matsutaku-library
This documentation is automatically generated by competitive-verifier/competitive-verifier
test/yosupo/predecessor_problem-yft.test.cpp
- View this file on GitHub
- Last update: 2024-07-11 22:21:57+09:00
- Link: https://judge.yosupo.jp/problem/predecessor_problem
Code
#define PROBLEM "https://judge.yosupo.jp/problem/predecessor_problem"
#define IGNORE
#include "include/mtl/yft.hpp"
#include <bits/stdc++.h>
using namespace std;
constexpr int max_value = 1e7;
constexpr int bits = 64 - bm::clz(max_value);
int main() {
int n,q; cin>>n>>q;
string t; cin>>t;
vector<int> V;
for (int i = 0; i < n; i++) if (t[i]=='1') V.push_back(i);
YFastTrieSet<unsigned int, bits> S(V.begin(), V.end());
for (int i = 0; i < q; i++) {
int t; cin>>t;
int k; cin>>k;
switch (t) {
case 0: {
S.insert(k);
}; break;
case 1: {
S.erase(S.find(k));
}; break;
case 2: {
cout << S.count(k) << endl;
}; break;
case 3: {
auto i = S.lower_bound(k);
cout << (i != S.end() ? (int)*i : -1) << endl;
}; break;
case 4: {
auto i = S.upper_bound(k);
cout << (i != S.begin() ? (int)*--i : -1) << endl;
}; break;
default: break;
}
}
}#line 1 "test/yosupo/predecessor_problem-yft.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/predecessor_problem"
#define IGNORE
#line 2 "include/mtl/traits/set_traits.hpp"
#include <cstddef>
#include <initializer_list>
#include <type_traits>
#include <iterator>
namespace traits {
template<typename T, typename M>
struct AssociativeArrayDefinition {
using key_type = T;
using mapped_type = M;
using value_type = std::pair<T const, M>;
using raw_key_type = typename std::remove_const<T>::type;
using raw_mapped_type = typename std::remove_const<M>::type;
using init_type = std::pair<raw_key_type, raw_mapped_type>;
using moved_type = std::pair<raw_key_type&&, raw_mapped_type&&>;
template<class K, class V>
static key_type const& key_of(std::pair<K,V> const& kv) {
return kv.first;
}
};
template<typename T>
struct AssociativeArrayDefinition<T, void> {
using key_type = T;
using value_type = T;
using init_type = T;
static key_type const& key_of(value_type const& k) { return k; }
};
template<class T, typename = std::void_t<>>
struct get_const_iterator {
using base = typename T::iterator;
struct type : base {
type(const base& r) : base(r) {}
type(base&& r) : base(std::move(r)) {}
};
};
template<class T>
struct get_const_iterator<T, std::void_t<typename T::const_iterator>> {
using type = typename T::const_iterator;
};
#if __cplusplus >= 202002L
#include <concepts>
template<class M>
concept IsAssociativeArray = requires (M m) {
typename M::key_type;
typename M::value_type;
typename M::iterator;
{m.size()} -> std::convertible_to<size_t>;
{m.empty()} -> std::same_as<bool>;
{m.clear()};
{m.begin()} -> std::same_as<typename M::iterator>;
{m.end()} -> std::same_as<typename M::iterator>;
};
#endif
template<class Base>
#if __cplusplus >= 202002L
requires IsAssociativeArray<Base>
#endif
class SetTraitsBase : public Base {
public:
using key_type = typename Base::key_type;
using value_type = typename Base::value_type;
using init_type = typename Base::init_type;
using iterator = typename Base::iterator;
SetTraitsBase() = default;
template<typename InputIt>
explicit SetTraitsBase(InputIt begin, InputIt end) : Base(begin, end) {
static_assert(std::is_convertible<typename std::iterator_traits<InputIt>::value_type, value_type>::value, "");
}
SetTraitsBase(std::initializer_list<value_type> init) : Base(init.begin(), init.end()) {}
using Base::size;
bool empty() const { return size() == 0; }
using Base::clear;
using const_iterator = typename get_const_iterator<Base>::type;
iterator begin() {
return Base::begin();
}
iterator end() {
return Base::end();
}
const_iterator begin() const {
return const_iterator(Base::begin());
}
const_iterator end() const {
return const_iterator(Base::end());
}
const_iterator cbegin() const {
return begin();
}
const_iterator cend() const {
return end();
}
using reverse_iterator = std::reverse_iterator<iterator>;
using reverse_const_iterator = std::reverse_iterator<const_iterator>;
reverse_iterator rbegin() {
return std::make_reverse_iterator(end());
}
reverse_iterator rend() {
return std::make_reverse_iterator(begin());
}
reverse_const_iterator rbegin() const {
return std::make_reverse_iterator(end());
}
reverse_const_iterator rend() const {
return std::make_reverse_iterator(begin());
}
reverse_const_iterator crbegin() const {
return rbegin();
}
reverse_const_iterator crend() const {
return rend();
}
template<class Key>
iterator lower_bound(const Key& x) const {
return Base::_lower_bound(x);
}
iterator lower_bound(const key_type& x) const {
return Base::_lower_bound(x);
}
template<class Key>
iterator upper_bound(const Key& x) const {
return Base::_upper_bound(x);
}
iterator upper_bound(const key_type& x) const {
return Base::_upper_bound(x);
}
template<class Key>
iterator find(const Key& x) {
return Base::_find(x);
}
iterator find(const key_type& x) {
return Base::_find(x);
}
template<class Key>
const_iterator find(const Key& x) const {
return Base::_find(x);
}
const_iterator find(const key_type& x) const {
return Base::_find(x);
}
template<class Key>
size_t count(const Key& x) const {
return find(x) != end();
}
size_t count(const key_type& x) const {
return find(x) != end();
}
std::pair<iterator, bool> insert(const init_type& v) {
return Base::_insert(v);
}
std::pair<iterator, bool> insert(init_type&& v) {
return Base::_insert(std::move(v));
}
template<typename=void>
std::pair<iterator, bool> insert(const value_type& v) {
return Base::_insert(v);
}
template<typename=void>
std::pair<iterator, bool> insert(value_type&& v) {
return Base::_insert(std::move(v));
}
template<class... Args>
std::pair<iterator, bool> emplace(Args&&... args) {
using emplace_type = typename std::conditional<
std::is_constructible<init_type, Args...>::value,
init_type,
value_type
>::type;
return Base::_insert(emplace_type(std::forward<Args>(args)...));
}
template<class... Args>
iterator emplace_hint(const_iterator hint, Args&&... args) {
using emplace_type = typename std::conditional<
std::is_constructible<init_type, Args...>::value,
init_type,
value_type
>::type;
return Base::_emplace_hint(hint, emplace_type(std::forward<Args>(args)...));
}
size_t erase(const key_type& x) {
return Base::_erase(x);
