cp-library-cpp
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Implicit Treap Segtree
(library/datastructure/bbst/implicit_treap_segtree.hpp)
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- Last update: 2023-02-04 08:57:06+09:00
- Include:
#include "library/datastructure/bbst/implicit_treap_segtree.hpp"
Implicit Treap Segtree
Depends on
Verified with
- test/src/datastructure/bbst/implicit_treap_segtree/abc238_f.test.cpp
- test/src/datastructure/bbst/implicit_treap_segtree/dummy.test.cpp
Code
#ifndef SUISEN_IMPLICIT_TREAP_SEGTREE
#define SUISEN_IMPLICIT_TREAP_SEGTREE
#include "library/datastructure/bbst/implicit_treap_base.hpp"
namespace suisen {
namespace internal::implicit_treap {
template <typename T, T(*op)(T, T), T(*e)()>
struct RangeProductNode: Node<T, RangeProductNode<T, op, e>> {
using base = Node<T, RangeProductNode<T, op, e>>;
using node_pointer = typename base::node_pointer;
using value_type = typename base::value_type;
value_type _sum;
RangeProductNode(const value_type& val): base(val), _sum(val) {}
// ----- override ----- //
static node_pointer update(node_pointer t) {
base::update(t);
prod_all(t) = op(op(safe_prod(base::child0(t)), base::value(t)), safe_prod(base::child1(t)));
return t;
}
// ----- new features ----- //
static value_type& prod_all(node_pointer t) {
return base::node(t)._sum;
}
static value_type safe_prod(node_pointer t) {
return base::is_null(t) ? e() : prod_all(t);
}
static std::pair<node_pointer, value_type> prod(node_pointer t, size_t l, size_t r) {
auto [tl, tm, tr] = base::split(t, l, r);
value_type res = safe_prod(tm);
return { base::merge(tl, tm, tr), res };
}
template <typename Func>
static node_pointer set(node_pointer t, size_t k, const Func& f) {
return base::set_update(t, k, f);
}
using const_iterator = typename base::const_iterator;
template <typename Predicate>
static std::pair<node_pointer, const_iterator> max_right(node_pointer t, size_t l, const Predicate& f) {
auto [tl, tr] = base::split(t, l);
value_type sum = e();
assert(f(sum));
const_iterator it = base::template binary_search<const_iterator>(
tr, [&](const_iterator it) {
value_type nxt_sum = op(op(sum, safe_prod(it.get_child0())), *it);
return f(nxt_sum) ? (sum = std::move(nxt_sum), false) : true;
}
);
it.set_root(t = base::merge(tl, tr), l + it.index());
return { t, it };
}
template <typename Predicate>
static std::pair<node_pointer, const_iterator> min_left(node_pointer t, size_t r, const Predicate& f) {
auto [tl, tr] = base::split(t, r);
value_type sum = e();
assert(f(sum));
const_iterator it = base::template binary_search<const_iterator>(
tl, [&](const_iterator it) {
value_type nxt_sum = op(*it, op(safe_prod(it.get_child1()), sum));
return f(nxt_sum) ? (sum = std::move(nxt_sum), true) : false;
}
);
it.set_root(t = base::merge(tl, tr), it.index());
return { t, it };
}
};
}
template <typename T, T(*op)(T, T), T(*e)()>
class DynamicSegmentTree {
using node_type = internal::implicit_treap::RangeProductNode<T, op, e>;
using node_pointer = typename node_type::node_pointer;
node_pointer _root;
struct node_pointer_construct {};
DynamicSegmentTree(node_pointer root, node_pointer_construct): _root(root) {}
public:
using value_type = typename node_type::value_type;
DynamicSegmentTree(): _root(node_type::empty_node()) {}
explicit DynamicSegmentTree(size_t n, const value_type& fill_value = {}): _root(node_type::build(n, fill_value)) {}
template <typename U>
DynamicSegmentTree(const std::vector<U>& dat) : _root(node_type::build(dat.begin(), dat.end())) {}
void free() {
node_type::delete_tree(_root);
_root = node_type::empty_node();
}
void clear() { free(); }
static void reserve(size_t capacity) { node_type::reserve(capacity); }
bool empty() const { return node_type::empty(_root); }
int size() const { return node_type::safe_size(_root); }
const value_type& operator[](size_t k) const { return get(k); }
const value_type& get(size_t k) const {
assert(k < size_t(size()));
return cbegin()[k];
}
const value_type& front() const { return *cbegin(); }
const value_type& back() const { return *crbegin(); }
void set(size_t k, const value_type& val) {
assert(k < size_t(size()));
_root = node_type::set(_root, k, [&](const value_type&) { return val; });
}
template <typename Func>
void apply(size_t k, const Func& f) {
assert(k < size_t(size()));
_root = node_type::set(_root, k, [&](const value_type& val) { return f(val); });
}
value_type prod_all() const { return node_type::safe_prod(_root); }
value_type prod(size_t l, size_t r) {
value_type res;
std::tie(_root, res) = node_type::prod(_root, l, r);
return res;
}
void insert(size_t k, const value_type& val) {
assert(k <= size_t(size()));
_root = node_type::insert(_root, k, val);
}
void push_front(const value_type& val) { insert(0, val); }
void push_back(const value_type& val) { insert(size(), val); }
value_type erase(size_t k) {
assert(k <= size_t(size()));
value_type v;
std::tie(_root, v) = node_type::erase(_root, k);
return v;
}
value_type pop_front() { return erase(0); }
value_type pop_back() { return erase(size() - 1); }
// Split immediately before the k-th element.
