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diff --git a/src/include/cpp-btree/btree.h b/src/include/cpp-btree/btree.h new file mode 100644 index 000000000..2eddc2abe --- /dev/null +++ b/src/include/cpp-btree/btree.h @@ -0,0 +1,2571 @@ +// Copyright 2018 The Abseil Authors. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// https://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// A btree implementation of the STL set and map interfaces. A btree is smaller +// and generally also faster than STL set/map (refer to the benchmarks below). +// The red-black tree implementation of STL set/map has an overhead of 3 +// pointers (left, right and parent) plus the node color information for each +// stored value. So a set<int32_t> consumes 40 bytes for each value stored in +// 64-bit mode. This btree implementation stores multiple values on fixed +// size nodes (usually 256 bytes) and doesn't store child pointers for leaf +// nodes. The result is that a btree_set<int32_t> may use much less memory per +// stored value. For the random insertion benchmark in btree_bench.cc, a +// btree_set<int32_t> with node-size of 256 uses 5.1 bytes per stored value. +// +// The packing of multiple values on to each node of a btree has another effect +// besides better space utilization: better cache locality due to fewer cache +// lines being accessed. Better cache locality translates into faster +// operations. +// +// CAVEATS +// +// Insertions and deletions on a btree can cause splitting, merging or +// rebalancing of btree nodes. And even without these operations, insertions +// and deletions on a btree will move values around within a node. In both +// cases, the result is that insertions and deletions can invalidate iterators +// pointing to values other than the one being inserted/deleted. Therefore, this +// container does not provide pointer stability. This is notably different from +// STL set/map which takes care to not invalidate iterators on insert/erase +// except, of course, for iterators pointing to the value being erased. A +// partial workaround when erasing is available: erase() returns an iterator +// pointing to the item just after the one that was erased (or end() if none +// exists). + +#pragma once + +#include <algorithm> +#include <cassert> +#include <cstddef> +#include <cstdint> +#include <cstring> +#include <experimental/type_traits> +#include <functional> +#include <iterator> +#include <limits> +#include <new> +#include <type_traits> +#include <utility> + +namespace btree::internal { + +template <typename Compare, typename T> +using btree_is_key_compare_to = + std::is_signed<std::invoke_result_t<Compare, T, T>>; + +template<typename T> +using compare_to_t = decltype(std::declval<T&>().compare(std::declval<const T&>())); +template<typename T> +inline constexpr bool has_compare_to = std::experimental::is_detected_v<compare_to_t, T>; +// A helper class to convert a boolean comparison into a three-way "compare-to" +// comparison that returns a negative value to indicate less-than, zero to +// indicate equality and a positive value to indicate greater-than. This helper +// class is specialized for less<std::string>, greater<std::string>, +// less<string_view>, and greater<string_view>. +// +// key_compare_to_adapter is provided so that btree users +// automatically get the more efficient compare-to code when using common +// google string types with common comparison functors. +// These string-like specializations also turn on heterogeneous lookup by +// default. +template <typename Compare, typename=void> +struct key_compare_to_adapter { + using type = Compare; +}; + +template <typename K> +struct key_compare_to_adapter<std::less<K>, std::enable_if_t<has_compare_to<K>>> +{ + struct type { + inline int operator()(const K& lhs, const K& rhs) const noexcept { + return lhs.compare(rhs); + } + }; +}; + +template <typename K> +struct key_compare_to_adapter<std::less<K>, std::enable_if_t<std::is_signed_v<K>>> +{ + struct type { + inline K operator()(const K& lhs, const K& rhs) const noexcept { + return lhs - rhs; + } + }; +}; + +template <typename K> +struct key_compare_to_adapter<std::less<K>, std::enable_if_t<std::is_unsigned_v<K>>> +{ + struct type { + inline int operator()(const K& lhs, const K& rhs) const noexcept { + if (lhs < rhs) { + return -1; + } else if (lhs > rhs) { + return 1; + } else { + return 0; + } + } + }; +}; + +template <typename Key, typename Compare, typename Alloc, + int TargetNodeSize, int ValueSize, + bool Multi> +struct common_params { + // If Compare is a common comparator for a std::string-like type, then we adapt it + // to use heterogeneous lookup and to be a key-compare-to comparator. + using key_compare = typename key_compare_to_adapter<Compare>::type; + // A type which indicates if we have a key-compare-to functor or a plain old + // key-compare functor. + using is_key_compare_to = btree_is_key_compare_to<key_compare, Key>; + + using allocator_type = Alloc; + using key_type = Key; + using size_type = std::make_signed<size_t>::type; + using difference_type = ptrdiff_t; + + // True if this is a multiset or multimap. + using is_multi_container = std::integral_constant<bool, Multi>; + + constexpr static int kTargetNodeSize = TargetNodeSize; + constexpr static int kValueSize = ValueSize; + // Upper bound for the available space for values. This is largest for leaf + // nodes, which have overhead of at least a pointer + 3 bytes (for storing + // 3 field_types) + paddings. if alignof(key_type) is 1, the size of padding + // would be 0. + constexpr static int kNodeValueSpace = + TargetNodeSize - /*minimum overhead=*/(sizeof(void *) + 4); + + // This is an integral type large enough to hold as many + // ValueSize-values as will fit a node of TargetNodeSize bytes. + using node_count_type = + std::conditional_t<(kNodeValueSpace / ValueSize > + (std::numeric_limits<uint8_t>::max)()), + uint16_t, + uint8_t>; +}; + +// The internal storage type +// +// It is convenient for the value_type of a btree_map<K, V> to be +// pair<const K, V>; the "const K" prevents accidental modification of the key +// when dealing with the reference returned from find() and similar methods. +// However, this creates other problems; we want to be able to emplace(K, V) +// efficiently with move operations, and similarly be able to move a +// pair<K, V> in insert(). +// +// The solution is this union, which aliases the const and non-const versions +// of the pair. This also allows flat_hash_map<const K, V> to work, even though +// that has the same efficiency issues with move in emplace() and insert() - +// but people do it anyway. +template <class K, class V> +union map_slot_type { + map_slot_type() {} + ~map_slot_type() = delete; + map_slot_type& operator=(const map_slot_type& slot) { + mutable_value = slot.mutable_value; + return *this; + } + map_slot_type& operator=(map_slot_type&& slot) { + mutable_value = std::move(slot.mutable_value); + return *this; + } + using value_type = std::pair<const K, V>; + using mutable_value_type = std::pair<K, V>; + + value_type value; + mutable_value_type mutable_value; + K key; +}; + +template <class K, class V> +void swap(map_slot_type<K, V>& lhs, map_slot_type<K, V>& rhs) { + std::swap(lhs.mutable_value, rhs.mutable_value); +} + +// A parameters structure for holding the type parameters for a btree_map. +// Compare and Alloc should be nothrow copy-constructible. +template <typename Key, typename Data, typename Compare, typename Alloc, + int TargetNodeSize, bool Multi> +struct map_params : common_params<Key, Compare, Alloc, TargetNodeSize, + sizeof(Key) + sizeof(Data), Multi> { + using super_type = typename map_params::common_params; + using mapped_type = Data; + using value_type = std::pair<const Key, mapped_type>; + using mutable_value_type = std::pair<Key, mapped_type>; + using slot_type = map_slot_type<Key, mapped_type>; + using pointer = value_type*; + using const_pointer = const value_type *; + using reference = value_type &; + using const_reference = const value_type &; + using key_compare = typename super_type::key_compare; + using init_type = mutable_value_type; + + static constexpr size_t kValueSize = sizeof(Key) + sizeof(mapped_type); + + // Inherit from key_compare for empty base class optimization. + struct value_compare : private key_compare { + value_compare() = default; + explicit value_compare(const key_compare &cmp) : key_compare(cmp) {} + + template <typename T, typename U> + auto operator()(const T &left, const U &right) const + -> decltype(std::declval<key_compare>()(left.first, right.first)) { + return key_compare::operator()(left.first, right.first); + } + }; + using is_map_container = std::true_type; + + static const Key &key(const value_type &value) { return value.first; } + static mapped_type &value(value_type *value) { return value->second; } + static const Key &key(const slot_type *slot) { return slot->key; } + static value_type& element(slot_type* slot) { return slot->value; } + static const value_type& element(const slot_type* slot) { return slot->value; } + template <class... Args> + static void construct(Alloc *alloc, slot_type *slot, Args &&... args) { + std::allocator_traits<Alloc>::construct(*alloc, + &slot->mutable_value, + std::forward<Args>(args)...); + } + // Construct this slot by moving from another slot. + static void construct(Alloc* alloc, slot_type* slot, slot_type* other) { + emplace(slot); + std::allocator_traits<Alloc>::construct(*alloc, &slot->value, + std::move(other->value)); + } + static void move(Alloc *alloc, slot_type *src, slot_type *dest) { + dest->mutable_value = std::move(src->mutable_value); + } + static void destroy(Alloc *alloc, slot_type *slot) { + std::allocator_traits<Alloc>::destroy(*alloc, &slot->mutable_value); + } + +private: + static void emplace(slot_type* slot) { + // The construction of union doesn't do anything at runtime but it allows us + // to access its members without violating aliasing rules. + new (slot) slot_type; + } +}; + +// A parameters structure for holding the type parameters for a btree_set. +template <typename Key, typename Compare, typename Alloc, int TargetNodeSize, bool Multi> +struct set_params + : public common_params<Key, Compare, Alloc, TargetNodeSize, + sizeof(Key), Multi> { + using value_type = Key; + using mutable_value_type = value_type; + using slot_type = Key; + using pointer = value_type *; + using const_pointer = const value_type *; + using value_compare = typename set_params::common_params::key_compare; + using reference = value_type &; + using const_reference = const value_type &; + using is_map_container = std::false_type; + using init_type = mutable_value_type; + + template <class... Args> + static void construct(Alloc *alloc, slot_type *slot, Args &&... args) { + std::allocator_traits<Alloc>::construct(*alloc, + slot, + std::forward<Args>(args)...); + } + static void construct(Alloc *alloc, slot_type *slot, slot_type *other) { + std::allocator_traits<Alloc>::construct(*alloc, slot, std::move(*other)); + } + static void move(Alloc *alloc, slot_type *src, slot_type *dest) { + *dest = std::move(*src); + } + static void destroy(Alloc *alloc, slot_type *slot) { + std::allocator_traits<Alloc>::destroy(*alloc, slot); + } + static const Key &key(const value_type &x) { return x; } + static const Key &key(const slot_type *slot) { return *slot; } + static value_type &element(slot_type *slot) { return *slot; } + static const value_type &element(const slot_type *slot) { return *slot; } +}; + +// Helper functions to do a boolean comparison of two keys given a boolean +// or three-way comparator. +// SFINAE prevents implicit conversions to bool (such as from int). +template <typename Result> +constexpr bool