Offline LCA(オフライン最小共通祖先) (graph/tree/offline-lca.hpp)

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Last update: 2024-04-22 02:14:31+09:00
Include: #include "graph/tree/offline-lca.hpp"

Depends on

Required by

Mo Tree(木上のMo) (other/mo-tree.hpp)

Verified with

Code

#include "../graph-template.hpp"
#include "../../structure/union-find/union-find.hpp"

/**
 * @brief Offline LCA(オフライン最小共通祖先)
 **/
template< typename T >
vector< int > offline_lca(const Graph< T > &g, vector< pair< int, int > > &qs, int root = 0) {
  int n = (int) g.size();
  UnionFind uf(n);
  vector< int > st(n), mark(n), ptr(n), ans(qs.size(), -1);
  int top = 0;
  st[top] = root;
  for(auto&[l, r]: qs) mark[l]++, mark[r]++;
  vector< vector< pair< int, int > > > q(n);
  for(int i = 0; i < n; i++) {
    q[i].reserve(mark[i]);
    mark[i] = -1;
    ptr[i] = (int) g[i].size();
  }
  for(int i = 0; i < qs.size(); i++) {
    q[qs[i].first].emplace_back(qs[i].second, i);
    q[qs[i].second].emplace_back(qs[i].first, i);
  }
  auto run = [&](int u) -> bool {
    while(ptr[u]) {
      int v = g[u][--ptr[u]];
      if(mark[v] == -1) {
        st[++top] = v;
        return true;
      }
    }
    return false;
  };
  while(~top) {
    int u = st[top];
    if(mark[u] == -1) {
      mark[u] = u;
    } else {
      uf.unite(u, g[u][ptr[u]]);
      mark[uf.find(u)] = u;
    }
    if(not run(u)) {
      for(auto&[v, i]: q[u]) {
        if(~mark[v] and ans[i] == -1) {
          ans[i] = mark[uf.find(v)];
        }
      }
      --top;
    }
  }
  return ans;
}

#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 2 "structure/union-find/union-find.hpp"

struct UnionFind {
  vector< int > data;

  UnionFind() = default;

  explicit UnionFind(size_t sz) : data(sz, -1) {}

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if(x == y) return false;
    if(data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if(data[k] < 0) return (k);
    return data[k] = find(data[k]);
  }

  int size(int k) {
    return -data[find(k)];
  }

  bool same(int x, int y) {
    return find(x) == find(y);
  }

  vector< vector< int > > groups() {
    int n = (int) data.size();
    vector< vector< int > > ret(n);
    for(int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(remove_if(begin(ret), end(ret), [&](const vector< int > &v) {
      return v.empty();
    }), end(ret));
    return ret;
  }
};
#line 3 "graph/tree/offline-lca.hpp"

/**
 * @brief Offline LCA(オフライン最小共通祖先)
 **/
template< typename T >
vector< int > offline_lca(const Graph< T > &g, vector< pair< int, int > > &qs, int root = 0) {
  int n = (int) g.size();
  UnionFind uf(n);
  vector< int > st(n), mark(n), ptr(n), ans(qs.size(), -1);
  int top = 0;
  st[top] = root;
  for(auto&[l, r]: qs) mark[l]++, mark[r]++;
  vector< vector< pair< int, int > > > q(n);
  for(int i = 0; i < n; i++) {
    q[i].reserve(mark[i]);
    mark[i] = -1;
    ptr[i] = (int) g[i].size();
  }
  for(int i = 0; i < qs.size(); i++) {
    q[qs[i].first].emplace_back(qs[i].second, i);
    q[qs[i].second].emplace_back(qs[i].first, i);
  }
  auto run = [&](int u) -> bool {
    while(ptr[u]) {
      int v = g[u][--ptr[u]];
      if(mark[v] == -1) {
        st[++top] = v;
        return true;
      }
    }
    return false;
  };
  while(~top) {
    int u = st[top];
    if(mark[u] == -1) {
      mark[u] = u;
    } else {
      uf.unite(u, g[u][ptr[u]]);
      mark[uf.find(u)] = u;
    }
    if(not run(u)) {
      for(auto&[v, i]: q[u]) {
        if(~mark[v] and ans[i] == -1) {
          ans[i] = mark[uf.find(v)];
        }
      }
      --top;
    }
  }
  return ans;
}