Luzhiled's Library

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:heavy_check_mark: test/verify/yosupo-dominatortree.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/dominatortree"

#include "../../template/template.hpp"

#include "../../graph/others/dominator-tree.hpp"

int main() {
  int N, M, S;
  cin >> N >> M >> S;
  DominatorTree<> g(N);
  g.read(M, 0, false, true);
  g.build(S);
  for(int i = 0; i < N; i++) cout << g[i] << " ";
  cout << endl;
}
#line 1 "test/verify/yosupo-dominatortree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/dominatortree"

#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 4 "test/verify/yosupo-dominatortree.test.cpp"

#line 2 "graph/others/dominator-tree.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/others/dominator-tree.hpp"

/**
 * @brief Dominator Tree
 * @docs docs/dominator-tree.md
 * @see http://sigma425.hatenablog.com/entry/2015/12/25/224053
 */
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[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 < (int)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 < (int)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;
    }
  }
};
#line 6 "test/verify/yosupo-dominatortree.test.cpp"

int main() {
  int N, M, S;
  cin >> N >> M >> S;
  DominatorTree<> g(N);
  g.read(M, 0, false, true);
  g.build(S);
  for(int i = 0; i < N; i++) cout << g[i] << " ";
  cout << endl;
}
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