}
iterator erase(iterator it) {
return Base::_erase(it);
}
iterator erase(const_iterator it) {
return Base::_erase(it);
}
};
template<typename Base>
using SetTraits = SetTraitsBase<Base>;
template<typename Base>
class MapTraits : public SetTraitsBase<Base> {
using SBase = SetTraitsBase<Base>;
public:
using typename SBase::key_type;
using typename SBase::mapped_type;
using typename SBase::value_type;
using reference = mapped_type&;
MapTraits() = default;
template<typename InputIt>
explicit MapTraits(InputIt begin, InputIt end) : SBase(begin, end) {}
MapTraits(std::initializer_list<value_type> init) : SBase(init) {}
template<typename Key>
reference operator[](Key&& x) {
auto i = SBase::lower_bound(x);
if (i == SBase::end() || x < i->first) {
i = SBase::emplace_hint(i, std::forward<Key>(x), mapped_type());
}
return i->second;
}
reference operator[](const key_type& x) {
auto i = SBase::lower_bound(x);
if (i == SBase::end() || x < i->first) {
i = SBase::emplace_hint(i, x, mapped_type());
}
return i->second;
}
reference operator[](key_type&& x) {
auto i = SBase::lower_bound(x);
if (i == SBase::end() || x < i->first) {
i = SBase::emplace_hint(i, std::move(x), mapped_type());
}
return i->second;
}
};
} // namespace traits
#line 2 "include/mtl/treap.hpp"
#include <memory>
#line 4 "include/mtl/treap.hpp"
#include <cassert>
#include <exception>
#include <random>
#include <iostream>
template<class T, class V=void,
class Compare = std::less<>,
bool UniqueKey = true>
class Treap {
public:
using key_type = T;
static constexpr bool kKeyOnly = std::is_same<V, void>::value;
using mapped_type = typename std::conditional<kKeyOnly, T, V>::type;
using value_type = typename std::conditional<
kKeyOnly,
T,
std::pair<T const, V>
>::type;
using raw_key_type = typename std::conditional<kKeyOnly, T, typename std::remove_const<T>::type>::type;
using raw_value_type = typename std::conditional<kKeyOnly, T, typename std::remove_const<V>::type>::type;
using init_type = typename std::conditional<
kKeyOnly,
T,
std::pair<raw_key_type, raw_value_type>
>::type;
using priority_type = uint32_t;
protected:
template<bool> struct iterator_base;
public:
using iterator = iterator_base<false>;
using const_iterator = iterator_base<true>;
private:
struct Node;
using node_ptr = std::shared_ptr<Node>;
using node_weak = std::weak_ptr<Node>;
struct Node {
node_ptr left, right;
node_weak parent;
priority_type p;
value_type v;
explicit Node(priority_type p)
: left(nullptr), right(nullptr), p(p) {}
explicit Node(priority_type p, const value_type& v)
: left(nullptr), right(nullptr), p(p), v(v) {}
explicit Node(priority_type p, value_type&& v)
: left(nullptr), right(nullptr), p(p), v(std::forward<value_type>(v)) {}
template<typename... Args>
explicit Node(priority_type p, Args&&... args)
: left(nullptr), right(nullptr), p(p),
v(std::forward<Args>(args)...) {}
const raw_key_type& key() const {
if constexpr (kKeyOnly)
return v;
else
return v.first;
}
};
node_ptr sentinel_;
size_t size_;
std::default_random_engine eng;
std::uniform_int_distribution<priority_type> dist;
Compare comp_;
public:
Treap(const Compare& comp = Compare())
: sentinel_(std::make_shared<Node>(0)), size_(0),
comp_(comp) {}
template<typename It>
explicit Treap(It begin, It end,
const Compare& comp = Compare()) : Treap(comp) {
insert(begin, end);
}
Treap(std::initializer_list<value_type> list) : Treap(list.begin(), list.end()) {}
private:
void _clone(node_ptr u, const node_ptr ru) {
if (ru->left) {
u->left = std::make_shared<Node>(ru->left->p, ru->left->v);
u->left->parent = u;
_clone(u->left, ru->left);
}
if (ru->right) {
u->right = std::make_shared<Node>(ru->right->p, ru->right->v);
u->right->parent = u;
_clone(u->right, ru->right);
}
}
public:
Treap(const Treap& r) : Treap() {
_clone(sentinel_, r.sentinel_);
size_ = r.size_;
}
Treap& operator=(const Treap& r) {
clear();
_clone(sentinel_, r.sentinel_);
size_ = r.size_;
return *this;
}
Treap(Treap&& r) noexcept = default;
Treap& operator=(Treap&& r) noexcept = default;
private:
bool _check_connection(node_ptr u) const {
if (!u)
return false;
assert(u != sentinel_ or sentinel_->right == nullptr);
if (u == sentinel_ and u->right)
return true;
if (u->left) {
assert(u->left->parent == u);
if (!(u->left->parent == u))
return true;
}
if (u->right) {
assert(u->right->parent == u);
if (!(u->right->parent == u))
return true;
}
if (_check_connection(u->left))
return true;
if (_check_connection(u->right))
return true;
return false;
}
node_ptr _root() const {
return sentinel_->left;
}
priority_type _pick_priority() { return dist(eng); }
bool _comp_priority(node_ptr u, node_ptr v) const {
return u->p < v->p;
}
void _turn_left(node_ptr u) {
auto p = u->parent.lock();
auto r = u->right;
assert(p);
assert(r);
if (p->left == u)
p->left = r;
else {
assert(p->right == u);
p->right = r;
}
r->parent = p;
auto rl = r->left;
u->right = rl;
if (rl) rl->parent = u;
r->left = u;
u->parent = r;
}
void _turn_right(node_ptr u) {
auto p = u->parent.lock();
auto l = u->left;
assert(p);
assert(l);
if (p->left == u)
p->left = l;
else {
assert(p->right == u);
p->right = l;
}
l->parent = p;
auto lr = l->right;
u->left = lr;
if (lr) lr->parent = u;
l->right = u;
u->parent = l;
}
template<typename Cond>
void _bubble_up_cond(node_ptr u, Cond cond) {
while (cond(u)) {
assert(!u->parent.expired());
auto p = u->parent.lock();
assert(p != sentinel_);
if (p->right == u) {
_turn_left(p);
} else {
assert(p->left == u);
_turn_right(p);
}
}
}
void _bubble_up(node_ptr u) {
_bubble_up_cond(u, [&](node_ptr u) { return _comp_priority(u, u->parent.lock()); });
}
void _bubble_up_force(node_ptr u) {
_bubble_up_cond(u, [&](node_ptr u) { return u->parent.lock() != sentinel_; });
assert(u->parent.lock() == sentinel_);
assert(_root() == u);
}
void _tricle_down(node_ptr u) {
while (u->left or u->right) {
if (!u->right) {
_turn_right(u);
} else if (!u->left) {
_turn_left(u);
} else if (_comp_priority(u->left, u->right)) {
_turn_right(u);
} else {
_turn_left(u);
}
}
}
// Used for leaf only (done after _tricle_down)
void _splice(node_ptr u) {
assert(!u->left and !u->right);
auto p = u->parent.lock();
assert(p);
if (p->left == u)
p->left = nullptr;
else {
assert(p->right == u);
p->right = nullptr;
}
u->parent.reset();
}
// NOTE: value of size_ is broken.
