結果

問題 No.1745 Selfish Spies 2 (à la Princess' Perfectionism)
コンテスト
ユーザー opt
提出日時 2021-11-09 14:24:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 560 ms / 5,000 ms
コード長 4,711 bytes
コンパイル時間 5,088 ms
コンパイル使用メモリ 284,192 KB
最終ジャッジ日時 2025-01-25 15:01:29
ジャッジサーバーID
（参考情報） 		judge6 / judge2
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ファイルパターン 結果
other AC * 59
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ソースコード

diff # 

#include<bits/stdc++.h>
using namespace std;
#include<atcoder/all>
using namespace atcoder;
#define rep_(i, a_, b_, a, b, ...) for (int i = (a), lim##i = (b); i < lim##i; ++i)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) // rep(i, a): [0, a); rep(i, a, b): [a, b)
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;

template<class T> istream &operator>>(istream &is, vector<T> &v) { for (auto &e : v) is >> e; return is; }
template<class T> ostream &operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <class Head, class... Tail> void debug_out(Head H, Tail... T) { cerr << ' ' << H; debug_out(T...); }
#define debug(...) cerr << 'L' << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << 'L' << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

struct dm_decomposition {
  using edge = pair<int, int>;
  int r, c;
  vector<edge> E;
  dm_decomposition(int _r, int _c) : r(_r), c(_c) {}
  void add_edge(int i, int j) { E.emplace_back(i, j); }

  pair<vector<vector<int>>, vector<vector<int>>> decompose() {
    int n = r + c, m = E.size();
    int s = n, t = s + 1;
    vector<vector<array<int, 3>>> G(n);
    vector<bool> is_used_V(n);
    {
      // max flow
      atcoder::mf_graph<int> mfg(n + 2);
      for (auto [i, j] : E) mfg.add_edge(i, r + j, 1);
      for (int i = 0; i < r; i++) mfg.add_edge(s, i, 1);
      for (int j = 0; j < c; j++) mfg.add_edge(r + j, t, 1);
      mfg.flow(s, t);

      // construct graph
      for (int k = 0; k < m; k++) {
        auto e = mfg.get_edge(k);
        if (e.flow == 1) {
          G[e.from].push_back({k, e.to, 3});
          G[e.to].push_back({k, e.from, 3});
          is_used_V[e.from] = is_used_V[e.to] = true;
        }
        else {
          G[e.from].push_back({k, e.to, 1});
          G[e.to].push_back({k, e.from, 2});
        }
      }
    }

    vector<int> V_0, V_inf;
    {
      // check reachability
      vector<int> R_unused, C_unused;
      for (int u = 0; u < r; u++) if (!is_used_V[u]) R_unused.push_back(u);
      for (int u = r; u < n; u++) if (!is_used_V[u]) C_unused.push_back(u);
      auto bfs = [&] (vector<int>& S, bool fwd) {
        vector<bool> seen(n);
        queue<int> que;
        for (auto u : S) seen[u] = true, que.push(u);
        while (!que.empty()) {
          auto u = que.front(); que.pop();
          for (auto [id, v, d] : G[u]) {
            if ((fwd && (d >> 0 & 1)) || (!fwd && (d >> 1 & 1))) {
              if (seen[v] == false) seen[v] = true, que.push(v);
            }
          }
        }
        vector<int> res;
        for (int u = 0; u < n; u++) if (seen[u]) res.push_back(u);
        return res;
      };
      V_inf = bfs(R_unused, true);
      V_0 = bfs(C_unused, false);
    }

    // erase nodes and edges
    vector<bool> is_erased_V(n), is_erased_E(m);
    for (auto u : V_0) {
      is_erased_V[u] = true;
      for (auto [id, v, d] : G[u]) is_erased_E[id] = true;
    }
    for (auto u : V_inf) {
      is_erased_V[u] = true;
      for (auto [id, v, d] : G[u]) is_erased_E[id] = true;
    }

    vector<vector<int>> Rs, Cs;
    auto push_nodes = [&] (vector<int>& V) {
      if (V.empty()) return;
      Rs.push_back({}), Cs.push_back({});
      for (auto u : V) {
        if (u < r) Rs.back().push_back(u);
        else Cs.back().push_back(u - r);
      }
    };
    push_nodes(V_0);

    // scc decomposition
    atcoder::scc_graph sccg(n);
    for (int u = 0; u < n; u++) {
      for (auto [id, v, d] : G[u]) {
        if ((d & 1) && !is_erased_E[id]) sccg.add_edge(u, v);
      }
    }
    for (auto vs : sccg.scc()) {
      if (is_erased_V[vs.front()]) continue;
      push_nodes(vs);
    }
    push_nodes(V_inf);
    return {Rs, Cs};
  }
};


void solve() {
  int n, m, l; cin >> n >> m >> l;
  assert(1 <= n && n <= int(1e5));
  assert(1 <= m && m <= int(1e5));
  assert(1 <= l && l <= int(2e5));

  dm_decomposition dm(n, m);
  set<pair<int, int>> S;
  rep(i, l) {
    int s, t; cin >> s >> t;
    assert(1 <= s && s <= n);
    assert(1 <= t && t <= m);
    S.emplace(s, t);
    --s, --t;
    dm.add_edge(s, t);
  }
  assert(S.size() == l);

  auto [rs, cs] = dm.decompose();

  vector<int> cid_R(n), cid_C(m);
  int cnum = rs.size();
  rep(k, cnum) for (auto i : rs[k]) cid_R[i] = k;
  rep(k, cnum) for (auto i : cs[k]) cid_C[i] = k;

  for (auto [i, j] : dm.E) {
    int p = cid_R[i], q = cid_C[j];
    cout << (p == q ? "Yes" : "No") << '\n';
  }
}


int main() {
  solve();
}
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