test/verify/aoj-grl-2-a-3.test.cpp

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• Last update: 2024-04-24 02:34:04+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_A

Depends on

• Boruvka(最小全域木) (graph/mst/boruvka.hpp)
• Union Find (structure/union-find/union-find.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_A

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

#include "../../graph/mst/boruvka.hpp"

int main() {
  int V, E;
  cin >> V >> E;
  vector< int > X(E), Y(E), Z(E);
  for(int i = 0; i < E; i++) {
    cin >> X[i] >> Y[i] >> Z[i];
  }
  Boruvka< int > mst(V);
  auto f = [&](vector< pair< int, int > > &ret) {
    for(int i = 0; i < E; i++) {
      X[i] = mst.find(X[i]);
      Y[i] = mst.find(Y[i]);
      if(X[i] == Y[i]) continue;
      ret[X[i]] = min(ret[X[i]], make_pair(Z[i], Y[i]));
      ret[Y[i]] = min(ret[Y[i]], make_pair(Z[i], X[i]));
    }
    return ret;
  };
  cout << mst.build(f) << endl;
}

#line 1 "test/verify/aoj-grl-2-a-3.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_A

#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-grl-2-a-3.test.cpp"

#line 2 "structure/union-find/union-find.hpp"

struct UnionFind {
  vector< int > data;

  UnionFind() = default;

  explicit UnionFind(size_t sz) : data(sz, -1) {}

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if(x == y) return false;
    if(data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if(data[k] < 0) return (k);
    return data[k] = find(data[k]);
  }

  int size(int k) {
    return -data[find(k)];
  }

  bool same(int x, int y) {
    return find(x) == find(y);
  }

  vector< vector< int > > groups() {
    int n = (int) data.size();
    vector< vector< int > > ret(n);
    for(int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(remove_if(begin(ret), end(ret), [&](const vector< int > &v) {
      return v.empty();
    }), end(ret));
    return ret;
  }
};
#line 2 "graph/mst/boruvka.hpp"

/**
 * @brief Boruvka(最小全域木)
 * 
 */
template< typename T >
struct Boruvka {
private:
  size_t V;
  UnionFind uf;
  const T INF;

public:
  explicit Boruvka(size_t V, T INF = numeric_limits< T >::max()) : V(V), uf(V), INF(INF) {}

  inline int find(int k) {
    return uf.find(k);
  }

  template< typename F >
  T build(const F &update) {
    T ret = T();
    while(uf.size(0) < (int)V) {
      vector< pair< T, int > > v(V, make_pair(INF, -1));
      update(v);
      bool con = false;
      for(int i = 0; i < (int)V; i++) {
        if(v[i].second >= 0 && uf.unite(i, v[i].second)) {
          ret += v[i].first;
          con = true;
        }
      }
      if(!con) return INF;
    }
    return ret;
  }
};
#line 6 "test/verify/aoj-grl-2-a-3.test.cpp"

int main() {
  int V, E;
  cin >> V >> E;
  vector< int > X(E), Y(E), Z(E);
  for(int i = 0; i < E; i++) {
    cin >> X[i] >> Y[i] >> Z[i];
  }
  Boruvka< int > mst(V);
  auto f = [&](vector< pair< int, int > > &ret) {
    for(int i = 0; i < E; i++) {
      X[i] = mst.find(X[i]);
      Y[i] = mst.find(Y[i]);
      if(X[i] == Y[i]) continue;
      ret[X[i]] = min(ret[X[i]], make_pair(Z[i], Y[i]));
      ret[Y[i]] = min(ret[Y[i]], make_pair(Z[i], X[i]));
    }
    return ret;
  };
  cout << mst.build(f) << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample1.in	AC	6 ms	4 MB
g++	00_sample2.in	AC	6 ms	4 MB
g++	critical1.in	AC	6 ms	4 MB
g++	critical2.in	AC	7 ms	4 MB
g++	critical3.in	AC	18 ms	5 MB
g++	out1.in	AC	6 ms	4 MB
g++	out10.in	AC	26 ms	5 MB
g++	out11.in	AC	11 ms	4 MB
g++	out12.in	AC	16 ms	4 MB
g++	out13.in	AC	14 ms	4 MB
g++	out14.in	AC	15 ms	4 MB
g++	out15.in	AC	12 ms	4 MB
g++	out2.in	AC	6 ms	4 MB
g++	out3.in	AC	6 ms	4 MB
g++	out4.in	AC	6 ms	4 MB
g++	out5.in	AC	6 ms	4 MB
g++	out6.in	AC	25 ms	5 MB
g++	out7.in	AC	27 ms	5 MB
g++	out8.in	AC	27 ms	5 MB
g++	out9.in	AC	25 ms	5 MB
clang++	00_sample1.in	AC	6 ms	4 MB
clang++	00_sample2.in	AC	6 ms	4 MB
clang++	critical1.in	AC	6 ms	4 MB
clang++	critical2.in	AC	7 ms	4 MB
clang++	critical3.in	AC	18 ms	5 MB
clang++	out1.in	AC	6 ms	4 MB
clang++	out10.in	AC	28 ms	5 MB
clang++	out11.in	AC	12 ms	4 MB
clang++	out12.in	AC	16 ms	4 MB
clang++	out13.in	AC	14 ms	4 MB
clang++	out14.in	AC	15 ms	4 MB
clang++	out15.in	AC	13 ms	4 MB
clang++	out2.in	AC	6 ms	4 MB
clang++	out3.in	AC	6 ms	4 MB
clang++	out4.in	AC	6 ms	4 MB
clang++	out5.in	AC	6 ms	4 MB
clang++	out6.in	AC	26 ms	5 MB
clang++	out7.in	AC	28 ms	5 MB
clang++	out8.in	AC	28 ms	5 MB
clang++	out9.in	AC	26 ms	5 MB

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