Luzhiled's Library

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:heavy_check_mark: Link Cut Tree Lazy Path
(structure/lct/link-cut-tree-lazy-path.hpp)

概要

Link Cut Tree とは動的木の一つで, 辺の追加や削除などの木構造の動的な変化がある場合でも効率的にクエリを処理できる.

使い方

計算量

Verified with

Code

/**
 * @brief Link Cut Tree Lazy Path
 * @docs docs/link-cut-tree-lazy-path.md
 */
template< typename T, typename E, typename F, typename G, typename H, typename S >
struct LinkCutTreeLazyPath {

private:
  F f;
  G g;
  H h;
  S s;
  E e0;

  struct Node {
    Node *l, *r, *p;
    T key, sum;
    E lazy;
    bool rev;
    size_t sz;

    explicit Node(const T &v, const E &e) : key(v), sum(v), lazy(e), sz(1), rev(false),
                                            l(nullptr), r(nullptr), p(nullptr) {}

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

public:
  using NP = Node *;

private:
  NP update(NP t) {
    t->sz = 1;
    t->sum = t->key;
    if(t->l) t->sz += t->l->sz, t->sum = f(t->l->sum, t->sum);
    if(t->r) t->sz += t->r->sz, t->sum = f(t->sum, t->r->sum);
    return t;
  }

  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;
      update(y);
    }
  }

  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;
      update(y);
    }
  }

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

  void propagate(NP t, const E &e) {
    t->lazy = h(t->lazy, e);
    t->key = g(t->key, e);
    t->sum = g(t->sum, e);
  }

  void push(NP t) {
    if(t->lazy != e0) {
      if(t->l) propagate(t->l, t->lazy);
      if(t->r) propagate(t->r, t->lazy);
      t->lazy = e0;
    }
    if(t->rev) {
      if(t->l) toggle(t->l);
      if(t->r) toggle(t->r);
      t->rev = false;
    }
  }

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

public:
  LinkCutTreeLazyPath(const F &f, const G &g, const H &h, const S &s, const E &e0) :
      f(f), g(g), h(h), s(s), e0(e0) {}

  NP alloc(const T &v = T()) {
    return new Node(v, e0);
  }

  vector< NP > build(vector< T > &vs) {
    vector< NP > nodes(vs.size());
    for(int i = 0; i < (int) vs.size(); i++) {
      nodes[i] = alloc(vs[i]);
    }
    return nodes;
  }

  NP expose(NP t) {
    NP rp = nullptr;
    for(NP cur = t; cur; cur = cur->p) {
      splay(cur);
      cur->r = rp;
      update(cur);
      rp = cur;
    }
    splay(t);
    return rp;
  }

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

  void link(NP child, NP parent) {
    if(is_connected(child, parent)) {
      throw runtime_error("child and parent must be different connected components");
    }
    if(child->l) {
      throw runtime_error("child must be root");
    }
    child->p = parent;
    parent->r = child;
    update(parent);
  }

  void cut(NP child) {
    expose(child);
    NP parent = child->l;
    if(not parent) {
      throw runtime_error("child must not be root");
    }
    child->l = nullptr;
    parent->p = nullptr;
    update(child);
  }

  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);
  }

  NP get_kth(NP x, int k) {
    expose(x);
    while(x) {
      push(x);
      if(x->r && x->r->sz > k) {
        x = x->r;
      } else {
        if(x->r) k -= x->r->sz;
        if(k == 0) return x;
        k -= 1;
        x = x->l;
      }
    }
    return nullptr;
  }

  const T &query(NP u) {
    expose(u);
    return u->sum;
  }

  const T &query(NP u, NP v) {
    evert(u);
    return query(v);
  }

  void set_key(NP t, T v) {
    expose(t);
    t->key = v;
    update(t);
  }

  void set_propagate(NP t, const E &e) {
    expose(t);
    propagate(t, e);
    push(t);
  }

  void set_propagate(NP u, NP v, const E &e) {
    evert(u);
    set_propagate(v, e);
  }
};