Treap(node_ptr node) : Treap() {
sentinel_->left = node;
if (node)
node->parent = sentinel_;
}
std::pair<iterator, bool> _insert_node_subtree(node_ptr u, node_ptr new_node) {
auto x = new_node->key();
while (true) {
if constexpr (UniqueKey) if (u != sentinel_ and x == u->key())
return std::make_pair(iterator(u), false);
auto& c = u == sentinel_ or comp_(x, u->key()) ? u->left : u->right;
if (!c) {
c = new_node;
c->parent = u;
u = c;
break;
} else {
u = c;
}
}
_bubble_up(u);
++size_;
return std::make_pair(iterator(u), true);
}
std::pair<iterator, bool> _insert_node(node_ptr new_node) {
return _insert_node_subtree(sentinel_, new_node);
}
iterator _insert_node_hint(const_iterator hint, node_ptr new_node) {
auto x = new_node->key();
auto u = hint.ptr_;
if (!u->parent.expired()) {
auto p = u->parent.lock();
if (p != sentinel_) {
T xp = p->key();
if constexpr (UniqueKey) if (xp == x) [[unlikely]]
return iterator(p);
// Check hint is malicious
if ( (p->left == u and comp_(xp, x))
or (p->right == u and comp_(x, xp))) [[unlikely]]
return _insert_node(new_node).first;
//
}
}
return _insert_node_subtree(u, new_node).first;
}
public:
size_t size() const { return size_; } // TODO: split break size
bool empty() const { return _root() == nullptr; }
void clear() {
sentinel_->left = nullptr;
size_ = 0;
}
iterator find(T x) const {
node_ptr u = _root();
while (u) {
if (u->key() == x)
return iterator(u);
if (comp_(x, u->key()))
u = u->left;
else
u = u->right;
}
return end();
}
size_t count(T x) const { return (size_t) (find(x) != end()); }
iterator lower_bound(T x) const {
node_ptr u = _root();
node_ptr lb = sentinel_;
while (u) {
if (u->key() == x)
return iterator(u);
if (comp_(x, u->key())) {
lb = u;
u = u->left;
} else {
u = u->right;
}
}
return iterator(lb);
}
iterator upper_bound(T x) const {
node_ptr u = _root();
node_ptr ub = sentinel_;
while (u) {
if (comp_(x, u->key())) {
ub = u;
u = u->left;
} else {
u = u->right;
}
}
return iterator(ub);
}
iterator successor(T x) const { return upper_bound(x); }
iterator predecessor(T x) const {
auto u = _root();
node_ptr pr = sentinel_;
while (u) {
if (!comp_(u->key(), x)) {
u = u->left;
} else {
pr = u;
u = u->right;
}
}
return iterator(pr);
}
private:
template<typename... Args>
node_ptr _create_node(Args&&... args) {
auto p = _pick_priority();
return std::make_shared<Node>(p, std::forward<Args>(args)...);
}
public:
template<typename ...Args>
std::pair<iterator, bool> emplace(Args&&... args) {
return _insert_node(_create_node(std::forward<Args>(args)...));
}
template<typename ...Args>
iterator emplace_hint(const_iterator hint, Args&&... args) {
return _insert_node_hint(hint, _create_node(std::forward<Args>(args)...));
}
std::pair<iterator, bool> insert(const init_type& e) {
return emplace(e);
}
std::pair<iterator, bool> insert(init_type&& e) {
return emplace(std::move(e));
}
template<typename=void>
std::pair<iterator, bool> insert(const value_type& e) {
return emplace(e);
}
template<typename=void>
std::pair<iterator, bool> insert(value_type&& e) {
return emplace(std::move(e));
}
template<class It>
void insert(It begin, It end) {
using traits = std::iterator_traits<It>;
static_assert(std::is_convertible<typename traits::value_type, value_type>::value, "");
static_assert(std::is_base_of<std::forward_iterator_tag, typename traits::iterator_category>::value, "");
for (auto it = begin; it != end; ++it)
emplace(*it);
}
void insert(std::initializer_list<value_type> list) {
insert(list.begin(), list.end());
}
iterator erase(iterator it) {
if (it == end())
return end();
auto u = it.ptr_;
auto p = u->parent;
_tricle_down(u);
auto ret = ++iterator(u);
_splice(u);
--size_;
return ret;
}
bool erase(T x) {
auto it = find(x);
if (it != end()) {
erase(it);
return 1;
} else {
return 0;
}
}
iterator erase(iterator begin, iterator end) {
auto _l = split(begin);
auto _m = split(end);
return absorb(&_l);
}
[[nodiscard]] Treap split(iterator it) {
// !!! Breaking size_ value !!!
auto u = it.ptr_;
auto d = std::make_shared<Node>(std::numeric_limits<priority_type>::max());
auto lu = u->left;
d->left = lu;
d->parent = u;
u->left = d;
if (lu) lu->parent = d;
_bubble_up_force(d);
auto l = d->left;
auto r = d->right;
sentinel_->left = r;
if (r) r->parent = sentinel_;
if (l) l->parent.reset();
return Treap(l);
}
iterator absorb(Treap* s) {
assert((s and s->empty()) or empty() or comp_(*--s->end(), *begin()));
auto it = begin();
if (!s or s->empty()) return it;
if (empty()) {
sentinel_->left = s->_root();
sentinel_->left->parent = sentinel_;
size_ = s->size_;
s->clear();
return begin();
}
auto d = std::make_shared<Node>(0);
d->left = s->_root();
d->right = _root();
d->parent = sentinel_;
if (d->left)
d->left->parent = d;
if (d->right)
d->right->parent = d;
sentinel_->left = d;
_tricle_down(d);
_splice(d);
size_ += s->size_;
s->clear();
return it;
}
protected:
template<bool Const>
struct iterator_base {
public:
using difference_type = ptrdiff_t;
using value_type = Treap::value_type;
using pointer = typename std::conditional<Const,
const value_type*,
value_type*>::type;
using reference = typename std::conditional<Const,
const value_type&,
value_type&>::type;
using iterator_category = std::bidirectional_iterator_tag;
private:
node_ptr ptr_;
friend class Treap;
public:
explicit iterator_base(node_ptr ptr) : ptr_(ptr) {}
template<bool C>
iterator_base(const iterator_base<C>& rhs) : ptr_(rhs.ptr_) {}
template<bool C>
iterator_base& operator=(const iterator_base<C>& rhs) {
ptr_ = rhs.ptr_;
return *this;
}
template<bool C>
iterator_base(iterator_base<C>&& rhs) : ptr_(std::move(rhs.ptr_)) {}
template<bool C>
iterator_base& operator=(iterator_base<C>&& rhs) {
ptr_ = std::move(rhs.ptr_);
return *this;
}
template<bool C>
bool operator==(const iterator_base<C>& r) const {
return ptr_ == r.ptr_;
}
template<bool C>
bool operator!=(const iterator_base<C>& r) const {
return ptr_ != r.ptr_;
}
reference operator*() const { return ptr_->v; }
pointer operator->() const { return &(ptr_->v); }
iterator_base& operator++() {
auto u = ptr_;
if (u->right) {
u = u->right;
while (u->left)
u = u->left;
ptr_ = u;
} else {
node_ptr p;
while ((p = u->parent.lock()) and p->left != u) {
u = p;
}
assert(!u->parent.expired());
assert(u->parent.lock()->left == u);
ptr_ = u->parent.lock();
}
return *this;
}
iterator_base operator++(int) {
iterator ret = *this;
++*this;
