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:warning: ds/segtree/dynamic_dual_segtree.hpp

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// Source: https://github.com/maspypy/library/blob/main/ds/segtree/dynamic_dual_segtree.hpp
#include "ds/node_pool.hpp"

// Q*2logN 程度必要
// https://qoj.ac/contest/1516/problem/8240
template <typename Monoid, bool PERSISTENT>
struct Dynamic_Dual_SegTree {
  using MX = Monoid;
  using X = typename MX::value_type;

  struct Node {
    Node *l, *r;
    X x;
  };

  const ll L0, R0;
  Node_Pool<Node> pool;
  using np = Node *;

  Dynamic_Dual_SegTree(ll L0, ll R0) : L0(L0), R0(R0) {}

  np new_root() { return new_node(MX::id()); }

  np new_node(const X x = MX::id()) {
    np c = pool.create();
    c->l = c->r = nullptr, c->x = x;
    return c;
  }

  np new_node(const vc<X> &dat) {
    assert(L0 == 0 && R0 == len(dat));
    auto dfs = [&](auto &dfs, ll l, ll r) -> Node * {
      if (l == r) return nullptr;
      if (r == l + 1) return new_node(dat[l]);
      ll m = (l + r) / 2;
      np l_root = dfs(dfs, l, m), r_root = dfs(dfs, m, r);
      X x = MX::op(l_root->x, r_root->x);
      np root = new_node();
      root->l = l_root, root->r = r_root;
      return root;
    };
    return dfs(dfs, 0, len(dat));
  }

  X get(np root, ll i) {
    if (!root) return MX::id();
    X x = MX::id();
    get_rec(root, L0, R0, i, x);
    return x;
  }

  np apply(np root, ll l, ll r, const X &x) {
    if (l == r) return root;
    assert(root && L0 <= l && l < r && r <= R0);
    root = clone(root);
    apply_rec(root, L0, R0, l, r, x);
    return root;
  }

  // root[l:r) を other[l:r)*x で上書きしたものを返す
  np copy_interval(np root, np other, ll l, ll r, X x) {
    if (root == other) return root;
    root = clone(root);
    copy_interval_rec(root, other, L0, R0, l, r, x);
    return root;
  }

  void reset() { pool.reset(); }

  vc<X> get_all(np root) {
    vc<X> res;
    auto dfs = [&](auto &dfs, np c, ll L, ll R, X x) -> void {
      if (!c) {
        FOR(R - L) res.eb(x);
        return;
      }
      x = MX::op(c->x, x);
      if (R == L + 1) {
        res.eb(x);
        return;
      }
      ll M = (L + R) / 2;
      dfs(dfs, c->l, L, M, x);
      dfs(dfs, c->r, M, R, x);
    };
    dfs(dfs, root, L0, R0, MX::id());
    return res;
  }

 private:
  np clone(np c) {
    if (!c || !PERSISTENT) return c;
    return pool.clone(c);
  }

  void apply_rec(np c, ll l, ll r, ll ql, ll qr, const X &a) {
    // もう c は新しくしてある
    assert(c);
    chmax(ql, l), chmin(qr, r);
    if (ql >= qr) return;
    if (l == ql && r == qr) {
      c->x = MX::op(c->x, a);
      return;
    }
    // push
    c->l = (c->l ? clone(c->l) : new_node());
    c->r = (c->r ? clone(c->r) : new_node());
    c->l->x = MX::op(c->l->x, c->x);
    c->r->x = MX::op(c->r->x, c->x);
    c->x = MX::id();
    ll m = (l + r) / 2;
    apply_rec(c->l, l, m, ql, qr, a), apply_rec(c->r, m, r, ql, qr, a);
    return;
  }