DynamicSegmentTree split(size_t k) {
assert(k <= size_t(size()));
node_pointer root_r;
std::tie(_root, root_r) = node_type::split(_root, k);
return DynamicSegmentTree(root_r, node_pointer_construct{});
}
void merge(DynamicSegmentTree r) { _root = node_type::merge(_root, r._root); }
void rotate(size_t k) {
assert(k <= size_t(size()));
_root = node_type::rotate(_root, k);
}
void rotate(size_t l, size_t m, size_t r) {
assert(l <= m and m <= r and r <= size_t(size()));
_root = node_type::rotate(_root, l, m, r);
}
std::vector<value_type> dump() const { return node_type::dump(_root); }
using iterator = typename node_type::const_iterator;
using reverse_iterator = typename node_type::const_reverse_iterator;
using const_iterator = typename node_type::const_iterator;
using const_reverse_iterator = typename node_type::const_reverse_iterator;
iterator begin() const { return cbegin(); }
iterator end() const { return cend(); }
reverse_iterator rbegin() const { return crbegin(); }
reverse_iterator rend() const { return crend(); }
const_iterator cbegin() const { return node_type::cbegin(_root); }
const_iterator cend() const { return node_type::cend(_root); }
const_reverse_iterator crbegin() const { return node_type::crbegin(_root); }
const_reverse_iterator crend() const { return node_type::crend(_root); }
// Returns the iterator with index max{ r | f(op(A[l], ..., A[r-1])) = true } (0 <= r <= size())
template <typename Predicate>
iterator max_right(size_t l, const Predicate& f) {
assert(l <= size_t(size()));
iterator it;
std::tie(_root, it) = node_type::max_right(_root, l, f);
return it;
}
// Returns the iterator with index min{ l | f(op(A[l], ..., A[r-1])) = true } (0 <= l <= size())
template <typename Predicate>
iterator min_left(size_t r, const Predicate& f) {
assert(r <= size_t(size()));
iterator it;
std::tie(_root, it) = node_type::min_left(_root, r, f);
return it;
}
// Find the first element that satisfies the condition f.
// Returns { position, optional(value) }
// Requirements: f(A[i]) must be monotonic
template <typename Predicate>
iterator binary_search(const Predicate& f) {
return node_type::template binary_search<iterator>(_root, f);
}
// comp(T t, U u) = (t < u)
// Requirements: sequence is sorted
template <typename U, typename Compare = std::less<>>
iterator lower_bound(const U& target, Compare comp = {}) {
return node_type::template lower_bound<iterator>(_root, target, comp);
}
// comp(T u, U t) = (u < t)
// Requirements: sequence is sorted
template <typename U, typename Compare = std::less<>>
iterator upper_bound(const U& target, Compare comp = {}) {
return node_type::template upper_bound<iterator>(_root, target, comp);
}
// Find the first element that satisfies the condition f.
