randomized-binary-search-tree-lazy.hpp

template <class Monoid, class OperatorMonoid = Monoid>
struct RandomizedBinarySearchTree {
  using F = function<Monoid(Monoid, Monoid)>;
  using G = function<Monoid(Monoid, OperatorMonoid)>;
  using H = function<OperatorMonoid(OperatorMonoid, OperatorMonoid)>;
  using P = function<OperatorMonoid(OperatorMonoid, int)>;

  inline int xor128() {
    static int x = 123456789;
    static int y = 362436069;
    static int z = 521288629;
    static int w = 88675123;
    int t;

    t = x ^ (x << 11);
    x = y;
    y = z;
    z = w;
    return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
  }

  struct Node {
    Node *l, *r;
    int cnt;
    Monoid key, sum;
    OperatorMonoid lazy;

    Node() = default;

    Node(const Monoid &k, const OperatorMonoid &p)
        : cnt(1), key(k), sum(k), lazy(p), l(nullptr), r(nullptr) {}
  };

  vector<Node> pool;
  int ptr;

  const Monoid M1;
  const OperatorMonoid OM0;
  const F f;
  const G g;
  const H h;
  const P p;

  RandomizedBinarySearchTree(int sz, const F &f, const Monoid &M1)
      : pool(sz),
        ptr(0),
        f(f),
        g(G()),
        h(H()),
        p(P()),
        M1(M1),
        OM0(OperatorMonoid()) {}

  RandomizedBinarySearchTree(int sz, const F &f, const G &g, const H &h,
                             const P &p, const Monoid &M1,
                             const OperatorMonoid &OM0)
      : pool(sz), ptr(0), f(f), g(g), h(h), p(p), M1(M1), OM0(OM0) {}

  inline Node *alloc(const Monoid &key) {
    return &(pool[ptr++] = Node(key, OM0));
  }

  virtual Node *clone(Node *t) { return t; }

  inline int count(const Node *t) { return t ? t->cnt : 0; }

  inline Monoid sum(const Node *t) { return t ? t->sum : M1; }

  inline Node *update(Node *t) {
    t->cnt = count(t->l) + count(t->r) + 1;
    t->sum = f(f(sum(t->l), t->key), sum(t->r));
    return t;
  }

  Node *propagate(Node *t) {
    t = clone(t);
    if (t->lazy != OM0) {
      t->key = g(t->key, p(t->lazy, 1));
      if (t->l) {
        t->l = clone(t->l);
        t->l->lazy = h(t->l->lazy, t->lazy);
        t->l->sum = g(t->l->sum, p(t->lazy, count(t->l)));
      }
      if (t->r) {
        t->r = clone(t->r);
        t->r->lazy = h(t->r->lazy, t->lazy);
        t->r->sum = g(t->r->sum, p(t->lazy, count(t->r)));
      }
      t->lazy = OM0;
    }
    return update(t);
  }

  Node *merge(Node *l, Node *r) {
    if (!l || !r) return l ? l : r;
    if (xor128() % (l->cnt + r->cnt) < l->cnt) {
      l = propagate(l);
      l->r = merge(l->r, r);
      return update(l);
    } else {
      r = propagate(r);
      r->l = merge(l, r->l);
      return update(r);
    }
  }

  pair<Node *, Node *> split(Node *t, int k) {
    if (!t) return {t, t};
    t = propagate(t);
    if (k <= count(t->l)) {
      auto s = split(t->l, k);
      t->l = s.second;
      return {s.first, update(t)};
    } else {
      auto s = split(t->r, k - count(t->l) - 1);
      t->r = s.first;
      return {update(t), s.second};
    }
  }

  Node *build(int l, int r, const vector<Monoid> &v) {
    if (l + 1 >= r) return alloc(v[l]);
    return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
  }

  Node *build(const vector<Monoid> &v) {
    ptr = 0;
    return build(0, (int)v.size(), v);
  }

  void dump(Node *r, typename vector<Monoid>::iterator &it) {
    if (!r) return;
    r = propagate(r);
    dump(r->l, it);
    *it = r->key;
    dump(r->r, ++it);
  }

  vector<Monoid> dump(Node *r) {
    vector<Monoid> v((size_t)count(r));
    auto it = begin(v);
    dump(r, it);
    return v;
  }

  string to_string(Node *r) {
    auto s = dump(r);
    string ret;
    for (int i = 0; i < s.size(); i++) ret += ", ";
    return (ret);
  }

  void insert(Node *&t, int k, const Monoid &v) {
    auto x = split(t, k);
    t = merge(merge(x.first, alloc(v)), x.second);
  }

  void erase(Node *&t, int k) {
    auto x = split(t, k);
    t = merge(x.first, split(x.second, 1).second);
  }

  Monoid query(Node *&t, int a, int b) {
    auto x = split(t, a);
    auto y = split(x.second, b - a);
    auto ret = sum(y.first);
    t = merge(x.first, merge(y.first, y.second));
    return ret;
  }

  void set_propagate(Node *&t, int a, int b, const OperatorMonoid &p) {
    auto x = split(t, a);
    auto y = split(x.second, b - a);
    y.first->lazy = h(y.first->lazy, p);
    t = merge(x.first, merge(propagate(y.first), y.second));
  }

  void set_element(Node *&t, int k, const Monoid &x) {
    t = propagate(t);
    if (k < count(t->l))
      set_element(t->l, k, x);
    else if (k == count(t->l))
      t->key = t->sum = x;
    else
      set_element(t->r, k - count(t->l) - 1, x);
    t = update(t);
  }

  int size(Node *t) { return count(t); }

  bool empty(Node *t) { return !t; }

  Node *makeset() { return nullptr; }
};