return ret;
}
iterator_base& operator--() {
auto u = ptr_;
if (u->left) {
u = u->left;
while (u->right)
u = u->right;
ptr_ = u;
} else {
node_ptr p;
while ((p = u->parent.lock()) and p->right != u) {
u = p;
}
ptr_ = u->parent.lock();
}
return *this;
}
iterator_base operator--(int) {
iterator ret = *this;
--*this;
return ret;
}
};
public:
const_iterator begin() const {
auto u = sentinel_;
while (u->left)
u = u->left;
return const_iterator(u);
};
const_iterator end() const {
return const_iterator(sentinel_);
};
const_iterator cbegin() const {
return begin();
}
const_iterator cend() const {
return end();
}
iterator begin() {
return iterator(cbegin());
};
iterator end() {
return iterator(cend());
};
void print_for_debug(node_ptr u = nullptr, int depth = -1) const {
if (_root())
std::cout<<_root()->key()<<std::endl;
auto show = [&](auto& f, node_ptr u, int d) {
if (d >= depth)
return;
if (!u)
return;
std::cout << u->key() << std::endl;
if (u->left)
std::cout << u->left->key() << ' ';
else
std::cout << "--- ";
if (u->right)
std::cout << u->right->key() << std::endl;
else
std::cout << "---" << std::endl;
f(f, u->left, d+1);
f(f, u->right, d+1);
};
if (!u)
u = _root();
show(show, u, 0);
std::cout<<std::endl;
}
};
template<class T, class Compare=std::less<>>
using TreapSet = Treap<T, void, Compare>;
template<class T, class Compare=std::less<>>
using TreapMultiset = Treap<T, void, Compare, false>;
template<class T, class V, class Compare=std::less<>, bool UniqueKey=true>
class _TreapMap : public Treap<T, V, Compare, UniqueKey> {
static_assert(!std::is_same<V, void>::value, "");
using _base = Treap<T, V>;
public:
using typename _base::mapped_type;
using reference = mapped_type&;
reference operator[](const T& x) {
return _base::insert({x, mapped_type()}).first->second;
}
reference operator[](T&& x) {
return _base::insert({std::move(x), mapped_type()}).first->second;
}
};
template<class T, class V, class Compare=std::less<>>
using TreapMap = _TreapMap<T, V, Compare, true>;
template<class T, class V, class Compare=std::less<>>
using TreapMultimap = _TreapMap<T, V, Compare, false>;
namespace treap {
template<class T, class Compare=std::less<>>
using set = TreapSet<T, Compare>;
template<class T, class Compare=std::less<>>
using multiset = TreapMultiset<T, Compare>;
template<class T, class V, class Compare=std::less<>>
using map = TreapMap<T, V, Compare>;
template<class T, class V, class Compare=std::less<>>
using multimap = TreapMultimap<T, V, Compare>;
} // naamespace treap
#line 2 "include/mtl/bit_manip.hpp"
#include <cstdint>
#line 4 "include/mtl/bit_manip.hpp"
#if __cplusplus >= 202002L
#ifndef MTL_CPP20
#define MTL_CPP20
#endif
#include <bit>
#endif
namespace bm {
/// Count 1s for each 8 bits
inline constexpr uint64_t popcnt_e8(uint64_t x) {
x = (x & 0x5555555555555555) + ((x>>1) & 0x5555555555555555);
x = (x & 0x3333333333333333) + ((x>>2) & 0x3333333333333333);
x = (x & 0x0F0F0F0F0F0F0F0F) + ((x>>4) & 0x0F0F0F0F0F0F0F0F);
return x;
}
/// Count 1s
inline constexpr unsigned popcnt(uint64_t x) {
#ifdef MTL_CPP20
return std::popcount(x);
#else
return (popcnt_e8(x) * 0x0101010101010101) >> 56;
#endif
}
/// Alias to mtl::popcnt(x)
constexpr unsigned popcount(uint64_t x) {
return popcnt(x);
}
/// Count trailing 0s. s.t. *11011000 -> 3
inline constexpr unsigned ctz(uint64_t x) {
#ifdef MTL_CPP20
return std::countr_zero(x);
#else
return popcnt((x & (-x)) - 1);
#endif
}
/// Alias to mtl::ctz(x)
constexpr unsigned countr_zero(uint64_t x) {
return ctz(x);
}
/// Count trailing 1s. s.t. *11011011 -> 2
inline constexpr unsigned cto(uint64_t x) {
#ifdef MTL_CPP20
return std::countr_one(x);
#else
return ctz(~x);
#endif
}
/// Alias to mtl::cto(x)
constexpr unsigned countr_one(uint64_t x) {
return cto(x);
}
inline constexpr unsigned ctz8(uint8_t x) {
return x == 0 ? 8 : popcnt_e8((x & (-x)) - 1);
}
/// [00..0](8bit) -> 0, [**..*](not only 0) -> 1
inline constexpr uint8_t summary(uint64_t x) {
constexpr uint64_t hmask = 0x8080808080808080ull;
constexpr uint64_t lmask = 0x7F7F7F7F7F7F7F7Full;
auto a = x & hmask;
auto b = x & lmask;
b = hmask - b;
b = ~b;
auto c = (a | b) & hmask;
c *= 0x0002040810204081ull;
return uint8_t(c >> 56);
}
/// Extract target area of bits
inline constexpr uint64_t bextr(uint64_t x, unsigned start, unsigned len) {
uint64_t mask = len < 64 ? (1ull<<len)-1 : 0xFFFFFFFFFFFFFFFFull;
return (x >> start) & mask;
}
/// 00101101 -> 00111111 -count_1s-> 6
inline constexpr unsigned log2p1(uint8_t x) {
if (x & 0x80)
return 8;
uint64_t p = uint64_t(x) * 0x0101010101010101ull;
p -= 0x8040201008040201ull;
p = ~p & 0x8080808080808080ull;
p = (p >> 7) * 0x0101010101010101ull;
p >>= 56;
return p;
}
/// 00101100 -mask_mssb-> 00100000 -to_index-> 5
inline constexpr unsigned mssb8(uint8_t x) {
assert(x != 0);
return log2p1(x) - 1;
}
/// 00101100 -mask_lssb-> 00000100 -to_index-> 2
inline constexpr unsigned lssb8(uint8_t x) {
assert(x != 0);
return popcnt_e8((x & -x) - 1);
}
/// Count leading 0s. 00001011... -> 4
inline constexpr unsigned clz(uint64_t x) {
#ifdef MTL_CPP20
return std::countl_zero(x);
#else
if (x == 0)
return 64;
auto i = mssb8(summary(x));
auto j = mssb8(bextr(x, 8 * i, 8));
return 63 - (8 * i + j);
#endif
}
/// Alias to mtl::clz(x)
constexpr unsigned countl_zero(uint64_t x) {
return clz(x);
}
/// Count leading 1s. 11110100... -> 4
inline constexpr unsigned clo(uint64_t x) {
#ifdef MTL_CPP20
return std::countl_one(x);
#else
return clz(~x);
#endif
}
/// Alias to mtl::clo(x)
constexpr unsigned countl_one(uint64_t x) {
return clo(x);
}
inline constexpr unsigned clz8(uint8_t x) {
return x == 0 ? 8 : 7 - mssb8(x);
}
inline constexpr uint64_t bit_reverse(uint64_t x) {
x = ((x & 0x00000000FFFFFFFF) << 32) | ((x & 0xFFFFFFFF00000000) >> 32);
x = ((x & 0x0000FFFF0000FFFF) << 16) | ((x & 0xFFFF0000FFFF0000) >> 16);
x = ((x & 0x00FF00FF00FF00FF) << 8) | ((x & 0xFF00FF00FF00FF00) >> 8);
x = ((x & 0x0F0F0F0F0F0F0F0F) << 4) | ((x & 0xF0F0F0F0F0F0F0F0) >> 4);
x = ((x & 0x3333333333333333) << 2) | ((x & 0xCCCCCCCCCCCCCCCC) >> 2);
x = ((x & 0x5555555555555555) << 1) | ((x & 0xAAAAAAAAAAAAAAAA) >> 1);
return x;
}
/// Check if x is power of 2. 00100000 -> true, 00100001 -> false
constexpr bool has_single_bit(uint64_t x) noexcept {
#ifdef MTL_CPP20
return std::has_single_bit(x);
#else
return x != 0 && (x & (x - 1)) == 0;
#endif
}
/// Bit width needs to represent x. 00110110 -> 6