// Returns { position, optional(value) }
// Requirements: f(A[i]) must be monotonic
template <typename Predicate>
const_iterator binary_search(const Predicate& f) const {
return node_type::template binary_search<const_iterator>(_root, f);
}
// comp(T t, U u) = (t < u)
// Requirements: sequence is sorted
template <typename U, typename Compare = std::less<>>
const_iterator lower_bound(const U& target, Compare comp = {}) const {
return node_type::template lower_bound<const_iterator>(_root, target, comp);
}
// comp(T u, U t) = (u < t)
// Requirements: sequence is sorted
template <typename U, typename Compare = std::less<>>
const_iterator upper_bound(const U& target, Compare comp = {}) const {
return node_type::template upper_bound<const_iterator>(_root, target, comp);
}
template <typename Iterator, std::enable_if_t<node_type::template is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
void insert(Iterator it, const value_type &val) {
_root = node_type::insert(it, val);
}
template <typename Iterator, std::enable_if_t<node_type::template is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
value_type erase(Iterator it) {
value_type erased;
std::tie(_root, erased) = node_type::erase(it);
return erased;
}
template <typename Iterator, std::enable_if_t<node_type::template is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
DynamicSegmentTree split(Iterator it) {
node_pointer root_r;
std::tie(_root, root_r) = node_type::split(it);
return DynamicSegmentTree(root_r, node_pointer_construct{});
}
// handling internal nodes
using internal_node = node_type;
using internal_node_pointer = node_pointer;
internal_node_pointer& root_node() { return _root; }
const internal_node_pointer& root_node() const { return _root; }
void set_root_node(internal_node_pointer new_root) { root_node() = new_root; }
};
} // namespace suisen
#endif // SUISEN_IMPLICIT_TREAP_SEGTREE#line 1 "library/datastructure/bbst/implicit_treap_segtree.hpp"
#line 1 "library/datastructure/bbst/implicit_treap_base.hpp"
#include <algorithm>
#include <cassert>
#include <cstdint>
#include <optional>
#include <string>
#include <random>
#include <tuple>
#include <vector>
#include <utility>
namespace suisen::internal::implicit_treap {
template <typename T, typename Derived>
struct Node {
using random_engine = std::mt19937;
static inline random_engine rng{ std::random_device{}() };
using priority_type = std::invoke_result_t<random_engine>;
static priority_type random_priority() { return rng(); }
using node_type = Derived;
using node_pointer = uint32_t;
using size_type = uint32_t;
using difference_type = int32_t;
using value_type = T;
using pointer = value_type*;
using const_pointer = const value_type*;
using reference = value_type&;
using const_reference = const value_type&;
static inline std::vector<node_type> _nodes{};
static inline std::vector<node_pointer> _erased{};
static constexpr node_pointer null = ~node_pointer(0);
node_pointer _ch[2]{ null, null };
value_type _val;
size_type _size;
priority_type _priority;
node_pointer _prev = null, _next = null;
Node(const value_type val = {}): _val(val), _size(1), _priority(random_priority()) {}
static void reserve(size_type capacity) { _nodes.reserve(capacity); }
static bool is_null(node_pointer t) { return t == null; }
static bool is_not_null(node_pointer t) { return not is_null(t); }
static node_type& node(node_pointer t) { return _nodes[t]; }
static const node_type& const_node(node_pointer t) { return _nodes[t]; }
static value_type& value(node_pointer t) { return node(t)._val; }
static value_type set_value(node_pointer t, const value_type& new_val) { return std::exchange(value(t), new_val); }
static bool empty(node_pointer t) { return is_null(t); }
static size_type& size(node_pointer t) { return node(t)._size; }
static size_type safe_size(node_pointer t) { return empty(t) ? 0 : size(t); }
static priority_type& priority(node_pointer t) { return node(t)._priority; }
static void set_priority(node_pointer t, priority_type new_priority) { priority(t) = new_priority; }
static node_pointer& prev(node_pointer t) { return node(t)._prev; }
static node_pointer& next(node_pointer t) { return node(t)._next; }
static void link(node_pointer l, node_pointer r) { next(l) = r, prev(r) = l; }
static node_pointer min(node_pointer t) {
while (true) {
node_pointer nt = child0(t);
if (is_null(nt)) return t;
t = nt;
}
}
static node_pointer max(node_pointer t) {
while (true) {
node_pointer nt = child1(t);
if (is_null(nt)) return t;
t = nt;
}
}
