tree/dynamic-rerooting.hpp

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• Last update: 2024-04-28 09:13:11+09:00
• Include: #include "tree/dynamic-rerooting.hpp"

Verified with

• verify/verify-aoj-grl/aoj-grl-5-a-dynamic-rerooting.test.cpp
• verify/verify-yosupo-graph/yosupo-point-set-tree-path-composite-sum-fixed-root-2.test.cpp
• verify/verify-yosupo-graph/yosupo-point-set-tree-path-composite-sum.test.cpp
• verify/verify-yuki/yuki-0768.test.cpp
• verify/verify-yuki/yuki-1787.test.cpp
• verify/verify-yuki/yuki-1976.test.cpp
• verify/verify-yuki/yuki-2360.test.cpp
• verify/verify-yuki/yuki-2677.test.cpp

Code

#pragma once

namespace DynamicRerootingImpl {
template <typename Point, Point (*rake)(const Point &, const Point &)>
struct SplayTreeforDashedEdge {
  struct Node {
    Node *l, *r, *p;
    Point key, sum;

    explicit Node(const Point &_key)
        : l(nullptr), r(nullptr), p(nullptr), key(_key), sum(_key) {}
  };

  SplayTreeforDashedEdge() {}

  using NP = Node *;

  void rotr(NP t) {
    NP x = t->p, y = x->p;
    if ((x->l = t->r)) t->r->p = x;
    t->r = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
    }
  }

  void rotl(NP t) {
    NP x = t->p, y = x->p;
    if ((x->r = t->l)) t->l->p = x;
    t->l = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
    }
  }

  void update(NP t) {
    t->sum = t->key;
    if (t->l) t->sum = rake(t->sum, t->l->sum);
    if (t->r) t->sum = rake(t->sum, t->r->sum);
  }

  NP get_right(NP t) {
    while (t->r) t = t->r;
    return t;
  }

  NP alloc(const Point &v) {
    auto t = new Node(v);
    update(t);
    return t;
  }

  void splay(NP t) {
    while (t->p) {
      NP q = t->p;
      if (!q->p) {
        if (q->l == t)
          rotr(t);
        else
          rotl(t);
      } else {
        NP r = q->p;
        if (r->l == q) {
          if (q->l == t)
            rotr(q), rotr(t);
          else
            rotl(t), rotr(t);
        } else {
          if (q->r == t)
            rotl(q), rotl(t);
          else
            rotr(t), rotl(t);
        }
      }
    }
  }

  NP insert(NP t, const Point &v) {
    if (not t) {
      t = alloc(v);
      return t;
    } else {
      NP cur = get_right(t), z = alloc(v);
      splay(cur);
      z->p = cur;
      cur->r = z;
      update(cur);
      splay(z);
      return z;
    }
  }

  NP erase(NP t) {
    splay(t);
    NP x = t->l, y = t->r;
    delete t;
    if (not x) {
      t = y;
      if (t) t->p = nullptr;
    } else if (not y) {
      t = x;
      t->p = nullptr;
    } else {
      x->p = nullptr;
      t = get_right(x);
      splay(t);
      t->r = y;
      y->p = t;
      update(t);
    }
    return t;
  }
};

template <typename Path, typename Point, typename Info,
          Path (*vertex)(const Info &),
          Path (*compress)(const Path &, const Path &),
          Point (*rake)(const Point &, const Point &),
          Point (*add_edge)(const Path &),
          Path (*add_vertex)(const Point &, const Info &)>
struct TopTree {
 private:
  struct Node {
    Node *l, *r, *p;
    Info info;
    Path key, sum, mus;
    typename SplayTreeforDashedEdge<Point, rake>::Node *light, *belong;
    bool rev;

    bool is_root() const { return not p or (p->l != this and p->r != this); }

    explicit Node(const Info _info)
        : l(nullptr),
          r(nullptr),
          p(nullptr),
          info(_info),
          light(nullptr),
          belong(nullptr),
          rev(false) {}
  };