  void copy_interval_rec(np c, np d, ll l, ll r, ll ql, ll qr, X x) {
    // c[ql,qr) <- d[ql,qr) * x
    // もう c は新しくしてある
    assert(c);
    chmax(ql, l), chmin(qr, r);
    if (ql >= qr) return;
    if (l == ql && r == qr) {
      if (d)
        c->x = MX::op(d->x, x), c->l = d->l, c->r = d->r;
      else
        c->x = x, c->l = nullptr, c->r = nullptr;
      return;
    }
    // push
    c->l = (c->l ? clone(c->l) : new_node());
    c->r = (c->r ? clone(c->r) : new_node());
    c->l->x = MX::op(c->l->x, c->x);
    c->r->x = MX::op(c->r->x, c->x);
    c->x = MX::id();
    ll m = (l + r) / 2;
    if (d) x = MX::op(d->x, x);
    copy_interval_rec(c->l, (d && d->l ? d->l : nullptr), l, m, ql, qr, x);
    copy_interval_rec(c->r, (d && d->r ? d->r : nullptr), m, r, ql, qr, x);
    return;
  }

  void get_rec(np c, ll l, ll r, ll i, X &x) {
    if (!c) return;
    x = MX::op(c->x, x);
    if (r == l + 1) {
      return;
    }
    ll m = (l + r) / 2;
    if (i < m) return get_rec(c->l, l, m, i, x);
    return get_rec(c->r, m, r, i, x);
  }
};
#line 1 "ds/segtree/dynamic_dual_segtree.hpp"
// Source: https://github.com/maspypy/library/blob/main/ds/segtree/dynamic_dual_segtree.hpp
#line 1 "ds/node_pool.hpp"
// Source: https://github.com/maspypy/library/blob/main/ds/node_pool.hpp
// マルチテストケースでも確保済み chunk を再利用する
template <class Node>
struct Node_Pool {
  union Slot {
    Node node;
    Slot* next;

    Slot() {}
    ~Slot() {}
  };
  using np = Node*;

  static constexpr int CHUNK_SIZE = 1 << 12;

  vc<unique_ptr<Slot[]>> chunks;
  int chunk_id = 0;
  int pos = 0;
  Slot* free_head = nullptr;

  ~Node_Pool() {
    auto& cache = chunk_cache();
    for (auto& p : chunks) cache.eb(std::move(p));
  }

  template <class... Args>
  np create(Args&&... args) {
    Slot* s = new_slot();
    return ::new (&s->node) Node(forward<Args>(args)...);
  }

  np clone(const np x) {
    assert(x);
    Slot* s = new_slot();
    return ::new (&s->node) Node(*x);
  }

  void destroy(np x) {
    if (!x) return;
    x->~Node();
    Slot* s = reinterpret_cast<Slot*>(x);
    s->next = free_head;
    free_head = s;
  }

  // 全 node を無効化する。
  // 確保済み chunk は解放せず、次回以降に再利用する。
  void reset() {
    free_head = nullptr;
    chunk_id = 0;
    pos = 0;
  }

  int used() const { return chunk_id * CHUNK_SIZE + pos; }

 private:
  static vc<unique_ptr<Slot[]>>& chunk_cache() {
    // static Node_Pool の destructor より先に破棄されないようにする。
    static auto* cache = new vc<unique_ptr<Slot[]>>();
    return *cache;
  }

  void alloc_chunk() {
    auto& cache = chunk_cache();
    if (cache.empty()) {
      chunks.eb(make_unique<Slot[]>(CHUNK_SIZE));
    } else {
      chunks.eb(std::move(cache.back()));
      cache.pop_back();
    }
  }

  Slot* new_slot() {
    if (free_head) {
      Slot* s = free_head;
      free_head = free_head->next;
      return s;
    }

    if (chunk_id == len(chunks)) alloc_chunk();

    Slot* s = &chunks[chunk_id][pos++];
    if (pos == CHUNK_SIZE) {
      ++chunk_id;
      pos = 0;
    }
    return s;
  }
};
#line 3 "ds/segtree/dynamic_dual_segtree.hpp"

// Q*2logN 程度必要
// https://qoj.ac/contest/1516/problem/8240
template <typename Monoid, bool PERSISTENT>
struct Dynamic_Dual_SegTree {
  using MX = Monoid;
  using X = typename MX::value_type;

  struct Node {
    Node *l, *r;
    X x;
  };

  const ll L0, R0;
  Node_Pool<Node> pool;
  using np = Node *;