static node_pointer& child0(node_pointer t) { return node(t)._ch[0]; }
static node_pointer& child1(node_pointer t) { return node(t)._ch[1]; }
static node_pointer& child(node_pointer t, bool b) { return node(t)._ch[b]; }
static node_pointer set_child0(node_pointer t, node_pointer cid) { return std::exchange(child0(t), cid); }
static node_pointer set_child1(node_pointer t, node_pointer cid) { return std::exchange(child1(t), cid); }
static node_pointer set_child(node_pointer t, bool b, node_pointer cid) { return std::exchange(child(t, b), cid); }
static node_pointer update(node_pointer t) { // t : not null
size(t) = safe_size(child0(t)) + safe_size(child1(t)) + 1;
return t;
}
static node_pointer empty_node() { return null; }
template <typename ...Args>
static node_pointer create_node(Args &&...args) {
if (_erased.size()) {
node_pointer res = _erased.back();
_erased.pop_back();
node(res) = node_type(std::forward<Args>(args)...);
return res;
} else {
node_pointer res = _nodes.size();
_nodes.emplace_back(std::forward<Args>(args)...);
return res;
}
}
static void delete_node(node_pointer t) { _erased.push_back(t); }
static void delete_tree(node_pointer t) {
if (is_null(t)) return;
delete_tree(child0(t));
delete_tree(child1(t));
delete_node(t);
}
template <typename ...Args>
static node_pointer build(Args &&... args) {
std::vector<value_type> dat(std::forward<Args>(args)...);
const size_t n = dat.size();
std::vector<priority_type> priorities(n);
std::generate(priorities.begin(), priorities.end(), random_priority);
std::make_heap(priorities.begin(), priorities.end());
std::vector<node_pointer> nodes(n);
auto rec = [&](auto rec, size_t heap_index, size_t dat_index_offset) -> std::pair<size_t, node_pointer> {
if (heap_index >= n) return { 0, null };
auto [lsiz, lch] = rec(rec, 2 * heap_index + 1, dat_index_offset);
dat_index_offset += lsiz;
node_pointer root = create_node(std::move(dat[dat_index_offset]));
nodes[dat_index_offset] = root;
set_priority(root, priorities[heap_index]);
if (dat_index_offset) {
link(nodes[dat_index_offset - 1], root);
}
dat_index_offset += 1;
auto [rsiz, rch] = rec(rec, 2 * heap_index + 2, dat_index_offset);
set_child0(root, lch);
set_child1(root, rch);
return { lsiz + 1 + rsiz, node_type::update(root) };
};
return rec(rec, 0, 0).second;
}
static std::pair<node_pointer, node_pointer> split(node_pointer t, size_type k) {
if (k == 0) return { null, t };
if (k == size(t)) return { t, null };
static std::vector<node_pointer> lp{}, rp{};
while (true) {
if (const size_type lsiz = safe_size(child0(t)); k <= lsiz) {
if (rp.size()) set_child0(rp.back(), t);
rp.push_back(t);
if (k == lsiz) {
if (lp.size()) set_child1(lp.back(), child0(t));
node_pointer lt = set_child0(t, null), rt = null;
while (lp.size()) node_type::update(lt = lp.back()), lp.pop_back();
while (rp.size()) node_type::update(rt = rp.back()), rp.pop_back();
return { lt, rt };
}
t = child0(t);
} else {
if (lp.size()) set_child1(lp.back(), t);
lp.push_back(t);
t = child1(t);
k -= lsiz + 1;
}
}
}
static std::tuple<node_pointer, node_pointer, node_pointer> split(node_pointer t, size_type l, size_type r) {
auto [tlm, tr] = split(t, r);
auto [tl, tm] = split(tlm, l);
return { tl, tm, tr };
}
static node_pointer merge_impl(node_pointer tl, node_pointer tr) {
if (priority(tl) < priority(tr)) {
if (node_pointer tm = child0(tr); is_null(tm)) {
link(max(tl), tr);
set_child0(tr, tl);
} else {
set_child0(tr, merge(tl, tm));
}
return node_type::update(tr);
} else {
if (node_pointer tm = child1(tl); is_null(tm)) {
link(tl, min(tr));
set_child1(tl, tr);
} else {
set_child1(tl, merge(tm, tr));
}
return node_type::update(tl);
}
}
static node_pointer merge(node_pointer tl, node_pointer tr) {
if (is_null(tl)) return tr;
if (is_null(tr)) return tl;
return merge_impl(tl, tr);
}
static node_pointer merge(node_pointer tl, node_pointer tm, node_pointer tr) {
return merge(merge(tl, tm), tr);
}
static node_pointer insert_impl(node_pointer t, size_type k, node_pointer new_node) {
if (is_null(t)) return new_node;
static std::vector<node_pointer> st;
bool b = false;
while (true) {
if (is_null(t) or priority(new_node) > priority(t)) {
if (is_null(t)) {
t = new_node;
} else {
auto [tl, tr] = split(t, k);
if (is_not_null(tl)) link(max(tl), new_node);
if (is_not_null(tr)) link(new_node, min(tr));
set_child0(new_node, tl);
set_child1(new_node, tr);
t = node_type::update(new_node);
}
if (st.size()) {
set_child(st.back(), b, t);
do t = node_type::update(st.back()), st.pop_back(); while (st.size());
}
return t;
