This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub ei1333/library
#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; } };