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#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"); }