} else {
if (const size_type lsiz = safe_size(child0(t)); k <= lsiz) {
if (k == lsiz) link(new_node, t);
st.push_back(t), b = false;
t = child0(t);
} else {
if (k == lsiz + 1) link(t, new_node);
st.push_back(t), b = true;
t = child1(t);
k -= lsiz + 1;
}
}
}
}
template <typename ...Args>
static node_pointer insert(node_pointer t, size_type k, Args &&...args) {
return insert_impl(t, k, create_node(std::forward<Args>(args)...));
}
static std::pair<node_pointer, value_type> erase(node_pointer t, size_type k) {
if (const size_type lsiz = safe_size(child0(t)); k == lsiz) {
delete_node(t);
return { merge(child0(t), child1(t)), std::move(value(t)) };
} else if (k < lsiz) {
auto [c0, v] = erase(child0(t), k);
set_child0(t, c0);
if (is_not_null(c0) and k == lsiz - 1) link(max(c0), t);
return { node_type::update(t), std::move(v) };
} else {
auto [c1, v] = erase(child1(t), k - (lsiz + 1));
set_child1(t, c1);
if (is_not_null(c1) and k == lsiz + 1) link(t, min(c1));
return { node_type::update(t), std::move(v) };
}
}
static node_pointer rotate(node_pointer t, size_type k) {
auto [tl, tr] = split(t, k);
return merge(tr, tl);
}
static node_pointer rotate(node_pointer t, size_type l, size_type m, size_type r) {
auto [tl, tm, tr] = split(t, l, r);
return merge(tl, rotate(tm, m - l), tr);
}
template <typename Func>
static node_pointer set_update(node_pointer t, size_type k, const Func& f) {
if (const size_type lsiz = safe_size(child0(t)); k == lsiz) {
value_type& val = value(t);
val = f(const_cast<const value_type&>(val));
} else if (k < lsiz) {
set_child0(t, set_update(child0(t), k, f));
} else {
set_child1(t, set_update(child1(t), k - (lsiz + 1), f));
}
return node_type::update(t);
}
static std::vector<value_type> dump(node_pointer t) {
std::vector<value_type> res;
res.reserve(safe_size(t));
auto rec = [&](auto rec, node_pointer t) -> void {
if (is_null(t)) return;
rec(rec, child0(t));
res.push_back(value(t));
rec(rec, child1(t));
};
rec(rec, t);
return res;
}
template <bool reversed_, bool constant_>
struct NodeIterator {
static constexpr bool constant = constant_;
static constexpr bool reversed = reversed_;
friend Node;
friend Derived;
using difference_type = Node::difference_type;
using value_type = Node::value_type;
using pointer = std::conditional_t<constant, Node::const_pointer, Node::pointer>;
using reference = std::conditional_t<constant, Node::const_reference, Node::reference>;
using iterator_category = std::random_access_iterator_tag;
NodeIterator(): NodeIterator(null) {}
explicit NodeIterator(node_pointer root): NodeIterator(root, 0, null) {}
NodeIterator(const NodeIterator<reversed, not constant>& it): NodeIterator(it._root, it._index, it._cur) {}
reference operator*() const {
if (is_null(_cur) and _index != safe_size(_root)) {
_cur = _root;
for (size_type k = _index;;) {
if (size_type siz = safe_size(child(_cur, reversed)); k == siz) {
break;
} else if (k < siz) {
_cur = child(_cur, reversed);
} else {
_cur = child(_cur, not reversed);
k -= siz + 1;
}
}
}
return value(_cur);
}
reference operator[](difference_type k) const { return *((*this) + k); }
NodeIterator& operator++() { return *this += 1; }
NodeIterator& operator--() { return *this -= 1; }
NodeIterator& operator+=(difference_type k) { return suc(+k), * this; }
NodeIterator& operator-=(difference_type k) { return suc(-k), * this; }
NodeIterator operator++(int) { NodeIterator res = *this; ++(*this); return res; }
NodeIterator operator--(int) { NodeIterator res = *this; --(*this); return res; }
friend NodeIterator operator+(NodeIterator it, difference_type k) { return it += k; }
friend NodeIterator operator+(difference_type k, NodeIterator it) { return it += k; }
friend NodeIterator operator-(NodeIterator it, difference_type k) { return it -= k; }
friend difference_type operator-(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index - rhs._index; }
friend bool operator==(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index == rhs._index; }
friend bool operator!=(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index != rhs._index; }
friend bool operator<(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index < rhs._index; }
friend bool operator>(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index > rhs._index; }
friend bool operator<=(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index <= rhs._index; }
friend bool operator>=(const NodeIterator& lhs, const NodeIterator& rhs) { return lhs._index >= rhs._index; }
static NodeIterator begin(node_pointer root) { return NodeIterator(root, 0, null); }
