	5 MB
clang++	testcase_23	AC	11 ms	5 MB
clang++	testcase_24	AC	6 ms	4 MB
clang++	testcase_25	AC	6 ms	4 MB
clang++	testcase_26	AC	6 ms	4 MB
clang++	testcase_27	AC	6 ms	4 MB
clang++	testcase_28	AC	6 ms	4 MB
clang++	testcase_29	AC	6 ms	4 MB
clang++	testcase_30	AC	6 ms	4 MB
clang++	testcase_31	AC	6 ms	4 MB
clang++	testcase_32	AC	7 ms	4 MB
clang++	testcase_33	AC	8 ms	4 MB
clang++	testcase_34	AC	6 ms	4 MB
clang++	testcase_35	AC	6 ms	4 MB
clang++	testcase_36	AC	6 ms	4 MB
clang++	testcase_37	AC	6 ms	4 MB
clang++	testcase_38	AC	6 ms	4 MB
clang++	testcase_39	AC	6 ms	4 MB
clang++	testcase_40	AC	6 ms	4 MB
clang++	testcase_41	AC	7 ms	4 MB
clang++	testcase_42	AC	7 ms	4 MB
clang++	testcase_43	AC	8 ms	4 MB
clang++	testcase_44	AC	6 ms	4 MB
clang++	testcase_45	AC	6 ms	4 MB
clang++	testcase_46	AC	6 ms	4 MB
clang++	testcase_47	AC	7 ms	4 MB
clang++	testcase_48	AC	6 ms	4 MB
clang++	testcase_49	AC	6 ms	4 MB
clang++	testcase_50	AC	6 ms	4 MB
clang++	testcase_51	AC	7 ms	4 MB
clang++	testcase_52	AC	7 ms	4 MB
clang++	testcase_53	AC	8 ms	4 MB
clang++	testcase_54	AC	6 ms	4 MB

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