constexpr int bit_width(uint64_t x) noexcept {
#ifdef MTL_CPP20
return std::bit_width(x);
#else
return 64 - clz(x);
#endif
}
/// Ceil power of 2. 00110110 -> 01000000
constexpr uint64_t bit_ceil(uint64_t x) {
#ifdef MTL_CPP20
return std::bit_ceil(x);
#else
if (x == 0) return 1;
return 1ull << bit_width(x - 1);
#endif
}
/// Floor power of 2. 00110110 -> 00100000
constexpr uint64_t bit_floor(uint64_t x) {
#ifdef MTL_CPP20
return std::bit_floor(x);
#else
if (x == 0) return 0;
return 1ull << (bit_width(x) - 1);
#endif
}
} // namespace bm
#line 4 "include/mtl/binary_trie.hpp"
#include <array>
#line 9 "include/mtl/binary_trie.hpp"
#include <algorithm>
#line 11 "include/mtl/binary_trie.hpp"
template<typename T, typename M,
int8_t W = sizeof(T) * 8>
class BinaryTrieBase : public traits::AssociativeArrayDefinition<T, M> {
static_assert(std::is_unsigned<T>::value, "");
public:
using types = traits::AssociativeArrayDefinition<T, M>;
using key_type = typename types::key_type;
using value_type = typename types::value_type;
using init_type = typename types::init_type;
struct Node;
using node_ptr = std::shared_ptr<Node>;
using node_weak_ptr = std::weak_ptr<Node>;
struct Leaf;
using leaf_ptr = std::shared_ptr<Leaf>;
struct Node {
std::array<node_ptr, 2> c;
leaf_ptr jump;
node_weak_ptr parent;
Node() = default;
node_ptr& left() { return c[0]; }
node_ptr& right() { return c[1]; }
};
struct Leaf : Node {
value_type v;
Leaf() = default;
Leaf(const value_type& v) : Node(), v(v) {}
Leaf(value_type&& v) : Node(), v(std::forward<value_type>(v)) {}
key_type key() const {
return types::key_of(v);
}
using Node::c;
leaf_ptr prev() const {
return std::static_pointer_cast<Leaf>(c[0]);
}
leaf_ptr next() const {
return std::static_pointer_cast<Leaf>(c[1]);
}
void set_prev(leaf_ptr l) {
c[0] = std::static_pointer_cast<Node>(l);
}
void set_next(leaf_ptr l) {
c[1] = std::static_pointer_cast<Node>(l);
}
};
protected:
node_ptr root_;
leaf_ptr dummy_;
size_t size_;
virtual void _init() {
root_ = create_node_at(0, 0);
dummy_ = std::make_shared<Leaf>();
root_->jump = dummy_;
dummy_->set_next(dummy_);
dummy_->set_prev(dummy_);
size_ = 0;
}
void _deinit() {
root_ = nullptr;
auto u = dummy_->next();
dummy_->set_next(nullptr);
u->set_prev(nullptr);
while (u != dummy_) {
auto n = u->next();
u->set_next(nullptr);
n->set_prev(nullptr);
u = n;
}
dummy_ = nullptr;
}
public:
BinaryTrieBase() {
_init();
}
BinaryTrieBase(const BinaryTrieBase& rhs) {
_insert_init(rhs.begin(), rhs.end());
}
virtual BinaryTrieBase& operator=(const BinaryTrieBase& rhs) {
_deinit();
_insert_init(rhs.begin(), rhs.end());
return *this;
}
BinaryTrieBase(BinaryTrieBase&&) noexcept = default;
virtual BinaryTrieBase& operator=(BinaryTrieBase&& rhs) noexcept {
_deinit();
root_ = std::move(rhs.root_);
dummy_ = std::move(rhs.dummy_);
size_ = std::move(rhs.size_);
return *this;
}
virtual ~BinaryTrieBase() {
_deinit();
}
protected:
template<class InputIt>
void _insert_init(InputIt begin, InputIt end) {
static_assert(std::is_convertible<typename std::iterator_traits<InputIt>::value_type, value_type>::value, "");
_init();
if (begin == end) return;
if (!std::is_sorted(begin, end, [](auto& l, auto& r) {
return types::key_of(l) < types::key_of(r);
})) {
for (auto it = begin; it != end; ++it)
_insert(*it);
return;
}
auto push_link = [&](leaf_ptr l) {
auto b = dummy_->prev();
l->set_prev(b);
l->set_next(dummy_);
l->prev()->set_next(l);
l->next()->set_prev(l);
};
std::array<node_ptr, W> us{};
auto grow = [&](key_type x, int k, leaf_ptr l) {
for (int i = k; i < W-1; i++) {
us[i+1] = create_node_at(x, i+1);
int c = (x >> (W-i-1)) & 1;
us[i]->c[c] = us[i+1];
us[i+1]->parent = us[i];
us[i+1]->jump = l;
}
int c = x & 1;
us[W-1]->c[c] = l;
l->parent = us[W-1];
};
us[0] = root_;
key_type x = types::key_of(*begin);
auto l = create_leaf_at(x, *begin);
push_link(l);
us[0]->jump = l;
grow(x, 0, l);
size_t sz = 1;
for (auto it = std::next(begin); it != end; ++it) {
key_type px = x;
x = types::key_of(*it);
auto m = x ^ px;
if (m == 0) continue;
// [[assume(m != 0)]]
int k = W-1;
while (m > 1) {
m >>= 1;
--k;
}
l = create_leaf_at(x, *it);
push_link(l);
for (int i = 0; i < k; i++)
if (!us[i]->c[1]) us[i]->jump = l;
us[k]->jump = nullptr;
grow(x, k, l);
++sz;
}
size_ = sz;
}
public:
template<typename InputIt>
explicit BinaryTrieBase(InputIt begin, InputIt end) {
_insert_init(begin, end);
}
size_t size() const {
return size_;
}
bool empty() const { return size() == 0; }
void clear() {
_deinit();
_init();
}
protected:
template<bool> struct iterator_base;
public:
using iterator = iterator_base<false>;
using const_iterator = iterator_base<true>;
iterator begin() {
return iterator(dummy_->next());
}
iterator end() {
return iterator(dummy_);
}
const_iterator begin() const {
return const_iterator(dummy_->next());
}
const_iterator end() const {
return const_iterator(dummy_);
}
template<class Rule>
const_iterator traverse(Rule rule) const {
auto u = root_;
for (int i = 0; i < W; i++) {
auto l = (bool)u->c[0];
auto r = (bool)u->c[1];
auto c = rule(W-1-i, l, r);
u = u->c[c];
}
return const_iterator(std::static_pointer_cast<Leaf>(u));
}
protected:
virtual std::pair<int, node_ptr> _traverse(const key_type& key,
int depth = 0,
node_ptr root = nullptr) const {
int i, c;
key_type x = key;
auto u = !root ? root_ : root;
for (i = depth; i < W; i++) {
c = (x >> (W-i-1)) & 1;
if (!u->c[c]) break;
u = u->c[c];
}
return std::make_pair(i, u);
}
iterator _lower_bound(const key_type& x) const {
auto reached = _traverse(x);
int i = reached.first;
node_ptr u = reached.second;
if (i == W) return iterator(std::static_pointer_cast<Leaf>(u));
auto l = (((x >> (W-i-1)) & 1) == 0) ? u->jump : u->jump->next();
return iterator(l);
}
iterator _upper_bound(const key_type& x) const {
auto it = _lower_bound(x);
if (types::key_of(*it) == x)
++it;
return it;
}
virtual iterator _find(const key_type& x) const {
auto reached = _traverse(x);
int i = reached.first;
node_ptr u = reached.second;
if (i == W)
return iterator(std::static_pointer_cast<Leaf>(u));
else
return end();
}
virtual node_ptr create_node_at(const key_type&, int) {
return std::make_shared<Node>();
}
virtual leaf_ptr create_leaf_at(const key_type&, const init_type& value) {
return std::make_shared<Leaf>(value);
}
virtual leaf_ptr create_leaf_at(const key_type&, init_type&& value) {
return std::make_shared<Leaf>(std::move(value));