static NodeIterator end(node_pointer root) { return NodeIterator(root, safe_size(root), null); }
int size() const { return safe_size(_root); }
int index() const { return _index; }
private:
node_pointer _root;
size_type _index;
mutable node_pointer _cur; // it==end() or uninitialized (updates only index)
NodeIterator(node_pointer root, size_type index, node_pointer cur): _root(root), _index(index), _cur(cur) {}
void suc(difference_type k) {
_index += k;
if (_index == safe_size(_root) or std::abs(k) >= 20) _cur = null;
if (is_null(_cur)) return;
const bool positive = k < 0 ? (k = -k, reversed) : not reversed;
if (positive) {
while (k-- > 0) _cur = next(_cur);
} else {
while (k-- > 0) _cur = prev(_cur);
}
}
node_pointer root() const { return _root; }
void set_root(node_pointer new_root, size_type new_index) { _root = new_root, _index = new_index; }
node_pointer get_child0() const { return child0(_cur); }
node_pointer get_child1() const { return child1(_cur); }
template <typename Predicate>
static NodeIterator binary_search(node_pointer t, const Predicate& f) {
NodeIterator res(t, safe_size(t), null);
if (is_null(t)) return res;
NodeIterator it(t, safe_size(child0(t)), t);
while (is_not_null(it._cur)) {
if (f(it)) {
res = it;
it._cur = it.get_child0();
it._index -= is_null(it._cur) ? 1 : safe_size(it.get_child1()) + 1;
} else {
it._cur = it.get_child1();
it._index += is_null(it._cur) ? 1 : safe_size(it.get_child0()) + 1;
}
}
return res;
}
size_type get_gap_index_left() const {
if constexpr (reversed) return size() - index();
else return index();
}
size_type get_element_index_left() const {
if constexpr (reversed) return size() - index() - 1;
else return index();
}
};
using iterator = NodeIterator<false, false>;
using reverse_iterator = NodeIterator<true, false>;
using const_iterator = NodeIterator<false, true>;
using const_reverse_iterator = NodeIterator<true, true>;
template <typename>
struct is_node_iterator: std::false_type {};
template <bool reversed_, bool constant_>
struct is_node_iterator<NodeIterator<reversed_, constant_>>: std::true_type {};
template <typename X>
static constexpr bool is_node_iterator_v = is_node_iterator<X>::value;
static iterator begin(node_pointer t) { return iterator::begin(t); }
static iterator end(node_pointer t) { return iterator::end(t); }
static reverse_iterator rbegin(node_pointer t) { return reverse_iterator::begin(t); }
static reverse_iterator rend(node_pointer t) { return reverse_iterator::end(t); }
static const_iterator cbegin(node_pointer t) { return const_iterator::begin(t); }
static const_iterator cend(node_pointer t) { return const_iterator::end(t); }
static const_reverse_iterator crbegin(node_pointer t) { return const_reverse_iterator::begin(t); }
static const_reverse_iterator crend(node_pointer t) { return const_reverse_iterator::end(t); }
// Find the first element that satisfies the condition f : iterator -> { false, true }.
// Returns const_iterator
template <typename Iterator, typename Predicate, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
static Iterator binary_search(node_pointer t, const Predicate& f) {
return Iterator::binary_search(t, f);
}
// comp(T t, U u) = (t < u)
template <typename Iterator, typename U, typename Compare = std::less<>, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
static Iterator lower_bound(node_pointer t, const U& target, Compare comp) {
return binary_search<Iterator>(t, [&](Iterator it) { return not comp(*it, target); });
}
// comp(T u, U t) = (u < t)
template <typename Iterator, typename U, typename Compare = std::less<>, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
static Iterator upper_bound(node_pointer t, const U& target, Compare comp) {
return binary_search<Iterator>(t, [&](Iterator it) { return comp(target, *it); });
}
template <typename Iterator, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
static node_pointer insert(Iterator it, const value_type& val) {
return insert(it.root(), it.get_gap_index_left(), val);
}
template <typename Iterator, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
static std::pair<node_pointer, value_type> erase(Iterator it) {
return erase(it.root(), it.get_element_index_left());
}
template <typename Iterator, std::enable_if_t<is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
static std::pair<node_pointer, node_pointer> split(Iterator it) {
return split(it.root(), it.get_gap_index_left());
}
};
} // namespace suisen::internal::implicit_treap
