test/verify/aoj-0275.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=0275

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)
• Offline Dag Reachability(DAGの到達可能性クエリ) (graph/others/offline-dag-reachability.hpp)
• Topological Sort(トポロジカルソート) (graph/others/topological-sort.hpp)
• Dijkstra(単一始点最短路) (graph/shortest-path/dijkstra.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0275

#include "../../template/template.hpp"
#include "../../graph/shortest-path/dijkstra.hpp"
#include "../../graph/others/offline-dag-reachability.hpp"

int main() {
  int S, R, A, B, Q;
  cin >> S >> R;
  Graph< int > g(S);
  vector< int > U(R), V(R), C(R);
  for(int i = 0; i < R; i++) {
    cin >> U[i] >> V[i] >> C[i];
    --U[i], --V[i];
    g.add_edge(U[i], V[i], C[i]);
  }
  cin >> A >> B >> Q;
  --A, --B;
  auto pre = dijkstra(g, A).dist;
  auto suf = dijkstra(g, B).dist;

  Graph< int > dag(S);
  for(int i = 0; i < R; i++) {
    if(pre[U[i]] + C[i] + suf[V[i]] == pre[B]) dag.add_directed_edge(U[i], V[i]);
    if(pre[V[i]] + C[i] + suf[U[i]] == pre[B]) dag.add_directed_edge(V[i], U[i]);
  }
  vector< pair< int, int > > qs(Q);
  for(auto &p : qs) {
    cin >> p.first >> p.second;
    --p.first, --p.second;
  }
  auto ans = offline_dag_reachability(dag, qs);
  for(auto &p : ans) cout << (p ? "Yes\n" : "No\n");
}

#line 1 "test/verify/aoj-0275.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0275

#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 2 "graph/shortest-path/dijkstra.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/shortest-path/dijkstra.hpp"

/**
 * @brief Dijkstra(単一始点最短路)
 *
 */
template <typename T>
struct ShortestPath {
  vector<T> dist;
  vector<int> from, id;
};

template <typename T>
ShortestPath<T> dijkstra(const Graph<T> &g, int s) {
  const auto INF = numeric_limits<T>::max();
  vector<T> dist(g.size(), INF);
  vector<int> from(g.size(), -1), id(g.size(), -1);
  using Pi = pair<T, int>;
  priority_queue<Pi, vector<Pi>, greater<> > que;
  dist[s] = 0;
  que.emplace(dist[s], s);
  while (!que.empty()) {
    T cost;
    int idx;
    tie(cost, idx) = que.top();
    que.pop();
    if (dist[idx] < cost) continue;
    for (auto &e : g[idx]) {
      auto next_cost = cost + e.cost;
      if (dist[e.to] <= next_cost) continue;
      dist[e.to] = next_cost;
      from[e.to] = idx;
      id[e.to] = e.idx;
      que.emplace(dist[e.to], e.to);
    }
  }
  return {dist, from, id};
}
#line 2 "graph/others/offline-dag-reachability.hpp"

#line 2 "graph/others/topological-sort.hpp"

#line 4 "graph/others/topological-sort.hpp"

/**
 * @brief Topological Sort(トポロジカルソート)
 *
 */
template <typename T>
vector<int> topological_sort(const Graph<T> &g) {
  const int N = (int)g.size();
  vector<int> deg(N);
  for (int i = 0; i < N; i++) {
    for (auto &to : g[i]) ++deg[to];
  }
  stack<int> st;
  for (int i = 0; i < N; i++) {
    if (deg[i] == 0) st.emplace(i);
  }
  vector<int> ord;
  while (!st.empty()) {
    auto p = st.top();
    st.pop();
    ord.emplace_back(p);
    for (auto &to : g[p]) {
      if (--deg[to] == 0) st.emplace(to);
    }
  }
  return ord;
}
#line 5 "graph/others/offline-dag-reachability.hpp"

/**
 * @brief Offline Dag Reachability(DAGの到達可能性クエリ)
 *
 */

template <typename T>
vector<int> offline_dag_reachability(const Graph<T> &g,
                                     vector<pair<int, int> > &qs) {
  const int N = (int)g.size();
  const int Q = (int)qs.size();
  auto ord = topological_sort(g);
  vector<int> ans(Q);
  for (int l = 0; l < Q; l += 64) {
    int r = min(Q, l + 64);
    vector<int64_t> dp(N);
    for (int k = l; k < r; k++) {
      dp[qs[k].first] |= int64_t(1) << (k - l);
    }
    for (auto &idx : ord) {
      for (auto &to : g[idx]) dp[to] |= dp[idx];
    }
    for (int k = l; k < r; k++) {
      ans[k] = (dp[qs[k].second] >> (k - l)) & 1;
    }
  }
  return ans;
}
#line 6 "test/verify/aoj-0275.test.cpp"

int main() {
  int S, R, A, B, Q;
  cin >> S >> R;
  Graph< int > g(S);
  vector< int > U(R), V(R), C(R);
  for(int i = 0; i < R; i++) {
    cin >> U[i] >> V[i] >> C[i];
    --U[i], --V[i];
    g.add_edge(U[i], V[i], C[i]);
  }
  cin >> A >> B >> Q;
  --A, --B;
  auto pre = dijkstra(g, A).dist;
  auto suf = dijkstra(g, B).dist;

  Graph< int > dag(S);
  for(int i = 0; i < R; i++) {
    if(pre[U[i]] + C[i] + suf[V[i]] == pre[B]) dag.add_directed_edge(U[i], V[i]);
    if(pre[V[i]] + C[i] + suf[U[i]] == pre[B]) dag.add_directed_edge(V[i], U[i]);
  }
  vector< pair< int, int > > qs(Q);
  for(auto &p : qs) {
    cin >> p.first >> p.second;
    --p.first, --p.second;
  }
  auto ans = offline_dag_reachability(dag, qs);
  for(auto &p : ans) cout << (p ? "Yes\n" : "No\n");
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	testcase_00	AC	7 ms	4 MB
g++	testcase_01	AC	7 ms	4 MB
g++	testcase_02	AC	6 ms	4 MB
g++	testcase_03	AC	84 ms	20 MB
g++	testcase_04	AC	7 ms	4 MB
g++	testcase_05	AC	6 ms	4 MB
g++	testcase_06	AC	78 ms	20 MB
g++	testcase_07	AC	204 ms	26 MB
g++	testcase_08	AC	257 ms	23 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	83 ms	20 MB
clang++	testcase_04	AC	6 ms	4 MB
clang++	testcase_05	AC	6 ms	4 MB
clang++	testcase_06	AC	83 ms	20 MB
clang++	testcase_07	AC	201 ms	26 MB
clang++	testcase_08	AC	117 ms	23 MB

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