template< typename T, typename E, typename F, typename G, typename H, typename S >
LinkCutTreeLazyPath< T, E, F, G, H, S > get_link_cut_tree_lazy_path(const F &f, const G &g, const H &h, const S &s, const E &e0) {
  return {f, g, h, s, e0};
}
#line 1 "structure/lct/link-cut-tree-lazy-path.hpp"
/**
 * @brief Link Cut Tree Lazy Path
 * @docs docs/link-cut-tree-lazy-path.md
 */
template< typename T, typename E, typename F, typename G, typename H, typename S >
struct LinkCutTreeLazyPath {

private:
  F f;
  G g;
  H h;
  S s;
  E e0;

  struct Node {
    Node *l, *r, *p;
    T key, sum;
    E lazy;
    bool rev;
    size_t sz;

    explicit Node(const T &v, const E &e) : key(v), sum(v), lazy(e), sz(1), rev(false),
                                            l(nullptr), r(nullptr), p(nullptr) {}

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

public:
  using NP = Node *;

private:
  NP update(NP t) {
    t->sz = 1;
    t->sum = t->key;
    if(t->l) t->sz += t->l->sz, t->sum = f(t->l->sum, t->sum);
    if(t->r) t->sz += t->r->sz, t->sum = f(t->sum, t->r->sum);
    return t;
  }

  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;
      update(y);
    }
  }

  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;
      update(y);
    }
  }

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

  void propagate(NP t, const E &e) {
    t->lazy = h(t->lazy, e);
    t->key = g(t->key, e);
    t->sum = g(t->sum, e);
  }

  void push(NP t) {
    if(t->lazy != e0) {
      if(t->l) propagate(t->l, t->lazy);
      if(t->r) propagate(t->r, t->lazy);
      t->lazy = e0;
    }
    if(t->rev) {
      if(t->l) toggle(t->l);
      if(t->r) toggle(t->r);
      t->rev = false;
    }
  }

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

public:
  LinkCutTreeLazyPath(const F &f, const G &g, const H &h, const S &s, const E &e0) :
      f(f), g(g), h(h), s(s), e0(e0) {}

  NP alloc(const T &v = T()) {
    return new Node(v, e0);
  }

  vector< NP > build(vector< T > &vs) {
    vector< NP > nodes(vs.size());
    for(int i = 0; i < (int) vs.size(); i++) {
      nodes[i] = alloc(vs[i]);
    }
    return nodes;
  }

  NP expose(NP t) {
    NP rp = nullptr;
    for(NP cur = t; cur; cur = cur->p) {
      splay(cur);
      cur->r = rp;
      update(cur);
      rp = cur;
    }
    splay(t);
    return rp;
  }

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

  void link(NP child, NP parent) {
    if(is_connected(child, parent)) {
      throw runtime_error("child and parent must be different connected components");
    }
    if(child->l) {
      throw runtime_error("child must be root");
    }
    child->p = parent;
    parent->r = child;
    update(parent);
  }

  void cut(NP child) {
    expose(child);
    NP parent = child->l;
    if(not parent) {
      throw runtime_error("child must not be root");
    }
    child->l = nullptr;
    parent->p = nullptr;
    update(child);
  }

  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);
  }

  NP get_kth(NP x, int k) {
    expose(x);
    while(x) {
      push(x);
      if(x->r && x->r->sz > k) {
        x = x->r;
      } else {
        if(x->r) k -= x->r->sz;
        if(k == 0) return x;
        k -= 1;
        x = x->l;
      }
    }
    return nullptr;
  }

  const T &query(NP u) {
    expose(u);
    return u->sum;
  }

  const T &query(NP u, NP v) {
    evert(u);
    return query(v);
  }

  void set_key(NP t, T v) {
    expose(t);
    t->key = v;
    update(t);
  }

  void set_propagate(NP t, const E &e) {
    expose(t);
    propagate(t, e);
    push(t);
  }

  void set_propagate(NP u, NP v, const E &e) {
    evert(u);
    set_propagate(v, e);
  }
};

template< typename T, typename E, typename F, typename G, typename H, typename S >
LinkCutTreeLazyPath< T, E, F, G, H, S > get_link_cut_tree_lazy_path(const F &f, const G &g, const H &h, const S &s, const E &e0) {
  return {f, g, h, s, e0};
}
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