Luzhiled's Library

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:heavy_check_mark: test/verify/aoj-0275.test.cpp

Depends on

Code

#define 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"
#define 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 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 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)
 * @docs docs/dijkstra.md
 */
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)
 * @docs docs/topological-sort.md
 */
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)
 * @docs docs/offline-dag-reachability.md
 */

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");
}
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