}
template<typename Value>
iterator _emplace_impl(key_type x, int height, node_ptr forked, Value&& value) {
assert(height < W);
int i = height;
node_ptr u = forked;
auto f = u;
int c = (x >> (W-i-1)) & 1;
auto fc = c;
auto fi = i;
auto pred = c == 1 ? u->jump : u->jump->prev();
u->jump = nullptr;
auto l = create_leaf_at(x, std::forward<Value>(value));
l->set_prev(pred);
l->set_next(pred->next());
l->prev()->set_next(l);
l->next()->set_prev(l);
for (; i < W-1; i++) {
c = (x >> (W-i-1)) & 1;
assert(!u->c[c]);
u->c[c] = create_node_at(x, i+1);
u->c[c]->parent = u;
u->c[c]->jump = l;
u = u->c[c];
}
{
c = (x >> (W-i-1)) & 1;
u->c[c] = l;
u->c[c]->parent = u;
}
if (f == root_) [[unlikely]] {
f->jump = l;
} else [[likely]] {
auto v = f->parent.lock();
fi--;
while (v) {
c = x >> (W-fi-1) & 1;
if (c != fc and !v->jump)
break;
if (!v->c[fc])
v->jump = l;
v = v->parent.lock();
fi--;
}
}
size_++;
return iterator(l);
}
template<typename Value>
std::pair<iterator, bool> _insert(Value&& value) {
static_assert(std::is_convertible<Value, value_type>::value, "");
key_type x = types::key_of(value);
auto reached = _traverse(x);
int i = reached.first;
node_ptr u = reached.second;
if (i == W)
return std::make_pair(iterator(std::static_pointer_cast<Leaf>(u)), false);
return std::make_pair(_emplace_impl(x, i, u, std::forward<Value>(value)), true);
}
virtual std::pair<int, node_ptr> climb_to_lca(leaf_ptr l, key_type x) {
key_type m = x ^ types::key_of(l->v);
if (m == 0)
return std::make_pair(W, std::static_pointer_cast<Node>(l));
int h = bm::clz(m) - (64 - W);
node_ptr f = std::static_pointer_cast<Node>(l);
for (int i = W; i > h; i--)
f = f->parent.lock();
return std::make_pair(h, f);
}
template<class Value>
iterator _emplace_hint(const_iterator hint, Value&& value) {
key_type x = types::key_of(value);
if (empty())
return _emplace_impl(x, 0, root_, std::forward<Value>(value));
if (hint == end())
--hint;
int h;
node_ptr f;
std::tie(h, f) = climb_to_lca(hint.ptr_, x);
std::tie(h, f) = _traverse(x, h, f);
if (h == W)
return iterator(std::static_pointer_cast<Leaf>(f));
return _emplace_impl(x, h, f, std::forward<Value>(value));
}
virtual void erase_node_at(const key_type&, int, node_ptr) {}
virtual bool _erase(const key_type& key) {
auto it = _find(key);
if (it != end()) {
_erase_from_leaf(types::key_of(*it), it.ptr_);
return true;
} else {
return false;
}
}
template<typename Key>
iterator _erase_from_leaf(Key&& key, leaf_ptr l) {
static_assert(std::is_convertible<Key, key_type>::value, "");
key_type x = std::forward<Key>(key);
assert(x == l->key());
l->prev()->set_next(l->next());
l->next()->set_prev(l->prev());
int i,c;
auto v = std::static_pointer_cast<Node>(l);
for (i = W-1; i >= 0; i--) {
erase_node_at(x, i+1, v);
v = v->parent.lock();
c = (x >> (W-i-1)) & 1;
v->c[c] = nullptr;
if (v->c[c^1]) break;
}
auto nj = c ? l->prev() : l->next();
auto fc = c;
v->jump = nj;
v = v->parent.lock();
i--;
for (; i >= 0; i--) {
assert(v);
c = (x >> (W-i-1)) & 1;
if (c != fc) {
if (!v->jump) break;
v->jump = nj;
}
v = v->parent.lock();
}
size_--;
return iterator(l->next());
}
iterator iterator_remove_const(const const_iterator& it) {
return iterator(it.ptr_);
}
iterator iterator_remove_const(const_iterator&& it) {
return iterator(std::move(it.ptr_));
}
iterator _erase(iterator it) {
if (it == end()) return it;
return _erase_from_leaf(types::key_of(*it), it.ptr_);
}
iterator _erase(const_iterator it) {
if (it == end()) return iterator_remove_const(it);
return _erase_from_leaf(types::key_of(*it), it.ptr_);
}
protected:
template<bool Const>
struct iterator_base {
using difference_type = ptrdiff_t;
using value_type = BinaryTrieBase::value_type;
using pointer = typename std::conditional<Const,
const value_type*,
value_type*>::type;
using reference = typename std::conditional<Const,
const value_type&,
value_type&>::type;
using iterator_category = std::bidirectional_iterator_tag;
leaf_ptr ptr_;
iterator_base(leaf_ptr p) : ptr_(p) {}
template<bool C>
iterator_base(const iterator_base<C>& rhs) : ptr_(rhs.ptr_) {}
template<bool C>
iterator_base& operator=(const iterator_base<C>& rhs) {
ptr_ = rhs.ptr_;
}
template<bool C>
iterator_base(iterator_base<C>&& rhs) : ptr_(std::move(rhs.ptr_)) {}
template<bool C>
iterator_base& operator=(iterator_base<C>&& rhs) {
ptr_ = std::move(rhs.ptr_);
}
reference operator*() {
return ptr_->v;
}
pointer operator->() {
return &(ptr_->v);
}
template<bool C>
bool operator==(const iterator_base<C>& rhs) const {
return ptr_ == rhs.ptr_;
}
template<bool C>
bool operator!=(const iterator_base<C>& rhs) const {
return !operator==(rhs);
}
iterator_base& operator++() {
ptr_ = ptr_->next();
return *this;
}
iterator_base operator++(int) const {
iterator_base ret = *this;
operator++();
return ret;
}
iterator_base& operator--() {
ptr_ = ptr_->prev();
return *this;
}
iterator_base operator--(int) const {
iterator_base ret = *this;
operator--();
return ret;
}
};
};
template<typename T, typename V, uint8_t W = sizeof(T)*8>
using BinaryTrie = traits::MapTraits<BinaryTrieBase<T, V, W>>;
template<typename T, uint8_t W = sizeof(T)*8>
using BinaryTrieSet = traits::SetTraits<BinaryTrieBase<T, void, W>>;
template<typename T, typename V, uint8_t W = sizeof(T)*8>
using BinaryTrieMap = BinaryTrie<T, V, W>;
#line 7 "include/mtl/xft.hpp"
#include <unordered_map>
#line 9 "include/mtl/xft.hpp"
template<class T, class M, int8_t W>
using XFastTrieHashTableMappedType = typename BinaryTrieBase<T, M, W>::node_ptr;
#define XFT_DEFAULT_HASH_TABLE std::unordered_map
#define XFT_HASH_TABLE_TYPE(HT,T,M,W) HT<T, XFastTrieHashTableMappedType<T, M, W>>
template<typename T, typename M,
int8_t W = sizeof(T) * 8,
class HashTable = XFT_HASH_TABLE_TYPE(XFT_DEFAULT_HASH_TABLE, T, M, W)>
class XFastTrieBase : public BinaryTrieBase<T, M, W> {
static_assert(std::is_unsigned<T>::value, "");
using Base = BinaryTrieBase<T, M, W>;
public:
using hash_table_type = HashTable;
using types = typename Base::types;
using value_type = typename types::value_type;
using init_type = typename types::init_type;
using typename Base::Node;
using typename Base::Leaf;
using typename Base::node_ptr;
using typename Base::leaf_ptr;
using typename Base::key_type;
protected:
using Base::root_;
using Base::dummy_;
using Base::size_;
std::array<hash_table_type, W+1> tb_;
void _store_node(const int i, const key_type& x, node_ptr u) {