 public:
  using NP = Node *;
  SplayTreeforDashedEdge<Point, rake> splay_tree;

 private:
  void toggle(NP t) {
    swap(t->l, t->r);
    swap(t->sum, t->mus);
    t->rev ^= true;
  }

  void rotr(NP t) {
    NP x = t->p, y = x->p;
    push(x), push(t);
    if ((x->l = t->r)) t->r->p = x;
    t->r = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
    }
  }

  void rotl(NP t) {
    NP x = t->p, y = x->p;
    push(x), push(t);
    if ((x->r = t->l)) t->l->p = x;
    t->l = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
    }
  }

 public:
  TopTree() : splay_tree{} {}

  void push(NP t) {
    if (t->rev) {
      if (t->l) toggle(t->l);
      if (t->r) toggle(t->r);
      t->rev = false;
    }
  }

  void push_rev(NP t) {
    if (t->rev) {
      if (t->l) toggle(t->l);
      if (t->r) toggle(t->r);
      t->rev = false;
    }
  }

  void update(NP t) {
    Path key = t->light ? add_vertex(t->light->sum, t->info) : vertex(t->info);
    Path sum = key, mus = key;
    if (t->l) sum = compress(t->l->sum, sum), mus = compress(mus, t->l->mus);
    if (t->r) sum = compress(sum, t->r->sum), mus = compress(t->r->mus, mus);
    t->key = key, t->sum = sum, t->mus = mus;
  }

  void splay(NP t) {
    push(t);
    {
      NP rot = t;
      while (not rot->is_root()) rot = rot->p;
      t->belong = rot->belong;
      if (t != rot) rot->belong = nullptr;
    }
    while (not t->is_root()) {
      NP q = t->p;
      if (q->is_root()) {
        push_rev(q), push_rev(t);
        if (q->l == t)
          rotr(t);
        else
          rotl(t);
      } else {
        NP r = q->p;
        push_rev(r), push_rev(q), push_rev(t);
        if (r->l == q) {
          if (q->l == t)
            rotr(q), rotr(t);
          else
            rotl(t), rotr(t);
        } else {
          if (q->r == t)
            rotl(q), rotl(t);
          else
            rotr(t), rotl(t);
        }
      }
    }
  }

  NP expose(NP t) {
    NP rp = nullptr;
    for (NP cur = t; cur; cur = cur->p) {
      splay(cur);
      if (cur->r) {
        cur->light = splay_tree.insert(cur->light, add_edge(cur->r->sum));
        cur->r->belong = cur->light;
      }
      cur->r = rp;
      if (cur->r) {
        splay_tree.splay(cur->r->belong);
        push(cur->r);
        cur->light = splay_tree.erase(cur->r->belong);
      }
      update(cur);
      rp = cur;
    }
    splay(t);
    return rp;
  }

  void link(NP child, NP parent) {
    expose(parent);
    expose(child);
    child->p = parent;
    parent->r = child;
    update(parent);
  }

  void cut(NP child) {
    expose(child);
    NP parent = child->l;
    child->l = nullptr;
    parent->p = nullptr;
    update(child);
  }

  void evert(NP t) {
    expose(t);
    toggle(t);
    push(t);
  }

  NP alloc(const Info &info) {
    NP t = new Node(info);
    update(t);
    return t;
  }

  bool is_connected(NP u, NP v) {
    expose(u), expose(v);
    return u == v or u->p;
  }

  NP lca(NP u, NP v) {
    if (not is_connected(u, v)) return nullptr;
    expose(u);
    return expose(v);
  }

  void set_key(NP t, const Info &v) {
    expose(t);
    t->info = v;
    update(t);
  }

