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#include "structure/bbst/weight-balanced-tree.hpp"
/**
* @brief Weight-Balanced-Tree(重み平衡木)
*/
template <typename Monoid, typename F>
struct WeightBalancedTree {
public:
struct Node {
Node *l, *r;
int cnt;
Monoid key, sum;
Node() {}
Node(const Monoid &k) : key(k), sum(k), l(nullptr), r(nullptr), cnt(1) {}
Node(Node *l, Node *r, const Monoid &k) : key(k), l(l), r(r) {}
bool is_leaf() { return !l || !r; }
};
private:
Node *update(Node *t) {
t->cnt = count(t->l) + count(t->r) + t->is_leaf();
t->sum = f(f(sum(t->l), t->key), sum(t->r));
return t;
}
inline Node *alloc(Node *l, Node *r) {
auto t = &(*pool.alloc() = Node(l, r, M1));
return update(t);
}
Node *submerge(Node *l, Node *r) {
if (count(l) > count(r) * 4) {
l = clone(l);
auto nl = clone(l->l);
auto nr = submerge(l->r, r);
if (count(nl) * 4 >= count(nr)) {
l->r = nr;
return update(l);
}
if (count(nr->l) * 3 <= count(nr->r) * 5) {
l->r = nr->l;
nr->l = l;
update(l);
return update(nr);
}
Node *t = clone(nr->l);
l->r = nr->l->l;
update(l);
nr->l = nr->l->r;
update(nr);
t->l = l;
t->r = nr;
return update(t);
}
if (count(l) * 4 < count(r)) {
r = clone(r);
auto nl = submerge(l, r->l);
auto nr = clone(r->r);
if (count(nl) <= count(nr) * 4) {
r->l = nl;
return update(r);
}
if (count(nl->l) * 5 >= count(nl->r) * 3) {
r->l = nl->r;
nl->r = r;
update(r);
return update(nl);
}
Node *t = clone(nl->r);
r->l = nl->r->r;
update(r);
nl->r = nl->r->l;
update(nl);
t->r = r;
t->l = nl;
return update(t);
}
return alloc(l, r);
}
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));
}
void dump(Node *r, typename vector<Monoid>::iterator &it) {
if (r->is_leaf()) {
*it++ = r->key;
return;
}
dump(r->l, it);
dump(r->r, it);
}
virtual Node *clone(Node *t) { return t; }
Node *merge(Node *l) { return l; }
Monoid query(Node *t, int a, int b, int l, int r) {
if (r <= a || b <= l) return M1;
if (a <= l && r <= b) return t->sum;
return f(query(t->l, a, b, l, l + count(t->l)),
query(t->r, a, b, r - count(t->r), r));
}
public:
VectorPool<Node> pool;
const F f;
const Monoid M1;
WeightBalancedTree(int sz, const F &f, const Monoid &M1)
: pool(sz), M1(M1), f(f) {
pool.clear();
}
inline Node *alloc(const Monoid &key) { return &(*pool.alloc() = Node(key)); }
static inline int count(const Node *t) { return t ? t->cnt : 0; }
inline const Monoid &sum(const Node *t) { return t ? t->sum : M1; }
pair<Node *, Node *> split(Node *t, int k) {
if (!t) return {nullptr, nullptr};
if (k == 0) return {nullptr, t};
if (k >= count(t)) return {t, nullptr};
t = clone(t);
Node *l = t->l, *r = t->r;
pool.free(t);
if (k < count(l)) {
auto pp = split(l, k);
return {pp.first, merge(pp.second, r)};
}
if (k > count(l)) {
auto pp = split(r, k - count(l));
return {merge(l, pp.first), pp.second};
}
return {l, r};
}
tuple<Node *, Node *, Node *> split3(Node *t, int a, int b) {
auto x = split(t, a);
auto y = split(x.second, b - a);
return make_tuple(x.first, y.first, y.second);
}
template <typename... Args>
Node *merge(Node *l, Args... rest) {
Node *r = merge(rest...);
if (!l || !r) return l ? l : r;
return submerge(l, r);
}
Node *build(const vector<Monoid> &v) { return build(0, (int)v.size(), v); }
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 += std::to_string(s[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);
}
Monoid erase(Node *&t, int k) {
auto x = split(t, k);
auto y = split(x.second, 1);
auto v = y.first->c;
pool.free(y.first);
t = merge(x.first, y.second);
return v;
}
Monoid query(Node *t, int a, int b) { return query(t, a, b, 0, count(t)); }
void set_element(Node *&t, int k, const Monoid &x) {
t = clone(t);
if (t->is_leaf()) {
t->key = t->sum = x;
return;
}
if (k < count(t->l))
set_element(t->l, k, x);
else
set_element(t->r, k - count(t->l), x);
t = update(t);
}
void push_front(Node *&t, const Monoid &v) { t = merge(alloc(v), t); }
void push_back(Node *&t, const Monoid &v) { t = merge(t, alloc(v)); }
Monoid pop_front(Node *&t) {
auto ret = split(t, 1);
t = ret.second;
return ret.first->key;
}
Monoid pop_back(Node *&t) {
auto ret = split(t, count(t) - 1);
t = ret.first;