#line 5 "library/datastructure/bbst/implicit_treap_segtree.hpp"
namespace suisen {
namespace internal::implicit_treap {
template <typename T, T(*op)(T, T), T(*e)()>
struct RangeProductNode: Node<T, RangeProductNode<T, op, e>> {
using base = Node<T, RangeProductNode<T, op, e>>;
using node_pointer = typename base::node_pointer;
using value_type = typename base::value_type;
value_type _sum;
RangeProductNode(const value_type& val): base(val), _sum(val) {}
// ----- override ----- //
static node_pointer update(node_pointer t) {
base::update(t);
prod_all(t) = op(op(safe_prod(base::child0(t)), base::value(t)), safe_prod(base::child1(t)));
return t;
}
// ----- new features ----- //
static value_type& prod_all(node_pointer t) {
return base::node(t)._sum;
}
static value_type safe_prod(node_pointer t) {
return base::is_null(t) ? e() : prod_all(t);
}
static std::pair<node_pointer, value_type> prod(node_pointer t, size_t l, size_t r) {
auto [tl, tm, tr] = base::split(t, l, r);
value_type res = safe_prod(tm);
return { base::merge(tl, tm, tr), res };
}
template <typename Func>
static node_pointer set(node_pointer t, size_t k, const Func& f) {
return base::set_update(t, k, f);
}
using const_iterator = typename base::const_iterator;
template <typename Predicate>
static std::pair<node_pointer, const_iterator> max_right(node_pointer t, size_t l, const Predicate& f) {
auto [tl, tr] = base::split(t, l);
value_type sum = e();
assert(f(sum));
const_iterator it = base::template binary_search<const_iterator>(
tr, [&](const_iterator it) {
value_type nxt_sum = op(op(sum, safe_prod(it.get_child0())), *it);
return f(nxt_sum) ? (sum = std::move(nxt_sum), false) : true;
}
);
it.set_root(t = base::merge(tl, tr), l + it.index());
return { t, it };
}
template <typename Predicate>
static std::pair<node_pointer, const_iterator> min_left(node_pointer t, size_t r, const Predicate& f) {
auto [tl, tr] = base::split(t, r);
value_type sum = e();
assert(f(sum));
const_iterator it = base::template binary_search<const_iterator>(
tl, [&](const_iterator it) {
value_type nxt_sum = op(*it, op(safe_prod(it.get_child1()), sum));
return f(nxt_sum) ? (sum = std::move(nxt_sum), true) : false;
}
);
it.set_root(t = base::merge(tl, tr), it.index());
return { t, it };
}
};
}
template <typename T, T(*op)(T, T), T(*e)()>
class DynamicSegmentTree {
using node_type = internal::implicit_treap::RangeProductNode<T, op, e>;
using node_pointer = typename node_type::node_pointer;
node_pointer _root;
struct node_pointer_construct {};
DynamicSegmentTree(node_pointer root, node_pointer_construct): _root(root) {}
public:
using value_type = typename node_type::value_type;
DynamicSegmentTree(): _root(node_type::empty_node()) {}
explicit DynamicSegmentTree(size_t n, const value_type& fill_value = {}): _root(node_type::build(n, fill_value)) {}
template <typename U>
DynamicSegmentTree(const std::vector<U>& dat) : _root(node_type::build(dat.begin(), dat.end())) {}
void free() {
node_type::delete_tree(_root);
_root = node_type::empty_node();
}
void clear() { free(); }
static void reserve(size_t capacity) { node_type::reserve(capacity); }
bool empty() const { return node_type::empty(_root); }
int size() const { return node_type::safe_size(_root); }
const value_type& operator[](size_t k) const { return get(k); }
const value_type& get(size_t k) const {
assert(k < size_t(size()));
return cbegin()[k];
}
const value_type& front() const { return *cbegin(); }
const value_type& back() const { return *crbegin(); }
void set(size_t k, const value_type& val) {
assert(k < size_t(size()));
_root = node_type::set(_root, k, [&](const value_type&) { return val; });
}
template <typename Func>
void apply(size_t k, const Func& f) {
assert(k < size_t(size()));
_root = node_type::set(_root, k, [&](const value_type& val) { return f(val); });
}
value_type prod_all() const { return node_type::safe_prod(_root); }
value_type prod(size_t l, size_t r) {
value_type res;
std::tie(_root, res) = node_type::prod(_root, l, r);
return res;
}
void insert(size_t k, const value_type& val) {
assert(k <= size_t(size()));
_root = node_type::insert(_root, k, val);
}
void push_front(const value_type& val) { insert(0, val); }
void push_back(const value_type& val) { insert(size(), val); }
value_type erase(size_t k) {
assert(k <= size_t(size()));
value_type v;
std::tie(_root, v) = node_type::erase(_root, k);
return v;
}
value_type pop_front() { return erase(0); }
value_type pop_back() { return erase(size() - 1); }
// Split immediately before the k-th element.