  // u を根とする sum
  Path query(NP u) {
    evert(u);
    return u->sum;
  }

  // root を根, u を部分木の根とする sum
  Path query_subtree(NP root, NP u) {
    evert(root);
    expose(u);
    NP l = u->l;
    u->l = nullptr;
    update(u);
    auto ret = u->sum;
    u->l = l;
    update(u);
    return ret;
  }
};

template <typename Path, typename Point, typename Info,
          Path (*vertex)(const Info &),
          Path (*compress)(const Path &, const Path &),
          Point (*rake)(const Point &, const Point &),
          Point (*Add_edge)(const Path &),
          Path (*add_vertex)(const Point &, const Info &)>
struct DynamicRerooting {
  int n;
  TopTree<Path, Point, Info, vertex, compress, rake, Add_edge, add_vertex> tt;
  using NP = typename decltype(tt)::NP;
  vector<NP> vs;

  DynamicRerooting(int _n, const vector<Info> &info) : n(_n), vs(n) {
    for (int i = 0; i < n; i++) vs[i] = tt.alloc(info[i]);
  }
  // u-v 間に辺を追加
  void add_edge(int u, int v) {
    tt.evert(vs[u]);
    tt.link(vs[u], vs[v]);
  }
  // u-v 間の辺を削除
  void del_edge(int u, int v) {
    tt.evert(vs[u]);
    tt.cut(vs[v]);
  }
  // 頂点 u の情報を取得
  Info get_info(int u) { return vs[u]->info; }
  // 頂点 u の情報を設定
  void set_info(int u, const Info &info) { tt.set_key(vs[u], info); }
  // 頂点 u を根とするクエリ
  Path query(int u) { return tt.query(vs[u]); }
  // 頂点 root を根, 頂点 u を部分木の根とするクエリ
  Path query_subtree(int root, int u) {
    return tt.query_subtree(vs[root], vs[u]);
  }
};

}  // namespace DynamicRerootingImpl

using DynamicRerootingImpl::DynamicRerooting;
using DynamicRerootingImpl::TopTree;

/*
struct Path {

};
struct Point {

};
struct Info {

};
Path vertex(const Info &i) {

}
Path compress(const Path &p, const Path &c) {

}
Point rake(const Point &a, const Point &b) {

}
Point add_edge(const Path &a) {

}
Path add_vertex(const Point &a, const Info &i) {

}

using DR = DynamicRerooting<Path, Point, Info, vertex, compress, rake, add_edge,
                            add_vertex>;
*/

#line 2 "tree/dynamic-rerooting.hpp"

namespace DynamicRerootingImpl {
template <typename Point, Point (*rake)(const Point &, const Point &)>
struct SplayTreeforDashedEdge {
  struct Node {
    Node *l, *r, *p;
    Point key, sum;

    explicit Node(const Point &_key)
        : l(nullptr), r(nullptr), p(nullptr), key(_key), sum(_key) {}
  };

  SplayTreeforDashedEdge() {}

  using NP = Node *;

  void rotr(NP t) {
    NP x = t->p, y = x->p;
    if ((x->l = t->r)) t->r->p = x;
    t->r = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
    }
  }

  void rotl(NP t) {
    NP x = t->p, y = x->p;
    if ((x->r = t->l)) t->l->p = x;
    t->l = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
    }
  }

  void update(NP t) {
    t->sum = t->key;
    if (t->l) t->sum = rake(t->sum, t->l->sum);
    if (t->r) t->sum = rake(t->sum, t->r->sum);
  }

  NP get_right(NP t) {
    while (t->r) t = t->r;
    return t;
  }

  NP alloc(const Point &v) {
    auto t = new Node(v);
    update(t);
    return t;
  }

  void splay(NP t) {
    while (t->p) {
      NP q = t->p;
      if (!q->p) {
        if (q->l == t)
          rotr(t);
        else
          rotl(t);
      } else {
        NP r = q->p;
        if (r->l == q) {
          if (q->l == t)
            rotr(q), rotr(t);
          else
            rotl(t), rotr(t);
        } else {
          if (q->r == t)
            rotl(q), rotl(t);
          else
            rotr(t), rotl(t);
        }
      }
    }
  }