return ret.second->key;
}
};
#line 1 "structure/bbst/weight-balanced-tree.hpp"
/**
* @brief Weight-Balanced-Tree(重み平衡木)
*/
template <typename Monoid, typename F>
struct WeightBalancedTree {
public:
struct Node {
Node *l, *r;
int cnt;
Monoid key, sum;
Node() {}
Node(const Monoid &k) : key(k), sum(k), l(nullptr), r(nullptr), cnt(1) {}
Node(Node *l, Node *r, const Monoid &k) : key(k), l(l), r(r) {}
bool is_leaf() { return !l || !r; }
};
private:
Node *update(Node *t) {
t->cnt = count(t->l) + count(t->r) + t->is_leaf();
t->sum = f(f(sum(t->l), t->key), sum(t->r));
return t;
}
inline Node *alloc(Node *l, Node *r) {
auto t = &(*pool.alloc() = Node(l, r, M1));
return update(t);
}
Node *submerge(Node *l, Node *r) {
if (count(l) > count(r) * 4) {
l = clone(l);
auto nl = clone(l->l);
auto nr = submerge(l->r, r);
if (count(nl) * 4 >= count(nr)) {
l->r = nr;
return update(l);
}
if (count(nr->l) * 3 <= count(nr->r) * 5) {
l->r = nr->l;
nr->l = l;
update(l);
return update(nr);
}
Node *t = clone(nr->l);
l->r = nr->l->l;
update(l);
nr->l = nr->l->r;
update(nr);
t->l = l;
t->r = nr;
return update(t);
}
if (count(l) * 4 < count(r)) {
r = clone(r);
auto nl = submerge(l, r->l);
auto nr = clone(r->r);
if (count(nl) <= count(nr) * 4) {
r->l = nl;
return update(r);
}
if (count(nl->l) * 5 >= count(nl->r) * 3) {
r->l = nl->r;
nl->r = r;
update(r);
return update(nl);
}
Node *t = clone(nl->r);
r->l = nl->r->r;
update(r);
nl->r = nl->r->l;
update(nl);
t->r = r;
t->l = nl;
return update(t);
}
return alloc(l, r);
}
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));
}
void dump(Node *r, typename vector<Monoid>::iterator &it) {
if (r->is_leaf()) {
*it++ = r->key;
return;
}
dump(r->l, it);
dump(r->r, it);
}
virtual Node *clone(Node *t) { return t; }
Node *merge(Node *l) { return l; }
Monoid query(Node *t, int a, int b, int l, int r) {
if (r <= a || b <= l) return M1;
if (a <= l && r <= b) return t->sum;
return f(query(t->l, a, b, l, l + count(t->l)),
query(t->r, a, b, r - count(t->r), r));
}
public:
VectorPool<Node> pool;
const F f;
const Monoid M1;
WeightBalancedTree(int sz, const F &f, const Monoid &M1)
: pool(sz), M1(M1), f(f) {
pool.clear();
}
inline Node *alloc(const Monoid &key) { return &(*pool.alloc() = Node(key)); }
static inline int count(const Node *t) { return t ? t->cnt : 0; }
inline const Monoid &sum(const Node *t) { return t ? t->sum : M1; }
pair<Node *, Node *> split(Node *t, int k) {
if (!t) return {nullptr, nullptr};
if (k == 0) return {nullptr, t};
if (k >= count(t)) return {t, nullptr};
t = clone(t);
Node *l = t->l, *r = t->r;
pool.free(t);
if (k < count(l)) {
auto pp = split(l, k);
return {pp.first, merge(pp.second, r)};
}
if (k > count(l)) {
auto pp = split(r, k - count(l));
return {merge(l, pp.first), pp.second};
}
return {l, r};
}
tuple<Node *, Node *, Node *> split3(Node *t, int a, int b) {
auto x = split(t, a);
auto y = split(x.second, b - a);
return make_tuple(x.first, y.first, y.second);
}
template <typename... Args>
Node *merge(Node *l, Args... rest) {
Node *r = merge(rest...);
if (!l || !r) return l ? l : r;
return submerge(l, r);
}
Node *build(const vector<Monoid> &v) { return build(0, (int)v.size(), v); }
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 += std::to_string(s[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);
}
Monoid erase(Node *&t, int k) {
auto x = split(t, k);
auto y = split(x.second, 1);
auto v = y.first->c;
pool.free(y.first);
t = merge(x.first, y.second);
return v;
}
Monoid query(Node *t, int a, int b) { return query(t, a, b, 0, count(t)); }
void set_element(Node *&t, int k, const Monoid &x) {
t = clone(t);
if (t->is_leaf()) {
t->key = t->sum = x;
return;
}
if (k < count(t->l))
set_element(t->l, k, x);
else
set_element(t->r, k - count(t->l), x);
t = update(t);
}
void push_front(Node *&t, const Monoid &v) { t = merge(alloc(v), t); }
void push_back(Node *&t, const Monoid &v) { t = merge(t, alloc(v)); }
Monoid pop_front(Node *&t) {
auto ret = split(t, 1);
t = ret.second;
return ret.first->key;
}
Monoid pop_back(Node *&t) {
auto ret = split(t, count(t) - 1);
t = ret.first;
return ret.second->key;
}
};