compare_result_as_less_than(const Result r) { + if constexpr (std::is_signed_v<Result>) { + return r < 0; + } else { + return r; + } +} +// An adapter class that converts a lower-bound compare into an upper-bound +// compare. Note: there is no need to make a version of this adapter specialized +// for key-compare-to functors because the upper-bound (the first value greater +// than the input) is never an exact match. +template <typename Compare> +struct upper_bound_adapter { + explicit upper_bound_adapter(const Compare &c) : comp(c) {} + template <typename K, typename LK> + bool operator()(const K &a, const LK &b) const { + // Returns true when a is not greater than b. + return !compare_result_as_less_than(comp(b, a)); + } +private: + const Compare& comp; +}; + +enum class MatchKind : uint8_t { kEq, kNe }; + +template <typename V, bool IsCompareTo> +struct SearchResult { + V value; + MatchKind match; + + static constexpr bool has_match = true; + bool IsEq() const { return match == MatchKind::kEq; } +}; + +// When we don't use CompareTo, `match` is not present. +// This ensures that callers can't use it accidentally when it provides no +// useful information. +template <typename V> +struct SearchResult<V, false> { + V value; + + static constexpr bool has_match = false; + static constexpr bool IsEq() { return false; } +}; + +// A node in the btree holding. The same node type is used for both internal +// and leaf nodes in the btree, though the nodes are allocated in such a way +// that the children array is only valid in internal nodes. +template <typename Params> +class btree_node { + using is_key_compare_to = typename Params::is_key_compare_to; + using is_multi_container = typename Params::is_multi_container; + using field_type = typename Params::node_count_type; + using allocator_type = typename Params::allocator_type; + using slot_type = typename Params::slot_type; + + public: + using params_type = Params; + using key_type = typename Params::key_type; + using value_type = typename Params::value_type; + using mutable_value_type = typename Params::mutable_value_type; + using pointer = typename Params::pointer; + using const_pointer = typename Params::const_pointer; + using reference = typename Params::reference; + using const_reference = typename Params::const_reference; + using key_compare = typename Params::key_compare; + using size_type = typename Params::size_type; + using difference_type = typename Params::difference_type; + + // Btree decides whether to use linear node search as follows: + // - If the key is arithmetic and the comparator is std::less or + // std::greater, choose linear. + // - Otherwise, choose binary. + // TODO(ezb): Might make sense to add condition(s) based on node-size. + using use_linear_search = std::integral_constant< + bool, + std::is_arithmetic_v<key_type> && + (std::is_same_v<std::less<key_type>, key_compare> || + std::is_same_v<std::greater<key_type>, key_compare>)>; + + ~btree_node() = default; + btree_node(const btree_node&) = delete; + btree_node& operator=(const btree_node&) = delete; + + protected: + btree_node() = default; + + private: + constexpr static size_type SizeWithNValues(size_type n) { + return sizeof(base_fields) + n * sizeof(value_type);; + } + // A lower bound for the overhead of fields other than values in a leaf node. + constexpr static size_type MinimumOverhead() { + return SizeWithNValues(1) - sizeof(value_type); + } + + // Compute how many values we can fit onto a leaf node taking into account + // padding. + constexpr static size_type NodeTargetValues(const int begin, const int end) { + return begin == end ? begin + : SizeWithNValues((begin + end) / 2 + 1) > + params_type::kTargetNodeSize + ? NodeTargetValues(begin, (begin + end) / 2) + : NodeTargetValues((begin + end) / 2 + 1, end); + } + + constexpr static int kValueSize = params_type::kValueSize; + constexpr static int kTargetNodeSize = params_type::kTargetNodeSize; + constexpr static int kNodeTargetValues = NodeTargetValues(0, kTargetNodeSize); + + // We need a minimum of 3 values per internal node in order to perform + // splitting (1 value for the two nodes involved in the split and 1 value + // propagated to the parent as the delimiter for the split). + constexpr static size_type kNodeValues = std::max(kNodeTargetValues, 3); + + // The node is internal (i.e. is not a leaf node) if and only if `max_count` + // has this value. + constexpr static size_type kInternalNodeMaxCount = 0; + + struct base_fields { + // A pointer to the node's parent. + btree_node *parent; + // The position of the node in the node's parent. + field_type position; + // The count of the number of values in the node. + field_type count; + // The maximum number of values the node can hold. + field_type max_count; + }; + + struct leaf_fields : public base_fields { + // The array of values. Only the first count of these values have been + // constructed and are valid. + slot_type values[kNodeValues]; + }; + + struct internal_fields : public leaf_fields { + // The array of child pointers. The keys in children_[i] are all less than + // key(i). The keys in children_[i + 1] are all greater than key(i). There + // are always count + 1 children. + btree_node *children[kNodeValues + 1]; + }; + + constexpr static size_type LeafSize(const int max_values = kNodeValues) { + return SizeWithNValues(max_values); + } + constexpr static size_type InternalSize() { + return sizeof(internal_fields); + } + + template<auto MemPtr> + auto& GetField() { + return reinterpret_cast<internal_fields*>(this)->*MemPtr; + } + + template<auto MemPtr> + auto& GetField() const { + return reinterpret_cast<const internal_fields*>(this)->*MemPtr; + } + + void set_parent(btree_node *p) { GetField<&base_fields::parent>() = p; } + field_type &mutable_count() { return GetField<&base_fields::count>(); } + slot_type *slot(int i) { return &GetField<&leaf_fields::values>()[i]; } + const slot_type *slot(int i) const { return &GetField<&leaf_fields::values>()[i]; } + void set_position(field_type v) { GetField<&base_fields::position>() = v; } + void set_count(field_type v) { GetField<&base_fields::count>() = v; } + // This method is only called by the node init methods. + void set_max_count(field_type v) { GetField<&base_fields::max_count>() = v; } + +public: + constexpr static size_type Alignment() { + static_assert(alignof(leaf_fields) == alignof(internal_fields), + "Alignment of all nodes must be equal."); + return alignof(internal_fields); + } + + // Getter/setter for whether this is a leaf node or not. This value doesn't + // change after the node is created. + bool leaf() const { return GetField<&base_fields::max_count>() != kInternalNodeMaxCount; } + + // Getter for the position of this node in its parent. + field_type position() const { return GetField<&base_fields::position>(); } + + // Getter for the number of values stored in this node. + field_type count() const { return GetField<&base_fields::count>(); } + field_type max_count() const { + // Internal nodes have max_count==kInternalNodeMaxCount. + // Leaf nodes have max_count in [1, kNodeValues]. + const field_type max_count = GetField<&base_fields::max_count>(); + return max_count == field_type{kInternalNodeMaxCount} + ? field_type{kNodeValues} + : max_count; + } + + // Getter for the parent of this node. + btree_node* parent() const { return GetField<&base_fields::parent>(); } + // Getter for whether the node is the root of the tree. The parent of the + // root of the tree is the leftmost node in the tree which is guaranteed to + // be a leaf. + bool is_root() const { return parent()->leaf(); } + void make_root() { + assert(parent()->is_root()); + set_parent(parent()->parent()); + } + + // Getters for the key/value at position i in the node. + const key_type& key(int i) const { return params_type::key(slot(i)); } + reference value(int i) { return params_type::element(slot(i)); } + const_reference value(int i) const { return params_type::element(slot(i)); } + + // Getters/setter for the child at position i in the node. + btree_node* child(int i) const { return GetField<&internal_fields::children>()[i]; } + btree_node*& mutable_child(int i) { return GetField<&internal_fields::children>()[i]; } + void clear_child(int i) { +#ifndef NDEBUG + memset(&mutable_child(i), 0, sizeof(btree_node*)); +#endif + } + void set_child(int i, btree_node *c) { + mutable_child(i) = c; + c->set_position(i); + } + void init_child(int i, btree_node *c) { + set_child(i, c); + c->set_parent(this); + } + // Returns the position of the first value whose key is not less than k. + template <typename K> + SearchResult<int, is_key_compare_to::value> lower_bound( + const K &k, const key_compare &comp) const { + return use_linear_search::value ? linear_search(k, comp) + : binary_search(k, comp); + } + // Returns the position of the first value whose key is greater than k. + template <typename K> + int upper_bound(const K &k, const key_compare &comp) const { + auto upper_compare = upper_bound_adapter<key_compare>(comp); + return use_linear_search::value ? linear_search(k, upper_compare).value + : binary_search(k, upper_compare).value; + } + + template <typename K, typename Compare> + SearchResult<int, btree_is_key_compare_to<Compare, key_type>::value> + linear_search(const K &k, const Compare &comp) const { + return linear_search_impl(k, 0, count(), comp, + btree_is_key_compare_to<Compare, key_type>()); + } + + template <typename K, typename Compare> + SearchResult<int, btree_is_key_compare_to<Compare, key_type>::value> + binary_search(const K &k, const Compare &comp) const { + return binary_search_impl(k, 0, count(), comp, + btree_is_key_compare_to<Compare, key_type>()); + } + // Returns the position of the first value whose key is not less than k using + // linear search performed using plain compare. + template <typename K, typename Compare> + SearchResult<int, false> linear_search_impl( + const K &k, int s, const int e, const Compare &comp, + std::false_type /* IsCompareTo */) const { + while (s < e) { + if (!comp(key(s), k)) { + break; + } + ++s; + } + return {s}; + } + + // Returns the position of the first value whose key is not less than k using + // linear search performed using compare-to. + template <typename K, typename Compare> + SearchResult<int, true> linear_search_impl( + const K &k, int s, const int e, const Compare &comp, + std::true_type /* IsCompareTo */) const { + while (s < e) { + const auto c = comp(key(s), k); + if (c == 0) { + return {s, MatchKind::kEq}; + } else if (c > 0) { + break; + } + ++s; + } + return {s, MatchKind::kNe}; + } + + // Returns the position of the first value whose key is not less than k using + // binary search performed using plain compare. + template <typename K, typename Compare> + SearchResult<int, false> binary_search_impl( + const K &k, int s, int e, const Compare &comp, + std::false_type /* IsCompareTo */) const { + while (s != e) { + const int mid = (s + e) >> 1; + if (comp(key(mid), k)) { + s = mid + 1; + } else { + e = mid; + } + } + return {s}; + } + + // Returns the position of the first value whose key is not less than k using + // binary search performed using compare-to. + template <typename K, typename CompareTo> + SearchResult<int, true> binary_search_impl( + const K &k, int s, int e, const CompareTo &comp, + std::true_type /* IsCompareTo */) const { + if constexpr (is_multi_container::value) { + MatchKind exact_match = MatchKind::kNe; + while (s != e) { + const int mid = (s + e) >> 1; + const auto c = comp(key(mid), k); + if (c < 0) { + s = mid + 1; + } else { + e = mid; + if (c == 0) { + // Need to return the first value whose key is not less than k, + // which requires continuing the binary search if this is a + // multi-container. + exact_match = MatchKind::kEq; + } + } + } + return {s, exact_match}; + } else { // Not a multi-container. + while (s != e) { + const int mid = (s + e) >> 1; + const auto c = comp(key(mid), k); + if (c < 0) { + s = mid + 1; + } else if (c > 0) { + e = mid; + } else { + return {mid, MatchKind::kEq}; + } + } + return {s, MatchKind::kNe}; + } + } + + // Emplaces a value at position i, shifting all existing values and + // children at positions >= i to the right by 1. + template <typename... Args> + void emplace_value(size_type i, allocator_type *alloc, Args &&... args); + + // Removes the value at position i, shifting all existing values and children + // at positions > i to the left by 1. + void remove_value(const int i, allocator_type *alloc); + + // Removes the values at positions [i, i + to_erase), shifting all values + // after that range to the left by to_erase. Does not change children at all. + void remove_values_ignore_children(int i, int to_erase, + allocator_type *alloc); + + // Rebalances a node with its right sibling. + void rebalance_right_to_left(const int to_move, btree_node *right, + allocator_type *alloc); + void rebalance_left_to_right(const int to_move, btree_node *right, + allocator_type *alloc); + + // Splits a node, moving a portion of the node's values to its right sibling. + void split(const int insert_position, btree_node *dest, allocator_type *alloc); + + // Merges a node with its right sibling, moving all of the values and the + // delimiting key in the parent node onto itself. + void merge(btree_node *sibling, allocator_type *alloc); + + // Swap the contents of "this" and "src". + void swap(btree_node *src, allocator_type *alloc); + + // Node allocation/deletion routines. + static btree_node *init_leaf(btree_node *n, btree_node *parent, + int max_count) { + n->set_parent(parent); + n->set_position(0); + n->set_count(0); + n->set_max_count(max_count); + return n; + } + static btree_node *init_internal(btree_node *n, btree_node *parent) { + init_leaf(n, parent, kNodeValues); + // Set `max_count` to a sentinel value to indicate that this node is + // internal. + n->set_max_count(kInternalNodeMaxCount); + return n; + } + void destroy(allocator_type *alloc) { + for (int i = 0; i < count(); ++i) { + value_destroy(i, alloc); + } + } + + private: + template <typename... Args> + void value_init(const size_type i, allocator_type *alloc, Args &&... args) { + params_type::construct(alloc, slot(i), std::forward<Args>(args)...); + } + void value_destroy(const size_type i, allocator_type *alloc) { + params_type::destroy(alloc, slot(i)); + } + + // Move n values starting at value i in this node into the values starting at + // value j in node x. + void uninitialized_move_n(const size_type n, const size_type i, + const size_type j, btree_node *x, + allocator_type *alloc) { + for (slot_type *src = slot(i), *end = src + n, *dest = x->slot(j); + src != end; ++src, ++dest) { + params_type::construct(alloc, dest, src); + } + } + + // Destroys a range of n values, starting at index i. + void value_destroy_n(const size_type i, const size_type n, + allocator_type *alloc) { + for (int j = 0; j < n; ++j) { + value_destroy(i + j, alloc); + } + } + +private: + template <typename P> + friend class btree; + template <typename N, typename R, typename P> + friend struct btree_iterator; +}; + +template <typename Node, typename Reference, typename Pointer> +struct btree_iterator { + private: + using key_type = typename Node::key_type; + using size_type = typename Node::size_type; + using params_type = typename Node::params_type; + + using node_type = Node; + using normal_node = typename std::remove_const<Node>::type; + using const_node = const Node; + using normal_pointer = typename params_type::pointer; + using normal_reference = typename params_type::reference; + using const_pointer = typename params_type::const_pointer; + using const_reference = typename params_type::const_reference; + using slot_type = typename params_type::slot_type; + + using iterator = + btree_iterator<normal_node, normal_reference, normal_pointer>; + using const_iterator = + btree_iterator<const_node, const_reference, const_pointer>; + + public: + // These aliases are public for std::iterator_traits. + using difference_type = typename Node::difference_type; + using value_type = typename params_type::value_type; + using pointer = Pointer; + using reference = Reference; + using iterator_category = std::bidirectional_iterator_tag; + + btree_iterator() = default; + btree_iterator(Node *n, int p) : node(n), position(p) {} + + // NOTE: this SFINAE allows for implicit conversions from iterator to + // const_iterator, but it specifically avoids defining copy constructors so + // that btree_iterator can be trivially copyable. This is for performance and + // binary size reasons. + template<typename N, typename R, typename P, + std::enable_if_t< + std::is_same_v<btree_iterator<N, R, P>, iterator> && + std::is_same_v<btree_iterator, const_iterator>, + int> = 0> + btree_iterator(const btree_iterator<N, R, P> &x) + : node(x.node), position(x.position) {} + + private: + // This SFINAE allows explicit conversions from const_iterator to + // iterator, but also avoids defining a copy constructor. + // NOTE: the const_cast is safe because this constructor is only called by + // non-const methods and the container owns the nodes. + template <typename N, typename R, typename P, + std::enable_if_t< + std::is_same_v<btree_iterator<N, R, P>, const_iterator> && + std::is_same_v<btree_iterator, iterator>, + int> = 0> + explicit btree_iterator(const btree_iterator<N, R, P> &x) + : node(const_cast<node_type *>(x.node)), position(x.position) {} + + // Increment/decrement the iterator. + void increment() { + if (node->leaf() && ++position < node->count()) { + return; + } + increment_slow(); + } + void increment_slow(); + + void decrement() { + if (node->leaf() && --position >= 0) { + return; + } + decrement_slow(); + } + void decrement_slow(); + + public: + bool operator==(const const_iterator &x) const { + return node == x.node && position == x.position; + } + bool operator!