  NP insert(NP t, const Point &v) {
    if (not t) {
      t = alloc(v);
      return t;
    } else {
      NP cur = get_right(t), z = alloc(v);
      splay(cur);
      z->p = cur;
      cur->r = z;
      update(cur);
      splay(z);
      return z;
    }
  }

  NP erase(NP t) {
    splay(t);
    NP x = t->l, y = t->r;
    delete t;
    if (not x) {
      t = y;
      if (t) t->p = nullptr;
    } else if (not y) {
      t = x;
      t->p = nullptr;
    } else {
      x->p = nullptr;
      t = get_right(x);
      splay(t);
      t->r = y;
      y->p = t;
      update(t);
    }
    return t;
  }
};

template <typename Path, typename Point, typename Info,
          Path (*vertex)(const Info &),
          Path (*compress)(const Path &, const Path &),
          Point (*rake)(const Point &, const Point &),
          Point (*add_edge)(const Path &),
          Path (*add_vertex)(const Point &, const Info &)>
struct TopTree {
 private:
  struct Node {
    Node *l, *r, *p;
    Info info;
    Path key, sum, mus;
    typename SplayTreeforDashedEdge<Point, rake>::Node *light, *belong;
    bool rev;

    bool is_root() const { return not p or (p->l != this and p->r != this); }

    explicit Node(const Info _info)
        : l(nullptr),
          r(nullptr),
          p(nullptr),
          info(_info),
          light(nullptr),
          belong(nullptr),
          rev(false) {}
  };

 public:
  using NP = Node *;
  SplayTreeforDashedEdge<Point, rake> splay_tree;

 private:
  void toggle(NP t) {
    swap(t->l, t->r);
    swap(t->sum, t->mus);
    t->rev ^= true;
  }

  void rotr(NP t) {
    NP x = t->p, y = x->p;
    push(x), push(t);
    if ((x->l = t->r)) t->r->p = x;
    t->r = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
    }
  }

  void rotl(NP t) {
    NP x = t->p, y = x->p;
    push(x), push(t);
    if ((x->r = t->l)) t->l->p = x;
    t->l = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
    }
  }

 public:
  TopTree() : splay_tree{} {}

  void push(NP t) {
    if (t->rev) {
      if (t->l) toggle(t->l);
      if (t->r) toggle(t->r);
      t->rev = false;
    }
  }

  void push_rev(NP t) {
    if (t->rev) {
      if (t->l) toggle(t->l);
      if (t->r) toggle(t->r);
      t->rev = false;
    }
  }

  void update(NP t) {
    Path key = t->light ? add_vertex(t->light->sum, t->info) : vertex(t->info);
    Path sum = key, mus = key;
    if (t->l) sum = compress(t->l->sum, sum), mus = compress(mus, t->l->mus);
    if (t->r) sum = compress(sum, t->r->sum), mus = compress(t->r->mus, mus);
    t->key = key, t->sum = sum, t->mus = mus;
  }

  void splay(NP t) {
    push(t);
    {
      NP rot = t;
      while (not rot->is_root()) rot = rot->p;
      t->belong = rot->belong;
      if (t != rot) rot->belong = nullptr;
    }
    while (not t->is_root()) {
      NP q = t->p;
      if (q->is_root()) {
        push_rev(q), push_rev(t);
        if (q->l == t)
          rotr(t);
        else
          rotl(t);
      } else {
        NP r = q->p;
        push_rev(r), push_rev(q), push_rev(t);
        if (r->l == q) {
          if (q->l == t)
            rotr(q), rotr(t);
          else
            rotl(t), rotr(t);
        } else {
          if (q->r == t)
            rotl(q), rotl(t);
          else
            rotr(t), rotl(t);
        }
      }
    }
  }

