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#include "structure/bbst/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; }
};
#line 1 "structure/bbst/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; }
};