結果

問題 No.1326 ふたりのDominator
コンテスト
ユーザー りあん
提出日時 2020-12-23 01:13:02
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 468 ms / 2,000 ms
コード長 6,878 bytes
コンパイル時間 3,209 ms
コンパイル使用メモリ 215,488 KB
最終ジャッジ日時 2025-01-17 06:19:32
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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ファイルパターン 結果
sample AC * 1
other AC * 24
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ソースコード

diff # 

// from: https://judge.yosupo.jp/submission/6489

#include <bits/stdc++.h>

using namespace std;

using int64 = long long;


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);
    }
  }
};

template< typename T = int >
using Edges = vector< Edge< T > >;

template< typename T = int >
struct DominatorTree : Graph< T > {
public:
  using Graph< T >::Graph;
  using Graph< T >::g;

  void build(int root) {
    rg = Graph< T >(g.size());
    par.assign(g.size(), 0);
    idom.assign(g.size(), -1);
    semi.assign(g.size(), -1);
    ord.reserve(g.size());
    UnionFind uf(semi);

    const int N = (int) g.size();
    dfs(root);
    for(int i = 0; i < N; i++) {
      for(auto &to : g[i]) {
        if(~semi[i]) rg.add_directed_edge(to, i);
      }
    }

    vector< vector< int > > bucket(N);
    vector< int > U(N);
    for(int i = (int) ord.size() - 1; i >= 0; i--) {
      int x = ord[i];
      for(int v : rg.g[x]) {
        v = uf.eval(v);
        if(semi[x] > semi[v]) semi[x] = semi[v];
      }
      bucket[ord[semi[x]]].emplace_back(x);
      for(int v : bucket[par[x]]) U[v] = uf.eval(v);
      bucket[par[x]].clear();
      uf.link(par[x], x);
    }
    for(int i = 1; i < ord.size(); i++) {
      int x = ord[i], u = U[x];
      idom[x] = semi[x] == semi[u] ? semi[x] : idom[u];
    }
    for(int i = 1; i < ord.size(); i++) {
      int x = ord[i];
      idom[x] = ord[idom[x]];
    }
    idom[root] = root;
  }

  int operator[](const int &k) const {
    return idom[k];
  }

private:
  Graph< T > rg;

  struct UnionFind {
    const vector< int > &semi;
    vector< int > par, m;

    explicit UnionFind(const vector< int > &semi) : semi(semi), par(semi.size()), m(semi.size()) {
      iota(begin(par), end(par), 0);
      iota(begin(m), end(m), 0);
    }

    int find(int v) {
      if(par[v] == v) return v;
      int r = find(par[v]);
      if(semi[m[v]] > semi[m[par[v]]]) m[v] = m[par[v]];
      return par[v] = r;
    }

    int eval(int v) {
      find(v);
      return m[v];
    }

    void link(int p, int c) {
      par[c] = p;
    }
  };

  vector< int > ord, par;
  vector< int > idom, semi;

  void dfs(int idx) {
    semi[idx] = (int) ord.size();
    ord.emplace_back(idx);
    for(auto &to : g[idx]) {
      if(~semi[to]) continue;
      dfs(to);
      par[to] = idx;
    }
  }
};


struct dsu {
  public:
    dsu() : _n(0) {}
    dsu(int n) : _n(n), parent_or_size(n, -1) {}

    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }

    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

  private:
    int _n;
    // root node: -1 * component size
    // otherwise: parent
    std::vector<int> parent_or_size;
};


int dfs(int p, const DominatorTree<>& g, vector<int>& dep, int root) {
  if (dep[p] != -1) return dep[p];
  if (p == root) return dep[p] = 0;
  return dep[p] = dfs(g[p], g, dep, root) + 1;
}

void climb(int& p, const vector<vector<int>>& par, int k) {
  for (int i = 19; i >= 0; --i) {
    if ((k >> i) & 1) {
      p = par[i][p];
    }
  }
}

int lca(int& p, int& q, const vector<vector<int>>& par) {
  // assert(p != q);
  int res = 0;
  for (int i = 19; i >= 0; --i) {
    if (par[i][p] != par[i][q]) {
      res += 1 << i;
      p = par[i][p];
      q = par[i][q];
    }
  }
  return res;
}

int main() {
  using P = pair<int, int>;
  int n, m;
  cin >> n >> m;
  vector<P> edge(m);
  DominatorTree<> g(n);
  for (int i = 0; i < m; ++i) {
    int u, v;
    cin >> u >> v;
    --u;
    --v;
    g.add_edge(u, v);
    edge[i] = {u, v};
  }
  int root = 0;
  g.build(root);

  dsu uf(n);
  for (auto& e : edge) {
    if (g[e.first] != e.second && g[e.second] != e.first) {
      uf.merge(e.first, e.second);
    }
  }
  vector<int> dep(n, -1);
  for (int i = 0; i < n; ++i) {
    if (dep[i] == -1) {
      dfs(i, g, dep, root);
    }
  }

  vector<vector<int>> par(20, vector<int>(n, -1));
  for (int i = 0; i < n; ++i) {
    par[0][i] = g[i];
  }
  for (int i = 0; i + 1 < 20; ++i) {
    for (int j = 0; j < n; ++j) {
      par[i + 1][j] = par[i][par[i][j]];
    }
  }

  int q;
  cin >> q;
  for (int i = 0; i < q; ++i) {
    int x, y;
    cin >> x >> y;
    --x;
    --y;
    if (x == y) {
      cout << 0 << '\n';
      continue;
    }
    int ans = 0;
    if (dep[x] > dep[y]) {
      ans += dep[x] - dep[y];
      climb(x, par, dep[x] - dep[y]);
    }
    if (dep[x] < dep[y]) {
      ans += dep[y] - dep[x];
      climb(y, par, dep[y] - dep[x]);
    }
    if (x == y) --ans;
    int k = lca(x, y, par);
    ans += k * 2;
    if (!uf.same(x, y)) {
      ++ans;
    }
    cout << ans << '\n';
  }
  return 0;
}
0