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#include "structure/bbst/lazy-reversible-splay-tree.hpp"
/** * @brief Lazy-Reversible-Splay-Tree(遅延伝搬反転可能Splay木) */ template< typename Monoid = int, typename OperatorMonoid = Monoid > struct LazyReversibleSplayTree { public: using F = function< Monoid(Monoid, Monoid) >; using G = function< Monoid(Monoid, OperatorMonoid) >; using H = function< OperatorMonoid(OperatorMonoid, OperatorMonoid) >; using S = function< Monoid(Monoid) >; struct Node { Node *l, *r, *p; Monoid key, sum; OperatorMonoid lazy; bool rev; size_t sz; bool is_root() const { return !p || (p->l != this && p->r != this); } Node(const Monoid &key, const OperatorMonoid &om) : key(key), sum(key), lazy(om), sz(1), rev(false), l(nullptr), r(nullptr), p(nullptr) {} }; LazyReversibleSplayTree(const F &f, const Monoid &M1) : LazyReversibleSplayTree(f, [](const Monoid &a) { return a; }, M1) {} LazyReversibleSplayTree(const F &f, const S &s, const Monoid &M1) : LazyReversibleSplayTree(f, G(), H(), s, M1, OperatorMonoid()) {} LazyReversibleSplayTree(const F &f, const G &g, const H &h, const S &s, const Monoid &M1, const OperatorMonoid &OM0) : f(f), g(g), h(h), s(s), M1(M1), OM0(OM0) {} inline size_t count(const Node *t) { return t ? t->sz : 0; } inline const Monoid &sum(const Node *t) { return t ? t->sum : M1; } Node *alloc(const Monoid &v = Monoid()) { return new Node(v, OM0); } void splay(Node *t) { push(t); while(!t->is_root()) { auto *q = t->p; if(q->is_root()) { push(q), push(t); if(q->l == t) rotr(t); else rotl(t); } else { auto *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); } } } } Node *push_front(Node *t, const Monoid &v = Monoid()) { if(!t) { t = alloc(v); return t; } else { splay(t); Node *cur = get_left(t), *z = alloc(v); splay(cur); z->p = cur; cur->l = z; splay(z); return z; } } Node *push_back(Node *t, const Monoid &v = Monoid()) { if(!t) { t = alloc(v); return t; } else { splay(t); Node *cur = get_right(t), *z = alloc(v); splay(cur); z->p = cur; cur->r = z; splay(z); return z; } } Node *erase(Node *t) { splay(t); Node *x = t->l, *y = t->r; delete t; if(!x) { t = y; if(t) t->p = nullptr; } else if(!y) { t = x; t->p = nullptr; } else { x->p = nullptr; t = get_right(x); splay(t); t->r = y; y->p = t; } return t; } Node *get_left(Node *t) const { while(t->l) t = t->l; return t; } Node *get_right(Node *t) const { while(t->r) t = t->r; return t; } void set_propagate(Node *&t, int a, int b, const OperatorMonoid &pp) { splay(t); auto x = split(t, a); auto y = split(x.second, b - a); set_propagate(y.first, pp); t = merge(x.first, y.first, y.second); } virtual void set_propagate(Node *&t, const OperatorMonoid &pp) { splay(t); propagate(t, pp); push(t); } pair< Node *, Node * > split(Node *t, int k) { if(!t) return {nullptr, nullptr}; push(t); if(k <= count(t->l)) { auto x = split(t->l, k); t->l = x.second; t->p = nullptr; if(x.second) x.second->p = t; return {x.first, update(t)}; } else { auto x = split(t->r, k - count(t->l) - 1); t->r = x.first; t->p = nullptr; if(x.first) x.first->p = t; return {update(t), x.second}; } } tuple< Node *, Node *, Node * > split3(Node *t, int a, int b) { splay(t); 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 nullptr; if(!l) return splay(r), r; if(!r) return splay(l), l; splay(l), splay(r); l = get_right(l); splay(l); l->r = r; r->p = l; update(l); return l; } void