=(const const_iterator &x) const { + return node != x.node || position != x.position; + } + bool operator==(const iterator& x) const { + return node == x.node && position == x.position; + } + bool operator!=(const iterator& x) const { + return node != x.node || position != x.position; + } + + // Accessors for the key/value the iterator is pointing at. + reference operator*() const { + return node->value(position); + } + pointer operator->() const { + return &node->value(position); + } + + btree_iterator& operator++() { + increment(); + return *this; + } + btree_iterator& operator--() { + decrement(); + return *this; + } + btree_iterator operator++(int) { + btree_iterator tmp = *this; + ++*this; + return tmp; + } + btree_iterator operator--(int) { + btree_iterator tmp = *this; + --*this; + return tmp; + } + + private: + template <typename Params> + friend class btree; + template <typename Tree> + friend class btree_container; + template <typename Tree> + friend class btree_set_container; + template <typename Tree> + friend class btree_map_container; + template <typename Tree> + friend class btree_multiset_container; + template <typename N, typename R, typename P> + friend struct btree_iterator; + + const key_type &key() const { return node->key(position); } + slot_type *slot() { return node->slot(position); } + + // The node in the tree the iterator is pointing at. + Node *node = nullptr; + // The position within the node of the tree the iterator is pointing at. + int position = -1; +}; + +template <size_t Alignment, class Alloc> +class AlignedAlloc { + struct alignas(Alignment) M {}; + using alloc_t = + typename std::allocator_traits<Alloc>::template rebind_alloc<M>; + using traits_t = + typename std::allocator_traits<Alloc>::template rebind_traits<M>; + static constexpr size_t num_aligned_objects(size_t size) { + return (size + sizeof(M) - 1) / sizeof(M); + } +public: + static void* allocate(Alloc* alloc, size_t size) { + alloc_t aligned_alloc(*alloc); + void* p = traits_t::allocate(aligned_alloc, + num_aligned_objects(size)); + assert(reinterpret_cast<uintptr_t>(p) % Alignment == 0 && + "allocator does not respect alignment"); + return p; + } + static void deallocate(Alloc* alloc, void* p, size_t size) { + alloc_t aligned_alloc(*alloc); + traits_t::deallocate(aligned_alloc, static_cast<M*>(p), + num_aligned_objects(size)); + } +}; + +template <typename Params> +class btree { + using node_type = btree_node<Params>; + using is_key_compare_to = typename Params::is_key_compare_to; + + // We use a static empty node for the root/leftmost/rightmost of empty btrees + // in order to avoid branching in begin()/end(). + struct alignas(node_type::Alignment()) EmptyNodeType : node_type { + using field_type = typename node_type::field_type; + node_type *parent; + field_type position = 0; + field_type count = 0; + // max_count must be != kInternalNodeMaxCount (so that this node is regarded + // as a leaf node). max_count() is never called when the tree is empty. + field_type max_count = node_type::kInternalNodeMaxCount + 1; + + constexpr EmptyNodeType(node_type *p) : parent(p) {} + }; + + static node_type *EmptyNode() { + static constexpr EmptyNodeType empty_node( + const_cast<EmptyNodeType *>(&empty_node)); + return const_cast<EmptyNodeType *>(&empty_node); + } + + constexpr static int kNodeValues = node_type::kNodeValues; + constexpr static int kMinNodeValues = kNodeValues / 2; + constexpr static int kValueSize = node_type::kValueSize; + + // A helper class to get the empty base class optimization for 0-size + // allocators. Base is allocator_type. + // (e.g. empty_base_handle<key_compare, allocator_type, node_type*>). If Base is + // 0-size, the compiler doesn't have to reserve any space for it and + // sizeof(empty_base_handle) will simply be sizeof(Data). Google [empty base + // class optimization] for more details. + template <typename Base1, typename Base2, typename Data> + struct empty_base_handle : public Base1, Base2 { + empty_base_handle(const Base1 &b1, const Base2 &b2, const Data &d) + : Base1(b1), + Base2(b2), + data(d) {} + Data data; + }; + + struct node_stats { + using size_type = typename Params::size_type; + + node_stats(size_type l, size_type i) + : leaf_nodes(l), + internal_nodes(i) { + } + + node_stats& operator+=(const node_stats &x) { + leaf_nodes += x.leaf_nodes; + internal_nodes += x.internal_nodes; + return *this; + } + + size_type leaf_nodes; + size_type internal_nodes; + }; + + public: + using key_type = typename Params::key_type; + using value_type = typename Params::value_type; + using size_type = typename Params::size_type; + using difference_type = typename Params::difference_type; + using key_compare = typename Params::key_compare; + using value_compare = typename Params::value_compare; + using allocator_type = typename Params::allocator_type; + using reference = typename Params::reference; + using const_reference = typename Params::const_reference; + using pointer = typename Params::pointer; + using const_pointer = typename Params::const_pointer; + using iterator = btree_iterator<node_type, reference, pointer>; + using const_iterator = typename iterator::const_iterator; + using reverse_iterator = std::reverse_iterator<iterator>; + using const_reverse_iterator = std::reverse_iterator<const_iterator>; + + // Internal types made public for use by btree_container types. + using params_type = Params; + + private: + // For use in copy_or_move_values_in_order. + const value_type &maybe_move_from_iterator(const_iterator x) { return *x; } + value_type &&maybe_move_from_iterator(iterator x) { return std::move(*x); } + + // Copies