Luzhiled's Library

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:heavy_check_mark: test/verify/aoj-2306.test.cpp

Depends on

Code

#define 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"
#define 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 int mod = 1e9 + 7;

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
 * @docs docs/enumerate-cliques.md
 */
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";
}
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