insert(Node *&t, int k, const Monoid &v) { splay(t); auto x = split(t, k); t = merge(x.first, alloc(v), x.second); } Monoid erase(Node *&t, int k) { splay(t); auto x = split(t, k); auto y = split(x.second, 1); auto v = y.first->c; delete y.first; t = merge(x.first, y.second); return v; } Monoid query(Node *&t, int a, int b) { splay(t); auto x = split(t, a); auto y = split(x.second, b - a); auto ret = sum(y.first); t = merge(x.first, y.first, y.second); return ret; } Node *build(const vector< Monoid > &v) { return build(0, (int) v.size(), v); } void toggle(Node *t) { swap(t->l, t->r); t->sum = s(t->sum); t->rev ^= true; } Node *update(Node *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 push(Node *t) { if(t->lazy != OM0) { if(t->l) propagate(t->l, t->lazy); if(t->r) propagate(t->r, t->lazy); t->lazy = OM0; } if(t->rev) { if(t->l) toggle(t->l); if(t->r) toggle(t->r); t->rev = false; } } void set_element(Node *&t, int k, const Monoid &x) { splay(t); sub_set_element(t, k, x); } private: const Monoid M1; const OperatorMonoid OM0; const F f; const G g; const H h; const S s; 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 propagate(Node *t, const OperatorMonoid &x) { t->lazy = h(t->lazy, x); t->key = g(t->key, x); t->sum = g(t->sum, x); } void rotr(Node *t) { auto *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(Node *t) { auto *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); } } Node *merge(Node *l) { return l; } Node *sub_set_element(Node *&t, int k, const Monoid &x) { push(t); if(k < count(t->l)) { return sub_set_element(t->l, k, x); } else if(k == count(t->l)) { t->key = x; splay(t); return t; } else { return sub_set_element(t->r, k - count(t->l) - 1, x); } } };
#line 1 "structure/bbst/lazy-reversible-splay-tree.hpp" /** * @brief Lazy-Reversible-Splay-Tree(遅延伝搬反転可能Splay木) */ template< typename Monoid = int, typename OperatorMonoid = Monoid > struct LazyReversibleSplayTree { public: using F = function< Monoid(Monoid, Monoid) >; using G = function< Monoid(Monoid, OperatorMonoid) >; using H = function< OperatorMonoid(OperatorMonoid, OperatorMonoid) >; using S = function< Monoid(Monoid) >; struct Node { Node *l, *r, *p; Monoid key, sum; OperatorMonoid lazy; bool rev; size_t sz; bool is_root() const { return !p || (p->l != this && p->r != this); } Node(const Monoid &key, const OperatorMonoid &om) : key(key), sum(key), lazy(om), sz(1), rev(false), l(nullptr), r(nullptr), p(nullptr) {} }; LazyReversibleSplayTree(const F &f, const Monoid &M1) : LazyReversibleSplayTree(f, [](const Monoid &a) { return a; }, M1) {} LazyReversibleSplayTree(const F &f, const S &s, const Monoid &M1) : LazyReversibleSplayTree(f, G(), H(), s, M1, OperatorMonoid()) {} LazyReversibleSplayTree(const F &f, const G &g, const H &h, const S &s, const Monoid &M1, const OperatorMonoid &OM0) : f(f), g(g), h(h), s(s), M1(M1), OM0(OM0) {} inline size_t count(const Node *t) { return t ? t->sz : 0; } inline const Monoid &sum(const Node *t) { return t ? t->sum : M1; } Node *alloc(const Monoid &v = Monoid()) { return new Node(v, OM0); } void splay(Node *t) { push(t); while(!t->is_root()) { auto *q = t->p; if(q->is_root()) { push(q), push(t); if(q->l == t) rotr(t); else rotl(t); } else { auto *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); } } } } Node *push_front(Node *t, const Monoid &v = Monoid()) { if(!t) { t = alloc(v); return