tb_[i].emplace(W-i < (int)sizeof(key_type)*8 ? (x >> (W-i)) : 0, u);
}
void _init() override {
for (auto& t:tb_) t.clear();
Base::_init();
}
public:
XFastTrieBase() : Base() {}
XFastTrieBase(const XFastTrieBase& rhs) {
Base::operator=(rhs);
}
XFastTrieBase& operator=(const XFastTrieBase& rhs) {
Base::operator=(rhs);
}
XFastTrieBase(XFastTrieBase&& rhs) noexcept {
Base::operator=(std::move(rhs));
}
XFastTrieBase& operator=(XFastTrieBase&& rhs) noexcept {
Base::operator=(std::move(rhs));
}
template<typename InputIt>
explicit XFastTrieBase(InputIt begin, InputIt end) {
Base::_insert_init(begin, end);
}
using iterator = typename Base::iterator;
using Base::end;
protected:
node_ptr create_node_at(const key_type& x, int i) override {
auto u = Base::create_node_at(x, i);
_store_node(i, x, u);
return u;
}
leaf_ptr create_leaf_at(const key_type& x, const init_type& value) override {
auto l = Base::create_leaf_at(x, value);
_store_node(W, x, std::static_pointer_cast<Node>(l));
return l;
}
leaf_ptr create_leaf_at(const key_type& x, init_type&& value) override {
auto l = Base::create_leaf_at(x, std::move(value));
_store_node(W, x, std::static_pointer_cast<Node>(l));
return l;
}
void erase_node_at(const key_type& x, int i, node_ptr u) override {
Base::erase_node_at(x, i, u);
auto it = tb_[i].find(W-i < (int)sizeof(key_type)*8 ? (x >> (W-i)) : 0);
assert(it != tb_[i].end());
assert(it->second == u);
tb_[i].erase(it);
}
std::pair<int, node_ptr> _traverse(const key_type& key,
int depth = 0,
node_ptr root = nullptr) const override {
key_type x = key;
int l = depth, h = W+1;
node_ptr u = !root ? root_ : root;
while (l+1 < h) {
int i = l+(h-l)/2;
auto p = W-i < (int)sizeof(key_type)*8 ? (x >> (W-i)) : 0;
auto it = tb_[i].find(p);
if (it != tb_[i].end()) {
l = i;
u = it->second;
} else {
h = i;
}
}
return std::make_pair(l, u);
}
iterator _find(const key_type& x) const override {
auto it = tb_[W].find(x);
if (it != tb_[W].end())
return iterator(std::static_pointer_cast<Leaf>(it->second));
else
return end();
}
using Base::_insert;
std::pair<int, node_ptr> climb_to_lca(leaf_ptr l, key_type x) override {
key_type m = x ^ types::key_of(l->v);
if (m == 0)
return std::make_pair(W, std::static_pointer_cast<Node>(l));
int h = bm::clz(m) - (64 - W);
key_type y = W-h < (int)sizeof(key_type)*8 ? (x >> (W-h)) : 0;
assert(tb_[h].count(y));
node_ptr f = tb_[h][y];
return std::make_pair(h, f);
}
using Base::_emplace_hint;
using Base::_erase;
bool _erase(const key_type& key) override {
auto it = tb_[W].find(key);
if (it != tb_[W].end()) {
Base::_erase_from_leaf(key, std::static_pointer_cast<Leaf>(it->second));
return true;
} else {
return false;
}
}
};
#line 137 "include/mtl/xft.hpp"
template<typename T, typename V, uint8_t W = sizeof(T)*8,
class HashTable = XFT_HASH_TABLE_TYPE(XFT_DEFAULT_HASH_TABLE, T, V, W)>
using XFastTrie = traits::MapTraits<XFastTrieBase<T, V, W, HashTable>>;
template<typename T, uint8_t W = sizeof(T)*8,
class HashTable = XFT_HASH_TABLE_TYPE(XFT_DEFAULT_HASH_TABLE, T, void, W)>
using XFastTrieSet = traits::SetTraits<XFastTrieBase<T, void, W, HashTable>>;
template<typename T, typename V, uint8_t W = sizeof(T)*8,
class HashTable = XFT_HASH_TABLE_TYPE(XFT_DEFAULT_HASH_TABLE, T, V, W)>
using XFastTrieMap = XFastTrie<T, V, W, HashTable>;
#line 12 "include/mtl/yft.hpp"
#include <vector>
#include <bitset>
#line 15 "include/mtl/yft.hpp"
template<class T, class M,
int8_t W = sizeof(T) * 8,
class TREAP = Treap<T, M>,
class HashTable = XFT_HASH_TABLE_TYPE(XFT_DEFAULT_HASH_TABLE,T,TREAP,W),
class XFT = XFastTrieMap<T, TREAP, W, HashTable>>
class YFastTrieBase : public traits::AssociativeArrayDefinition<T, M> {
static_assert(std::is_unsigned<T>::value, "");
using Def = traits::AssociativeArrayDefinition<T, M>;
public:
using typename Def::key_type;
using typename Def::value_type;
using treap_type = TREAP;
using xft_type = XFT;
static constexpr key_type const kKeyMax = std::numeric_limits<T>::max() >> (sizeof(T)*8-W);
protected:
template<bool> struct iterator_base;
public:
using iterator = iterator_base<false>;
using const_iterator = iterator_base<true>;
protected:
xft_type xft_;
iterator end_;
size_t size_;
std::default_random_engine eng_;
std::uniform_int_distribution<uint8_t> dist_;
void _init() {
xft_.clear();
auto xit = xft_.emplace(kKeyMax, treap_type()).first;
end_ = iterator(&xft_, xit, xit->second.end());
size_ = 0;
}
public:
YFastTrieBase()
: xft_({{kKeyMax, treap_type()}}),
end_(&xft_, std::prev(xft_.end()), std::prev(xft_.end())->second.end()),
size_(0),
dist_(0, W-1) {}
YFastTrieBase(const YFastTrieBase& rhs)
: xft_(rhs.xft_),
end_(&xft_, std::prev(xft_.end()), std::prev(xft_.end())->second.end()),
size_(rhs.size_),
dist_(0, W-1) {}
YFastTrieBase& operator=(const YFastTrieBase& rhs) {
xft_ = rhs.xft_;
end_ = iterator(&xft_, std::prev(xft_.end()), std::prev(xft_.end())->second.end());
size_ = rhs.size_;
eng_ = rhs.eng_;
dist_ = rhs.dist_;
return *this;
}
YFastTrieBase(YFastTrieBase&&) noexcept = default;
YFastTrieBase& operator=(YFastTrieBase&&) noexcept = default;
template<typename InputIt>
explicit YFastTrieBase(InputIt begin, InputIt end) : YFastTrieBase() {
static_assert(std::is_convertible<typename std::iterator_traits<InputIt>::value_type, value_type>::value, "");
if (begin == end) return;
if (!std::is_sorted(begin, end, [](auto& l, auto& r) {
return Def::key_of(l) < Def::key_of(r);
})) {
for (auto it = begin; it != end; ++it)
_insert(*it);
return;
}
auto b = begin;
while (b != end) {
auto px = Def::key_of(*b);
auto e = std::next(b);
while (e != end and !_pivot_selected()) {
px = Def::key_of(*(e++));
while (e != end and Def::key_of(*e) == px)
px = Def::key_of(*(e++));
}
if (e != end) { // shift on pivot
px = Def::key_of(*(e++));
while (e != end and Def::key_of(*e) == px)
px = Def::key_of(*(e++));
}
if (e != end) {
assert(px < end_.xit_->first);
xft_.emplace_hint(end_.xit_, px, treap_type(b, e));
b = e;
} else {
end_.xit_->second.insert(b,e);
end_.tit_ = end_.xit_->second.end();
break;
}
}
size_ = std::distance(begin, end);
}
size_t size() const { return size_; }
bool empty() const { return size() == 0; }
void clear() {
_init();
}
iterator begin() const {
return make_raw_iterator(&xft_, xft_.begin(), xft_.begin()->second.begin());
}
iterator end() const {
return end_;
}
protected:
template<class Key>
iterator _lower_bound(const Key& key) const {
