Algorithm-Library

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:heavy_check_mark: data-structure/HLD.hpp

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Code

#include "../graph/template.hpp"
#include "../SegmentTree/segtree.hpp"

template <class T, T(*op)(const T&,const T&), T(*rev_op)(const T&,const T&), T(*e)()>
struct HLD {
  graph root;
  int n, in_cnt = 0;
  vector<int> pre, sh, sz, p;
  SegmentTree<T,op,e> seg;
  SegmentTree<T,rev_op,e> rseg;
  HLD(const graph &g) : root(g), n(g.size()), pre(n), sh(n), sz(n), p(n), seg(n), rseg(n){
    size(0, -1);
    calc(0, -1, 0);
  }
  void size(int pos, int par){
    sz[pos] = 1;
    int mx = -1, idx = -1, cnt = -1;
    for(const int &x : root[pos]){
      cnt++;
      if(x == par) continue;
      size(x, pos);
      sz[pos] += sz[x];
      if(chmax(mx, sz[x])) idx = cnt;
    }
    if(idx != -1) swap(root[pos][0], root[pos][idx]);
  }
  void calc(int pos, int par, int v){
    p[pos] = in_cnt++;
    sh[pos] = v;
    pre[pos] = par;
    int cnt = -1;
    for(const int &x : root[pos]){
      cnt++;
      if(x == par) continue;
      if(cnt) calc(x, pos, x);
      else calc(x, pos, v);
    }
  }
  void set(int u, const T &x){
    seg.set(p[u], x);
    rseg.set(p[u], x);
  }
  void build(){
    seg.build();
    rseg.build();
  }

  void update(int u, const T &x){
    seg.update(p[u], x);
    rseg.update(p[u], x);
  }
  vector<pair<int,int>> query_path(int u, int v){
    vector<pair<int,int>> lef, rig;
    while(sh[u] != sh[v]){
      if(p[u] < p[v]){
        rig.emplace_back(p[sh[v]], p[v]);
        v = pre[sh[v]];
      }
      else{
        lef.emplace_back(p[u], p[sh[u]]);
        u = pre[sh[u]];
      }
    }
    if(p[u] < p[v]) rig.emplace_back(p[u], p[v]);
    else lef.emplace_back(p[u], p[v]);
    reverse(all(rig));
    lef.insert(lef.end(), all(rig));
    return lef;
  }
  T query(int u, int v){
    T res = e();
    for(const auto &x : query_path(u, v)){
      if(x.first <= x.second){
        res = op(res, seg.query(x.first, x.second+1));
      }else{
        res = op(res, rseg.query(x.second, x.first+1));
      }
    }
    return res;
  }
  T get(const int i){ return seg.get(p[i]); }
};
#line 2 "graph/template.hpp"