t; } else { splay(t); Node *cur = get_left(t), *z = alloc(v); splay(cur); z->p = cur; cur->l = z; splay(z); return z; } } Node *push_back(Node *t, const Monoid &v = Monoid()) { if(!t) { t = alloc(v); return t; } else { splay(t); Node *cur = get_right(t), *z = alloc(v); splay(cur); z->p = cur; cur->r = z; splay(z); return z; } } Node *erase(Node *t) { splay(t); Node *x = t->l, *y = t->r; delete t; if(!x) { t = y; if(t) t->p = nullptr; } else if(!y) { t = x; t->p = nullptr; } else { x->p = nullptr; t = get_right(x); splay(t); t->r = y; y->p = t; } return t; } Node *get_left(Node *t) const { while(t->l) t = t->l; return t; } Node *get_right(Node *t) const { while(t->r) t = t->r; return t; } void set_propagate(Node *&t, int a, int b, const OperatorMonoid &pp) { splay(t); auto x = split(t, a); auto y = split(x.second, b - a); set_propagate(y.first, pp); t = merge(x.first, y.first, y.second); } virtual void set_propagate(Node *&t, const OperatorMonoid &pp) { splay(t); propagate(t, pp); push(t); } pair< Node *, Node * > split(Node *t, int k) { if(!t) return {nullptr, nullptr}; push(t); if(k <= count(t->l)) { auto x = split(t->l, k); t->l = x.second; t->p = nullptr; if(x.second) x.second->p = t; return {x.first, update(t)}; } else { auto x = split(t->r, k - count(t->l) - 1); t->r = x.first; t->p = nullptr; if(x.first) x.first->p = t; return {update(t), x.second}; } } tuple< Node *, Node *, Node * > split3(Node *t, int a, int b) { splay(t); 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 nullptr; if(!l) return splay(r), r; if(!r) return splay(l), l; splay(l), splay(r); l = get_right(l); splay(l); l->r = r; r->p = l; update(l); return l; } void insert(Node *&t, int k, const Monoid &v) { splay(t); auto x = split(t, k); t = merge(x.first, alloc(v), x.second); } Monoid erase(Node *&t, int k) { splay(t); auto x = split(t, k); auto y = split(x.second, 1); auto v = y.first->c; delete y.first; t = merge(x.first, y.second); return v; } Monoid query(Node *&t, int a, int b) { splay(t); auto x = split(t, a); auto y = split(x.second, b - a); auto ret = sum(y.first); t = merge(x.first, y.first, y.second); return ret; } Node *build(const vector< Monoid > &v) { return build(0, (int) v.size(), v); } void toggle(Node *t) { swap(t->l, t->r); t->sum = s(t->sum); t->rev ^= true; } Node *update(Node *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 push(Node *t) { if(t->lazy != OM0) { if(t->l) propagate(t->l, t->lazy); if(t->r) propagate(t->r, t->lazy); t->lazy = OM0; } if(t->rev) { if(t->l) toggle(t->l); if(t->r) toggle(t->r); t->rev = false; } } void set_element(Node *&t, int k, const Monoid &x) { splay(t); sub_set_element(t, k, x); } private: const Monoid M1; const OperatorMonoid OM0; const F f; const G g; const H h; const S s; 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 propagate(Node *t, const OperatorMonoid &x) { t->lazy = h(t->lazy, x); t->key = g(t->key, x); t->sum = g(t->sum, x); } void rotr(Node *t) { auto *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(Node *t) { auto *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); } } Node *merge(Node *l) { return l; } Node *sub_set_element(Node *&t, int k, const Monoid &x) { push(t); if(k < count(t->l)) { return sub_set_element(t->l, k, x); } else if(k == count(t->l)) { t->key = x; splay(t); return t; } else { return sub_set_element(t->r, k - count(t->l) - 1, x); } } };