  Dynamic_Dual_SegTree(ll L0, ll R0) : L0(L0), R0(R0) {}

  np new_root() { return new_node(MX::id()); }

  np new_node(const X x = MX::id()) {
    np c = pool.create();
    c->l = c->r = nullptr, c->x = x;
    return c;
  }

  np new_node(const vc<X> &dat) {
    assert(L0 == 0 && R0 == len(dat));
    auto dfs = [&](auto &dfs, ll l, ll r) -> Node * {
      if (l == r) return nullptr;
      if (r == l + 1) return new_node(dat[l]);
      ll m = (l + r) / 2;
      np l_root = dfs(dfs, l, m), r_root = dfs(dfs, m, r);
      X x = MX::op(l_root->x, r_root->x);
      np root = new_node();
      root->l = l_root, root->r = r_root;
      return root;
    };
    return dfs(dfs, 0, len(dat));
  }

  X get(np root, ll i) {
    if (!root) return MX::id();
    X x = MX::id();
    get_rec(root, L0, R0, i, x);
    return x;
  }

  np apply(np root, ll l, ll r, const X &x) {
    if (l == r) return root;
    assert(root && L0 <= l && l < r && r <= R0);
    root = clone(root);
    apply_rec(root, L0, R0, l, r, x);
    return root;
  }

  // root[l:r) を other[l:r)*x で上書きしたものを返す
  np copy_interval(np root, np other, ll l, ll r, X x) {
    if (root == other) return root;
    root = clone(root);
    copy_interval_rec(root, other, L0, R0, l, r, x);
    return root;
  }

  void reset() { pool.reset(); }

  vc<X> get_all(np root) {
    vc<X> res;
    auto dfs = [&](auto &dfs, np c, ll L, ll R, X x) -> void {
      if (!c) {
        FOR(R - L) res.eb(x);
        return;
      }
      x = MX::op(c->x, x);
      if (R == L + 1) {
        res.eb(x);
        return;
      }
      ll M = (L + R) / 2;
      dfs(dfs, c->l, L, M, x);
      dfs(dfs, c->r, M, R, x);
    };
    dfs(dfs, root, L0, R0, MX::id());
    return res;
  }

 private:
  np clone(np c) {
    if (!c || !PERSISTENT) return c;
    return pool.clone(c);
  }

  void apply_rec(np c, ll l, ll r, ll ql, ll qr, const X &a) {
    // もう c は新しくしてある
    assert(c);
    chmax(ql, l), chmin(qr, r);
    if (ql >= qr) return;
    if (l == ql && r == qr) {
      c->x = MX::op(c->x, a);
      return;
    }
    // push
    c->l = (c->l ? clone(c->l) : new_node());
    c->r = (c->r ? clone(c->r) : new_node());
    c->l->x = MX::op(c->l->x, c->x);
    c->r->x = MX::op(c->r->x, c->x);
    c->x = MX::id();
    ll m = (l + r) / 2;
    apply_rec(c->l, l, m, ql, qr, a), apply_rec(c->r, m, r, ql, qr, a);
    return;
  }

  void copy_interval_rec(np c, np d, ll l, ll r, ll ql, ll qr, X x) {
    // c[ql,qr) <- d[ql,qr) * x
    // もう c は新しくしてある
    assert(c);
    chmax(ql, l), chmin(qr, r);
    if (ql >= qr) return;
    if (l == ql && r == qr) {
      if (d)
        c->x = MX::op(d->x, x), c->l = d->l, c->r = d->r;
      else
        c->x = x, c->l = nullptr, c->r = nullptr;
      return;
    }
    // push
    c->l = (c->l ? clone(c->l) : new_node());
    c->r = (c->r ? clone(c->r) : new_node());
    c->l->x = MX::op(c->l->x, c->x);
    c->r->x = MX::op(c->r->x, c->x);
    c->x = MX::id();
    ll m = (l + r) / 2;
    if (d) x = MX::op(d->x, x);
    copy_interval_rec(c->l, (d && d->l ? d->l : nullptr), l, m, ql, qr, x);
    copy_interval_rec(c->r, (d && d->r ? d->r : nullptr), m, r, ql, qr, x);
    return;
  }

  void get_rec(np c, ll l, ll r, ll i, X &x) {
    if (!c) return;
    x = MX::op(c->x, x);
    if (r == l + 1) {
      return;
    }
    ll m = (l + r) / 2;
    if (i < m) return get_rec(c->l, l, m, i, x);
    return get_rec(c->r, m, r, i, x);
  }
};
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