or moves (depending on the template parameter) the values in + // x into this btree in their order in x. This btree must be empty before this + // method is called. This method is used in copy construction, copy + // assignment, and move assignment. + template <typename Btree> + void copy_or_move_values_in_order(Btree *x); + + // Validates that various assumptions/requirements are true at compile time. + constexpr static bool static_assert_validation(); + + public: + btree(const key_compare &comp, const allocator_type &alloc); + + btree(const btree &x); + btree(btree &&x) noexcept + : root_(std::move(x.root_)), + rightmost_(std::exchange(x.rightmost_, EmptyNode())), + size_(std::exchange(x.size_, 0)) { + x.mutable_root() = EmptyNode(); + } + + ~btree() { + // Put static_asserts in destructor to avoid triggering them before the type + // is complete. + static_assert(static_assert_validation(), "This call must be elided."); + clear(); + } + + // Assign the contents of x to *this. + btree &operator=(const btree &x); + btree &operator=(btree &&x) noexcept; + + iterator begin() { + return iterator(leftmost(), 0); + } + const_iterator begin() const { + return const_iterator(leftmost(), 0); + } + iterator end() { + return iterator(rightmost_, rightmost_->count()); + } + const_iterator end() const { + return const_iterator(rightmost_, rightmost_->count()); + } + reverse_iterator rbegin() { + return reverse_iterator(end()); + } + const_reverse_iterator rbegin() const { + return const_reverse_iterator(end()); + } + reverse_iterator rend() { + return reverse_iterator(begin()); + } + const_reverse_iterator rend() const { + return const_reverse_iterator(begin()); + } + + // Finds the first element whose key is not less than key. + template <typename K> + iterator lower_bound(const K &key) { + return internal_end(internal_lower_bound(key)); + } + template <typename K> + const_iterator lower_bound(const K &key) const { + return internal_end(internal_lower_bound(key)); + } + + // Finds the first element whose key is greater than key. + template <typename K> + iterator upper_bound(const K &key) { + return internal_end(internal_upper_bound(key)); + } + template <typename K> + const_iterator upper_bound(const K &key) const { + return internal_end(internal_upper_bound(key)); + } + + // Finds the range of values which compare equal to key. The first member of + // the returned pair is equal to lower_bound(key). The second member pair of + // the pair is equal to upper_bound(key). + template <typename K> + std::pair<iterator, iterator> equal_range(const K &key) { + return {lower_bound(key), upper_bound(key)}; + } + template <typename K> + std::pair<const_iterator, const_iterator> equal_range(const K &key) const { + return {lower_bound(key), upper_bound(key)}; + } + + // Inserts a value into the btree only if it does not already exist. The + // boolean return value indicates whether insertion succeeded or failed. + // Requirement: if `key` already exists in the btree, does not consume `args`. + // Requirement: `key` is never referenced after consuming `args`. + template <typename... Args> + std::pair<iterator, bool> insert_unique(const key_type &key, Args &&... args); + + // Inserts with hint. Checks to see if the value should be placed immediately + // before `position` in the tree. If so, then the insertion will take + // amortized constant time. If not, the insertion will take amortized + // logarithmic time as if a call to insert_unique() were made. + // Requirement: if `key` already exists in the btree, does not consume `args`. + // Requirement: `key` is never referenced after consuming `args`. + template <typename... Args> + std::pair<iterator, bool> insert_hint_unique(iterator position, + const key_type &key, + Args &&... args); + + // Insert a range of values into the btree. + template <typename InputIterator> + void insert_iterator_unique(InputIterator b, InputIterator e); + + // Inserts a value into the btree. + template <typename ValueType> + iterator insert_multi(const key_type &key, ValueType &&v); + + // Inserts a value into the btree. + template <typename ValueType> + iterator insert_multi(ValueType &&v) { + return insert_multi(params_type::key(v), std::forward<ValueType>(v)); + } + + // Insert with hint. Check to see if the value should be placed immediately + // before position in the tree. If it does, then the insertion will take + // amortized constant time. If not, the insertion will take amortized + // logarithmic time as if a call to insert_multi(v) were made. + template <typename ValueType> + iterator insert_hint_multi(iterator position, ValueType &&v); + + // Insert a range of values into the btree. + template <typename InputIterator> + void insert_iterator_multi(InputIterator b, InputIterator e); + + // Erase the specified iterator from the btree. The iterator must be valid + // (i.e. not equal to end()). Return an iterator pointing to the node after + // the one that was erased (or end() if none exists). + // Requirement: does not read the value at `*iter`. + iterator erase(iterator iter); + + // Erases range. Returns the number of keys erased and an iterator pointing + // to the element after the last erased element. + std::pair<size_type, iterator> erase(iterator begin, iterator end); + + // Erases the specified key from the btree. Returns 1 if an element was + // erased and 0 otherwise. + template <typename K> + size_type erase_unique(const K &key); + + // Erases all of the entries matching the specified key from the + // btree. Returns the number of elements erased. + template <typename K> + size_type erase_multi(const K &key); + + // Finds the iterator corresponding to a key or returns end() if the key is + // not present. + template <typename K> + iterator find(const K &key) { + return internal_end(internal_find(key)); + } + template <typename K> + const_iterator