test/verify/aoj-grl-2-b.test.cpp

• View this file on GitHub
• Last update: 2024-04-27 01:27:28+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_B

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)
• Directed MST(最小有向全域木) (graph/mst/directed-mst.hpp)
• Skew-Heap (structure/heap/skew-heap.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_B

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

#include "../../graph/mst/directed-mst.hpp"

int main() {
  int V, E, R;
  cin >> V >> E >> R;
  Edges< int > edges;
  for(int i = 0; i < E; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    edges.emplace_back(a, b, c);
  }
  cout << directed_mst(V, R, edges).cost << "\n";
}

#line 1 "test/verify/aoj-grl-2-b.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_B

#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-b.test.cpp"

#line 2 "graph/mst/directed-mst.hpp"

#line 1 "structure/heap/skew-heap.hpp"
/**
 * @brief Skew-Heap
 */
template <typename T, bool isMin = true>
struct SkewHeap {
  struct Node {
    T key, lazy;
    Node *l, *r;
    int idx;

    explicit Node(const T &key, int idx)
        : key(key), idx(idx), lazy(0), l(nullptr), r(nullptr) {}
  };

  SkewHeap() = default;

  Node *alloc(const T &key, int idx = -1) { return new Node(key, idx); }

  Node *propagate(Node *t) {
    if (t && t->lazy != 0) {
      if (t->l) t->l->lazy += t->lazy;
      if (t->r) t->r->lazy += t->lazy;
      t->key += t->lazy;
      t->lazy = 0;
    }
    return t;
  }

  Node *meld(Node *x, Node *y) {
    propagate(x), propagate(y);
    if (!x || !y) return x ? x : y;
    if ((x->key < y->key) ^ isMin) swap(x, y);
    x->r = meld(y, x->r);
    swap(x->l, x->r);
    return x;
  }

  Node *push(Node *t, const T &key, int idx = -1) {
    return meld(t, alloc(key, idx));
  }

  Node *pop(Node *t) {
    assert(t != nullptr);
    return meld(t->l, t->r);
  }

  Node *add(Node *t, const T &lazy) {
    if (t) {
      t->lazy += lazy;
      propagate(t);
    }
    return t;
  }

  Node *make_root() { return nullptr; }
};
#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 5 "graph/mst/directed-mst.hpp"

/**
 * @brief Directed MST(最小有向全域木)
 *
 */
template <typename T>
struct MinimumSpanningTree {
  T cost;
  Edges<T> edges;
};

template <typename T>
MinimumSpanningTree<T> directed_mst(int V, int root, Edges<T> edges) {
  for (int i = 0; i < V; ++i) {
    if (i != root) edges.emplace_back(i, root, 0);
  }

  int x = 0;
  vector<int> par(2 * V, -1), vis(par), link(par);

  using Heap = SkewHeap<T, true>;
  using Node = typename Heap::Node;

  Heap heap;
  vector<Node *> ins(2 * V, heap.make_root());

  for (int i = 0; i < (int)edges.size(); i++) {
    auto &e = edges[i];
    ins[e.to] = heap.push(ins[e.to], e.cost, i);
  }
  vector<int> st;
  auto go = [&](int x) {
    x = edges[ins[x]->idx].from;
    while (link[x] != -1) {
      st.emplace_back(x);
      x = link[x];
    }
    for (auto &p : st) {
      link[p] = x;
    }
    st.clear();
    return x;
  };
  for (int i = V; ins[x]; i++) {
    for (; vis[x] == -1; x = go(x)) vis[x] = 0;
    for (; x != i; x = go(x)) {
      auto w = ins[x]->key;
      auto v = heap.pop(ins[x]);
      v = heap.add(v, -w);
      ins[i] = heap.meld(ins[i], v);
      par[x] = i;
      link[x] = i;
    }
    for (; ins[x] && go(x) == x; ins[x] = heap.pop(ins[x]));
  }
  T cost = 0;
  Edges<T> ans;
  for (int i = root; i != -1; i = par[i]) {
    vis[i] = 1;
  }
  for (int i = x; i >= 0; i--) {
    if (vis[i] == 1) continue;
    cost += edges[ins[i]->idx].cost;
    ans.emplace_back(edges[ins[i]->idx]);
    for (int j = edges[ins[i]->idx].to; j != -1 && vis[j] == 0; j = par[j]) {
      vis[j] = 1;
    }
  }
  return {cost, ans};
}
#line 6 "test/verify/aoj-grl-2-b.test.cpp"

int main() {
  int V, E, R;
  cin >> V >> E >> R;
  Edges< int > edges;
  for(int i = 0; i < E; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    edges.emplace_back(a, b, c);
  }
  cout << directed_mst(V, R, edges).cost << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_00.in	AC	6 ms	4 MB
g++	00_sample_01.in	AC	6 ms	4 MB
g++	critical1.in	AC	6 ms	4 MB
g++	critical2.in	AC	6 ms	4 MB
g++	critical3.in	AC	6 ms	4 MB
g++	critical4.in	AC	6 ms	4 MB
g++	critical5.in	AC	6 ms	4 MB
g++	critical6.in	AC	6 ms	4 MB
g++	critical7.in	AC	6 ms	4 MB
g++	critical8.in	AC	6 ms	4 MB
g++	out1.in	AC	6 ms	4 MB
g++	out10.in	AC	6 ms	4 MB
g++	out11.in	AC	6 ms	4 MB
g++	out12.in	AC	6 ms	4 MB
g++	out13.in	AC	6 ms	4 MB
g++	out14.in	AC	6 ms	4 MB
g++	out15.in	AC	6 ms	4 MB
g++	out2.in	AC	6 ms	4 MB
g++	out3.in	AC	5 ms	4 MB
g++	out4.in	AC	6 ms	4 MB
g++	out5.in	AC	6 ms	4 MB
g++	out6.in	AC	6 ms	4 MB
g++	out7.in	AC	6 ms	4 MB
g++	out8.in	AC	6 ms	4 MB
g++	out9.in	AC	6 ms	4 MB
clang++	00_sample_00.in	AC	6 ms	4 MB
clang++	00_sample_01.in	AC	6 ms	4 MB
clang++	critical1.in	AC	6 ms	4 MB
clang++	critical2.in	AC	6 ms	4 MB
clang++	critical3.in	AC	6 ms	4 MB
clang++	critical4.in	AC	5 ms	4 MB
clang++	critical5.in	AC	6 ms	4 MB
clang++	critical6.in	AC	6 ms	4 MB
clang++	critical7.in	AC	6 ms	4 MB
clang++	critical8.in	AC	6 ms	4 MB
clang++	out1.in	AC	6 ms	4 MB
clang++	out10.in	AC	6 ms	4 MB
clang++	out11.in	AC	6 ms	4 MB
clang++	out12.in	AC	6 ms	4 MB
clang++	out13.in	AC	6 ms	4 MB
clang++	out14.in	AC	6 ms	4 MB
clang++	out15.in	AC	6 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	6 ms	4 MB
clang++	out7.in	AC	6 ms	4 MB
clang++	out8.in	AC	6 ms	4 MB
clang++	out9.in	AC	6 ms	4 MB

Back to top page