/**
 * @brief Graph Template
*/
template <class T>
struct Edge {
  int from,to;
  T cost;
  int idx;
  Edge(){};
  Edge(int f, int t, T c=1, int i=-1) : from(f), to(t), cost(c), idx(i){}
  Edge(int t) : to(t), from(-1), cost(1), idx(-1){}
  operator int() const{ return to; }
  bool operator<(const Edge &e){ return cost < e.cost; }
};
template <class T>
struct Graph : vector<vector<Edge<T>>> {
  Graph(){}
  Graph(const int &n) : vector<vector<Edge<T>>>(n){}
  void add_edge(int a, int b, T c=1, int i=-1){
    (*this)[a].push_back({ a, b, c, i });
  }
};
using graph = Graph<int>;
#line 1 "SegmentTree/segtree.hpp"
template <class T, T(*op)(const T&,const T&), T(*e)()>
struct SegmentTree {
  SegmentTree(const int _n) : n(_n){
    while((1 << log) < n) log++;
    len = 1 << log;
    d.resize(len * 2, e());
  }
  void update(int k, const T &x){
    assert(0 <= k && k < n);
    k += len;
    d[k] = x;
    while(k > 1){
      k >>= 1;
      d[k] = op(d[k*2], d[k*2+1]);
    }
  }
  void set(const int i, const T &x){
    assert(0 <= i && i < n);
    d[i + len] = x;
  }
  T get(const int i) const{
    assert(0 <= i && i < n);
    return d[i + len];
  }
  void build(){
    for(int k = len - 1; k >= 1; k--)
      d[k] = op(d[2*k], d[2*k+1]);
  }
  T query(int l, int r){
    assert(0 <= l && l <= r && r <= n);
    l += len; r += len;
    T left = e(), right = e();
    while(l < r){
      if(l & 1) left = op(left, d[l++]);
      if(r & 1) right = op(d[--r], right);
      l >>= 1; r >>= 1;
    }
    return op(left, right);
  }
  template <class F>
  int max_right(int l, F f) const{
    assert(0 <= l && l <= n);
    assert(f(e()));
    if(l == n) return n;
    l += len;
    T sm = e();
    do {
      l /= l & -l;
      if(!f(op(sm, d[l]))){
        while(l < len){
          l <<= 1;
          if(f(op(sm, d[l]))){
            sm = op(sm, d[l]);
            l++;
          }
        }
        return l - len;
      }
      sm = op(sm, d[l]);
      l++;
    }while(l & (l - 1));
    return n;
  }
  template <class F>
  int min_left(int r, F f) const{
    assert(0 <= r && r <= n);
    assert(f(e()));
    if(r == 0) return 0;
    r += len;
    T sm = e();
    do {
      r /= r & -r;
      if(r > 1) r--;
      if(!f(op(d[r], sm))){
        while(r < len){
          r = r * 2 + 1;
          if(f(op(d[r], sm))){
            sm = op(d[r], sm);
            r--;
          }
        }
        return r + 1 - len;
      }
      sm = op(d[r], sm);
    }while(r & (r - 1));
    return 0;
  }
  private:
  int n = 1, log = 0, len = 0;
  vector<T> d;
};
#line 3 "data-structure/HLD.hpp"

template <class T, T(*op)(const T&,const T&), T(*rev_op)(const T&,const T&), T(*e)()>
struct HLD {
  graph root;
  int n, in_cnt = 0;
  vector<int> pre, sh, sz, p;
  SegmentTree<T,op,e> seg;
  SegmentTree<T,rev_op,e> rseg;
  HLD(const graph &g) : root(g), n(g.size()), pre(n), sh(n), sz(n), p(n), seg(n), rseg(n){
    size(0, -1);
    calc(0, -1, 0);
  }
  void size(int pos, int par){
    sz[pos] = 1;
    int mx = -1, idx = -1, cnt = -1;
    for(const int &x : root[pos]){
      cnt++;
      if(x == par) continue;
      size(x, pos);
      sz[pos] += sz[x];
      if(chmax(mx, sz[x])) idx = cnt;
    }
    if(idx != -1) swap(root[pos][0], root[pos][idx]);
  }
  void calc(int pos, int par, int v){
    p[pos] = in_cnt++;
    sh[pos] = v;
    pre[pos] = par;
    int cnt = -1;
    for(const int &x : root[pos]){
      cnt++;
      if(x == par) continue;
      if(cnt) calc(x, pos, x);
      else calc(x, pos, v);
    }
  }
  void set(int u, const T &x){
    seg.set(p[u], x);
    rseg.set(p[u], x);
  }
  void build(){
    seg.build();
    rseg.build();
  }

  void update(int u, const T &x){
    seg.update(p[u], x);
    rseg.update(p[u], x);
  }
  vector<pair<int,int>> query_path(int u, int v){
    vector<pair<int,int>> lef, rig;
    while(sh[u] != sh[v]){
      if(p[u] < p[v]){
        rig.emplace_back(p[sh[v]], p[v]);
        v = pre[sh[v]];
      }
      else{
        lef.emplace_back(p[u], p[sh[u]]);
        u = pre[sh[u]];
      }
    }
    if(p[u] < p[v]) rig.emplace_back(p[u], p[v]);
    else lef.emplace_back(p[u], p[v]);
    reverse(all(rig));
    lef.insert(lef.end(), all(rig));
    return lef;
  }
  T query(int u, int v){
    T res = e();
    for(const auto &x : query_path(u, v)){
      if(x.first <= x.second){
        res = op(res, seg.query(x.first, x.second+1));
      }else{
        res = op(res, rseg.query(x.second, x.first+1));
      }
    }
    return res;
  }
  T get(const int i){ return seg.get(p[i]); }
};
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