DynamicSegmentTree split(size_t k) {
assert(k <= size_t(size()));
node_pointer root_r;
std::tie(_root, root_r) = node_type::split(_root, k);
return DynamicSegmentTree(root_r, node_pointer_construct{});
}
void merge(DynamicSegmentTree r) { _root = node_type::merge(_root, r._root); }
void rotate(size_t k) {
assert(k <= size_t(size()));
_root = node_type::rotate(_root, k);
}
void rotate(size_t l, size_t m, size_t r) {
assert(l <= m and m <= r and r <= size_t(size()));
_root = node_type::rotate(_root, l, m, r);
}
std::vector<value_type> dump() const { return node_type::dump(_root); }
using iterator = typename node_type::const_iterator;
using reverse_iterator = typename node_type::const_reverse_iterator;
using const_iterator = typename node_type::const_iterator;
using const_reverse_iterator = typename node_type::const_reverse_iterator;
iterator begin() const { return cbegin(); }
iterator end() const { return cend(); }
reverse_iterator rbegin() const { return crbegin(); }
reverse_iterator rend() const { return crend(); }
const_iterator cbegin() const { return node_type::cbegin(_root); }
const_iterator cend() const { return node_type::cend(_root); }
const_reverse_iterator crbegin() const { return node_type::crbegin(_root); }
const_reverse_iterator crend() const { return node_type::crend(_root); }
// Returns the iterator with index max{ r | f(op(A[l], ..., A[r-1])) = true } (0 <= r <= size())
template <typename Predicate>
iterator max_right(size_t l, const Predicate& f) {
assert(l <= size_t(size()));
iterator it;
std::tie(_root, it) = node_type::max_right(_root, l, f);
return it;
}
// Returns the iterator with index min{ l | f(op(A[l], ..., A[r-1])) = true } (0 <= l <= size())
template <typename Predicate>
iterator min_left(size_t r, const Predicate& f) {
assert(r <= size_t(size()));
iterator it;
std::tie(_root, it) = node_type::min_left(_root, r, f);
return it;
}
// Find the first element that satisfies the condition f.
// Returns { position, optional(value) }
// Requirements: f(A[i]) must be monotonic
template <typename Predicate>
iterator binary_search(const Predicate& f) {
return node_type::template binary_search<iterator>(_root, f);
}
// comp(T t, U u) = (t < u)
// Requirements: sequence is sorted
template <typename U, typename Compare = std::less<>>
iterator lower_bound(const U& target, Compare comp = {}) {
return node_type::template lower_bound<iterator>(_root, target, comp);
}
// comp(T u, U t) = (u < t)
// Requirements: sequence is sorted
template <typename U, typename Compare = std::less<>>
iterator upper_bound(const U& target, Compare comp = {}) {
return node_type::template upper_bound<iterator>(_root, target, comp);
}
// Find the first element that satisfies the condition f.
// Returns { position, optional(value) }
// Requirements: f(A[i]) must be monotonic
template <typename Predicate>
const_iterator binary_search(const Predicate& f) const {
return node_type::template binary_search<const_iterator>(_root, f);
}
// comp(T t, U u) = (t < u)
// Requirements: sequence is sorted
template <typename U, typename Compare = std::less<>>
const_iterator lower_bound(const U& target, Compare comp = {}) const {
return node_type::template lower_bound<const_iterator>(_root, target, comp);
}
// comp(T u, U t) = (u < t)
// Requirements: sequence is sorted
template <typename U, typename Compare = std::less<>>
const_iterator upper_bound(const U& target, Compare comp = {}) const {
return node_type::template upper_bound<const_iterator>(_root, target, comp);
}
template <typename Iterator, std::enable_if_t<node_type::template is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
void insert(Iterator it, const value_type &val) {
_root = node_type::insert(it, val);
}
template <typename Iterator, std::enable_if_t<node_type::template is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
value_type erase(Iterator it) {
value_type erased;
std::tie(_root, erased) = node_type::erase(it);
return erased;
}
template <typename Iterator, std::enable_if_t<node_type::template is_node_iterator_v<Iterator>, std::nullptr_t> = nullptr>
DynamicSegmentTree split(Iterator it) {
node_pointer root_r;
std::tie(_root, root_r) = node_type::split(it);
return DynamicSegmentTree(root_r, node_pointer_construct{});
}
// handling internal nodes
using internal_node = node_type;
using internal_node_pointer = node_pointer;
internal_node_pointer& root_node() { return _root; }
const internal_node_pointer& root_node() const { return _root; }
void set_root_node(internal_node_pointer new_root) { root_node() = new_root; }
};
} // namespace suisen