key_type x = key;
auto tit = xft_.lower_bound(x);
assert(tit != xft_.end());
auto tres = tit->second.lower_bound(x);
return make_raw_iterator(&xft_, tit, tres);
}
template<class Key>
iterator _upper_bound(const Key& key) const {
key_type x = key;
auto tit = xft_.upper_bound(x);
if (tit == xft_.end()) [[unlikely]]
return end();
assert(tit != xft_.end());
auto tres = tit->second.upper_bound(x);
return make_raw_iterator(&xft_, tit, tres);
}
template<class Key>
iterator _find(const Key& key) const {
key_type x = key;
auto tit = xft_.lower_bound(x);
assert(tit != xft_.end());
auto tres = tit->second.find(x);
if (tres != tit->second.end())
return make_raw_iterator(&xft_, tit, tres);
else
return end();
}
bool _pivot_selected() {
return dist_(eng_) == 0;
}
iterator activate_new_treap_node(const key_type& x,
typename xft_type::iterator xlb,
typename treap_type::iterator new_tit) {
size_++;
if (_pivot_selected()) [[unlikely]] {
auto lt = std::move(xlb->second.split(std::next(new_tit)));
xlb = xft_.emplace_hint(xlb, x, std::move(lt));
}
return iterator(&xft_, xlb, new_tit);
}
template<class Value>
std::pair<iterator, bool> _insert(Value&& value) {
key_type x = Def::key_of(value);
auto xlb = xft_.lower_bound(x);
assert(xlb != xft_.end());
auto& t = xlb->second;
auto tins = t.insert(std::forward<Value>(value));
if (tins.second) {
return std::make_pair(activate_new_treap_node(x, xlb, tins.first), true);
}
return std::make_pair(iterator(&xft_, xlb, tins.first), false);
}
template<class Value>
iterator _emplace_hint_unique(const_iterator hint, Value&& value) {
assert(hint == end() || Def::key_of(value) < hint->first);
auto xit = hint.xit_;
auto tins = xit->second.emplace_hint(hint.tit_, std::forward<Value>(value));
return activate_new_treap_node(tins->first, xit, tins);
}
template<class Value>
iterator _emplace_hint(const_iterator hint, Value&& value) {
key_type x = Def::key_of(value);
if (hint != end() and x == hint->first) {
return hint;
}
return _emplace_hint_unique(hint, std::forward<Value>(value));
}
bool _erase(const key_type& key) {
auto xlb = xft_.lower_bound(key);
assert(xlb != xft_.end());
auto& t = xlb->second;
if (t.erase(key)) {
size_--;
auto nxlb = std::next(xlb);
assert(nxlb != xlb);
if (xlb->first == key and nxlb != xft_.end()) [[unlikely]] {
nxlb->second.absorb(&t);
xft_.erase(xlb);
}
return true;
}
return false;
}
iterator _erase(const_iterator it) {
if (it == end()) return it;
auto next = std::next(it);
auto xlb = it.xit_;
auto x = Def::key_of(*it);
auto* t = &xlb->second;
t->erase(it.tit_);
size_--;
if (xlb->first == x and xlb != std::prev(xft_.end())) {
auto& rt = std::next(xlb)->second;
rt.absorb(t);
xft_.erase(xlb);
}
return next;
}
protected:
template<bool Const>
struct iterator_base {
using difference_type = ptrdiff_t;
using value_type = typename YFastTrieBase::value_type;
using pointer = typename std::conditional<Const,
const value_type*,
value_type*>::type;
using reference = typename std::conditional<Const,
const value_type&,
value_type&>::type;
using iterator_category = std::bidirectional_iterator_tag;
using xft_pointer = xft_type*;
using xiterator = typename xft_type::iterator;
using titerator = typename treap_type::iterator;
xft_pointer xft_;
xiterator xit_;
titerator tit_;
iterator_base(xft_pointer xft, xiterator xit, titerator tit) :
xft_(xft), xit_(xit), tit_(tit) {}
template<bool C>
iterator_base(const iterator_base<C>& rhs) :
xft_(rhs.xft_), xit_(rhs.xit_), tit_(rhs.tit_) {}
template<bool C>
iterator_base& operator=(const iterator_base<C>& rhs) {
xft_ = rhs.xft_;
xit_ = rhs.xit_;
tit_ = rhs.tit_;
return *this;
}
template<bool C>
iterator_base(iterator_base<C>&& rhs) :
xft_(std::move(rhs.xft_)),
xit_(std::move(rhs.xit_)),
tit_(std::move(rhs.tit_)) {}
template<bool C>
iterator_base& operator=(iterator_base<C>&& rhs) {
xft_ = std::move(rhs.xft_);
xit_ = std::move(rhs.xit_);
tit_ = std::move(rhs.tit_);
return *this;
}
reference operator*() const {
return *tit_;
}
pointer operator->() const {
return tit_.operator->();
}
template<bool C>
bool operator==(const iterator_base<C>& rhs) const {
return xit_ == rhs.xit_ and tit_ == rhs.tit_;
}
template<bool C>
bool operator!=(const iterator_base<C>& rhs) const {
return !operator==(rhs);
}
iterator_base& operator++() {
++tit_;
if (tit_ == xit_->second.end() and std::next(xit_) != xft_->end()) {
++xit_;
tit_ = xit_->second.begin();
}
return *this;
}
iterator_base operator++(int) {
iterator_base ret = *this;
operator++();
return ret;
}
iterator_base& operator--() {
if (tit_ == xit_->second.begin()) {
--xit_;
assert(!xit_->second.empty());
tit_ = std::prev(xit_->second.end());
} else {
--tit_;
}
return *this;
}
iterator_base operator--(int) {
iterator_base ret = *this;
operator--();
return ret;
}
};
protected:
using xft_pointer = xft_type*;
using xft_iterator = typename xft_type::iterator;
using treap_iterator = typename treap_type::iterator;
using const_xft_pointer = const xft_type*;
using const_xft_iterator = typename xft_type::const_iterator;
using const_treap_iterator = typename treap_type::const_iterator;
static iterator make_raw_iterator(const_xft_pointer xft,
const_xft_iterator xit,
const_treap_iterator tit) {
return iterator(const_cast<xft_pointer>(xft), xit, tit);
}
};
template<typename Key, typename T, uint8_t W = sizeof(Key)*8>
using YFastTrie = traits::MapTraits<YFastTrieBase<Key, T, W>>;
template<typename T, uint8_t W = sizeof(T)*8>
using YFastTrieSet = traits::SetTraits<YFastTrieBase<T, void, W>>;
template<typename Key, typename T, uint8_t W = sizeof(Key)*8>
using YFastTrieMap = YFastTrie<Key, T, W>;
#line 4 "test/yosupo/predecessor_problem-yft.test.cpp"
#include <bits/stdc++.h>
using namespace std;
constexpr int max_value = 1e7;
constexpr int bits = 64 - bm::clz(max_value);
int main() {
int n,q; cin>>n>>q;
string t; cin>>t;
vector<int> V;
for (int i = 0; i < n; i++) if (t[i]=='1') V.push_back(i);
YFastTrieSet<unsigned int, bits> S(V.begin(), V.end());
for (int i = 0; i < q; i++) {
int t; cin>>t;
int k; cin>>k;
switch (t) {
case 0: {
S.insert(k);
}; break;
case 1: {
S.erase(S.find(k));
}; break;
case 2: {
cout << S.count(k) << endl;
}; break;
case 3: {
auto i = S.lower_bound(k);
cout << (i != S.end() ? (int)*i : -1) << endl;
}; break;
case 4: {
auto i = S.upper_bound(k);
cout << (i != S.begin() ? (int)*--i : -1) << endl;
}; break;
default: break;
}
}
}