  NP expose(NP t) {
    NP rp = nullptr;
    for (NP cur = t; cur; cur = cur->p) {
      splay(cur);
      if (cur->r) {
        cur->light = splay_tree.insert(cur->light, add_edge(cur->r->sum));
        cur->r->belong = cur->light;
      }
      cur->r = rp;
      if (cur->r) {
        splay_tree.splay(cur->r->belong);
        push(cur->r);
        cur->light = splay_tree.erase(cur->r->belong);
      }
      update(cur);
      rp = cur;
    }
    splay(t);
    return rp;
  }

  void link(NP child, NP parent) {
    expose(parent);
    expose(child);
    child->p = parent;
    parent->r = child;
    update(parent);
  }

  void cut(NP child) {
    expose(child);
    NP parent = child->l;
    child->l = nullptr;
    parent->p = nullptr;
    update(child);
  }

  void evert(NP t) {
    expose(t);
    toggle(t);
    push(t);
  }

  NP alloc(const Info &info) {
    NP t = new Node(info);
    update(t);
    return t;
  }

  bool is_connected(NP u, NP v) {
    expose(u), expose(v);
    return u == v or u->p;
  }

  NP lca(NP u, NP v) {
    if (not is_connected(u, v)) return nullptr;
    expose(u);
    return expose(v);
  }

  void set_key(NP t, const Info &v) {
    expose(t);
    t->info = v;
    update(t);
  }

  // u を根とする sum
  Path query(NP u) {
    evert(u);
    return u->sum;
  }

  // root を根, u を部分木の根とする sum
  Path query_subtree(NP root, NP u) {
    evert(root);
    expose(u);
    NP l = u->l;
    u->l = nullptr;
    update(u);
    auto ret = u->sum;
    u->l = l;
    update(u);
    return ret;
  }
};

template <typename Path, typename Point, typename Info,
          Path (*vertex)(const Info &),
          Path (*compress)(const Path &, const Path &),
          Point (*rake)(const Point &, const Point &),
          Point (*Add_edge)(const Path &),
          Path (*add_vertex)(const Point &, const Info &)>
struct DynamicRerooting {
  int n;
  TopTree<Path, Point, Info, vertex, compress, rake, Add_edge, add_vertex> tt;
  using NP = typename decltype(tt)::NP;
  vector<NP> vs;

  DynamicRerooting(int _n, const vector<Info> &info) : n(_n), vs(n) {
    for (int i = 0; i < n; i++) vs[i] = tt.alloc(info[i]);
  }
  // u-v 間に辺を追加
  void add_edge(int u, int v) {
    tt.evert(vs[u]);
    tt.link(vs[u], vs[v]);
  }
  // u-v 間の辺を削除
  void del_edge(int u, int v) {
    tt.evert(vs[u]);
    tt.cut(vs[v]);
  }
  // 頂点 u の情報を取得
  Info get_info(int u) { return vs[u]->info; }
  // 頂点 u の情報を設定
  void set_info(int u, const Info &info) { tt.set_key(vs[u], info); }
  // 頂点 u を根とするクエリ
  Path query(int u) { return tt.query(vs[u]); }
  // 頂点 root を根, 頂点 u を部分木の根とするクエリ
  Path query_subtree(int root, int u) {
    return tt.query_subtree(vs[root], vs[u]);
  }
};

}  // namespace DynamicRerootingImpl

using DynamicRerootingImpl::DynamicRerooting;
using DynamicRerootingImpl::TopTree;

/*
struct Path {

};
struct Point {

};
struct Info {

};
Path vertex(const Info &i) {

}
Path compress(const Path &p, const Path &c) {

}
Point rake(const Point &a, const Point &b) {

}
Point add_edge(const Path &a) {

}
Path add_vertex(const Point &a, const Info &i) {

}

using DR = DynamicRerooting<Path, Point, Info, vertex, compress, rake, add_edge,
                            add_vertex>;
*/

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