cpp/graph/tree/lowest-common-ancestor.cpp

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• Last update: 2023-11-13 13:19:52+09:00

Depends on

• cpp/data-structure/segment-tree/segment-tree.cpp

Required by

• cpp/geometry/two-points-distance.cpp

Verified with

• cpp/z_test/yosupo-lca.test.cpp

Code

#include "../../data-structure/segment-tree/segment-tree.cpp"

struct EulerTourForLCA {
  int n;
  vector<vector<int>> edge;
  vector<pair<int, int>> timeline;
  vector<pair<int,int>> stump;
  vector<int> parent;
  EulerTourForLCA(int n, vector<vector<int>> edge):
    n(n), edge(edge), timeline(2*n, {-1, 0}), stump(n, {-1,-1}), parent(n, 0), lock(n, false) {}

  void build(int top){
    timer = 0;
    lock.assign(n, false);
    lock[top] = true;
    dfs(top, 0);
  }
  const pair<int,int> operator[](int index){
    return stump[index];
  }
private:
  vector<bool> lock;
  int timer = 0;
  void dfs(int vertex, int depth){
    stump[vertex].first = timer;
    timeline[timer].first = vertex;
    timeline[timer].second = depth;
    timer++;
    for(int i = 0; (int)edge[vertex].size() > i; i++){
      if(!lock[edge[vertex][i]]){
        lock[edge[vertex][i]] = true;
        parent[edge[vertex][i]] = vertex;
        dfs(edge[vertex][i], depth+1);
      }
    }
    stump[vertex].second = timer;
    timeline[timer].first = parent[vertex];
    timeline[timer].second = depth-1;
    timer++;
  }
};


struct LowestCommonAncestor {
  int n;
  vector<vector<int>> edge;
  EulerTourForLCA et;
  function<pair<int,int>(pair<int,int>, pair<int,int>)> RMQ = [](pair<int,int> a, pair<int,int> b){
    if(a.second < b.second)return a;
    return b;
  };
  //function<const pair<int,int>> RMQ = [](pair<int,int> a, pair<int,int> b){
  //};
  SegmentTree<pair<int,int>, decltype(RMQ)> st;

  LowestCommonAncestor(int n, vector<vector<int>> edge):n(n), edge(edge), et(n, edge), st(2*n, RMQ, {n+1, n+1}){
    et.build(0);
    st.set(et.timeline);
  }

  int compute(int l, int r){
    auto ls = et[l].first;
    auto rs = et[r].first;
    if(ls > rs)swap(ls, rs);
    auto mn = st.getf(ls, rs);
    return mn.first;
  }
};
using LCA = LowestCommonAncestor;

#line 1 "cpp/data-structure/segment-tree/segment-tree.cpp"
template< typename T, typename F>
struct SegmentTree{
  private:
    int n;
    vector<T> node;

    F f;
    T initer;

  public:
    SegmentTree(int n_, F f, T initer) : f(f),initer(initer) {
      n = 1;
      while(n < n_)n*=2;
      node.resize(2*n-1, initer);
    }

    SegmentTree(int n_, F f,T initer, vector<T> x) : f(f),initer(initer) {
      n = 1;
      while(n < n_)n*=2;
      node.resize(2*n-1, initer);
      set(x);
    }

    void set(vector<T> x){
      for(int i = 0; (int)x.size() > i; i++){
        update(i,x[i]);
      }
    }

    void update(int x, T val){
      x += (n-1);

      node[x] = val;

      while(x > 0){
        x = (x-1)/2;
        node[x] = f(node[2*x+1],node[2*x+2]);
      }
    }

    void add(int x, T val){
      x += (n-1);
      
      node[x] += val;
      while(x > 0){
        x = (x-1)/2;
        node[x] = f(node[2*x+1],node[2*x+2]);
      }
    }

    T getf(int a,int b, int k=0, int l=0, int r=-1){
      
      if(r < 0){
        r = n-1;
      }
      if(r < a || b < l){
        return initer;
      }
      if(a <= l && r <= b){
        return node[k];
      }

      T vl = getf(a,b,2*k+1,l,(l+r)/2);
      T vr = getf(a,b,2*k+2,(l+r)/2+1,r);
      return f(vl,vr);
    }

    void debug(){
      int nw = 1;
      int curr = 1;
      cout << "---begin---" << endl;
      for(int i = 0; 2*n-1 > i; i++){
        cout << node[i] << " ";
        if(nw == curr)cout << endl,nw *= 2, curr=1;
        else curr++;
      }
      cout << "---end---" << endl;
    }
};

template <typename T, typename F>
SegmentTree<T, F> get_segment_tree(int N, const F &f, T initer){
  return SegmentTree<T,F>{N,f,initer};
}

template <typename T, typename F>
SegmentTree<T, F> get_segment_tree(int N, const F &f, T initer, vector<T> x){
  return SegmentTree<T,F>{N,f,initer,x};
}
#line 2 "cpp/graph/tree/lowest-common-ancestor.cpp"

struct EulerTourForLCA {
  int n;
  vector<vector<int>> edge;
  vector<pair<int, int>> timeline;
  vector<pair<int,int>> stump;
  vector<int> parent;
  EulerTourForLCA(int n, vector<vector<int>> edge):
    n(n), edge(edge), timeline(2*n, {-1, 0}), stump(n, {-1,-1}), parent(n, 0), lock(n, false) {}

  void build(int top){
    timer = 0;
    lock.assign(n, false);
    lock[top] = true;
    dfs(top, 0);
  }
  const pair<int,int> operator[](int index){
    return stump[index];
  }
private:
  vector<bool> lock;
  int timer = 0;
  void dfs(int vertex, int depth){
    stump[vertex].first = timer;
    timeline[timer].first = vertex;
    timeline[timer].second = depth;
    timer++;
    for(int i = 0; (int)edge[vertex].size() > i; i++){
      if(!lock[edge[vertex][i]]){
        lock[edge[vertex][i]] = true;
        parent[edge[vertex][i]] = vertex;
        dfs(edge[vertex][i], depth+1);
      }
    }
    stump[vertex].second = timer;
    timeline[timer].first = parent[vertex];
    timeline[timer].second = depth-1;
    timer++;
  }
};


struct LowestCommonAncestor {
  int n;
  vector<vector<int>> edge;
  EulerTourForLCA et;
  function<pair<int,int>(pair<int,int>, pair<int,int>)> RMQ = [](pair<int,int> a, pair<int,int> b){
    if(a.second < b.second)return a;
    return b;
  };
  //function<const pair<int,int>> RMQ = [](pair<int,int> a, pair<int,int> b){
  //};
  SegmentTree<pair<int,int>, decltype(RMQ)> st;

  LowestCommonAncestor(int n, vector<vector<int>> edge):n(n), edge(edge), et(n, edge), st(2*n, RMQ, {n+1, n+1}){
    et.build(0);
    st.set(et.timeline);
  }

  int compute(int l, int r){
    auto ls = et[l].first;
    auto rs = et[r].first;
    if(ls > rs)swap(ls, rs);
    auto mn = st.getf(ls, rs);
    return mn.first;
  }
};
using LCA = LowestCommonAncestor;

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