find(const K &key) const { + return internal_end(internal_find(key)); + } + + // Returns a count of the number of times the key appears in the btree. + template <typename K> + size_type count_unique(const K &key) const { + const iterator begin = internal_find(key); + if (begin.node == nullptr) { + // The key doesn't exist in the tree. + return 0; + } + return 1; + } + // Returns a count of the number of times the key appears in the btree. + template <typename K> + size_type count_multi(const K &key) const { + const auto range = equal_range(key); + return std::distance(range.first, range.second); + } + + // Clear the btree, deleting all of the values it contains. + void clear(); + + // Swap the contents of *this and x. + void swap(btree &x); + + const key_compare &key_comp() const noexcept { + return *static_cast<const key_compare*>(&root_); + } + template <typename K, typename LK> + bool compare_keys(const K &x, const LK &y) const { + return compare_result_as_less_than(key_comp()(x, y)); + } + + // Verifies the structure of the btree. + void verify() const; + + // Size routines. + size_type size() const { return size_; } + size_type max_size() const { return std::numeric_limits<size_type>::max(); } + bool empty() const { return size_ == 0; } + + // The height of the btree. An empty tree will have height 0. + size_type height() const { + size_type h = 0; + if (!empty()) { + // Count the length of the chain from the leftmost node up to the + // root. We actually count from the root back around to the level below + // the root, but the calculation is the same because of the circularity + // of that traversal. + const node_type *n = root(); + do { + ++h; + n = n->parent(); + } while (n != root()); + } + return h; + } + + // The number of internal, leaf and total nodes used by the btree. + size_type leaf_nodes() const { + return internal_stats(root()).leaf_nodes; + } + size_type internal_nodes() const { + return internal_stats(root()).internal_nodes; + } + size_type nodes() const { + node_stats stats = internal_stats(root()); + return stats.leaf_nodes + stats.internal_nodes; + } + + // The total number of bytes used by the btree. + size_type bytes_used() const { + node_stats stats = internal_stats(root()); + if (stats.leaf_nodes == 1 && stats.internal_nodes == 0) { + return sizeof(*this) + + node_type::LeafSize(root()->max_count()); + } else { + return sizeof(*this) + + stats.leaf_nodes * node_type::LeafSize() + + stats.internal_nodes * node_type::InternalSize(); + } + } + + // The average number of bytes used per value stored in the btree. + static double average_bytes_per_value() { + // Returns the number of bytes per value on a leaf node that is 75% + // full. Experimentally, this matches up nicely with the computed number of + // bytes per value in trees that had their values inserted in random order. + return node_type::LeafSize() / (kNodeValues * 0.75); + } + + // The fullness of the btree. Computed as the number of elements in the btree + // divided by the maximum number of elements a tree with the current number + // of nodes could hold. A value of 1 indicates perfect space + // utilization. Smaller values indicate space wastage. + // Returns 0 for empty trees. + double fullness() const { + if (empty()) return 0.0; + return static_cast<double>(size()) / (nodes() * kNodeValues); + } + // The overhead of the btree structure in bytes per node. Computed as the + // total number of bytes used by the btree minus the number of bytes used for + // storing elements divided by the number of elements. + // Returns 0 for empty trees. + double overhead() const { + if (empty()) return 0.0; + return (bytes_used() - size() * sizeof(value_type)) / + static_cast<double>(size()); + } + + // The allocator used by the btree. + allocator_type get_allocator() const { + return allocator(); + } + + private: + // Internal accessor routines. + node_type *root() { return root_.data; } + const node_type *root() const { return root_.data; } + node_type *&mutable_root() { return root_.data; } + key_compare *mutable_key_comp() noexcept { + return static_cast<key_compare*>(&root_); + } + + node_type* rightmost() { + return rightmost_; + } + const node_type* rightmost() const { + return rightmost_; + } + // The leftmost node is stored as the parent of the root node. + node_type* leftmost() { return root() ? root()->parent() : NULL; } + const node_type* leftmost() const { return root() ? root()->parent() : NULL; } + + // The size of the tree is stored in the root node. + size_type* mutable_size() { return root()->mutable_size(); } + + // Allocator routines. + allocator_type* mutable_allocator() noexcept { + return static_cast<allocator_type*>(&root_); + } + const allocator_type& allocator() const noexcept { + return *static_cast<const allocator_type*>(&root_); + } + + node_type *allocate(const size_type size) { + using aligned_alloc_t = + AlignedAlloc<node_type::Alignment(), allocator_type>; + return static_cast<node_type*>( + aligned_alloc_t::allocate(mutable_allocator(), size)); + } + + // Node creation/deletion routines. + node_type* new_internal_node(node_type *parent) { + node_type *p = allocate(node_type::InternalSize()); + return node_type::init_internal(p, parent); + } + node_type* new_leaf_node(node_type *parent) { + node_type *p = allocate(node_type::LeafSize()); + return node_type::init_leaf(p, parent, kNodeValues); + } + node_type *new_leaf_root_node(const int max_count) { + node_type *p = allocate(node_type::LeafSize(max_count)); + return node_type::init_leaf(p, p, max_count); + } + + // Deletion helper routines. + void erase_same_node(iterator begin, iterator end); + iterator erase_from_leaf_node(iterator begin, size_type to_erase); + iterator rebalance_after_delete(iterator iter); + + // Deallocates a node of a certain size in bytes using the allocator. + void deallocate(const size_type size, node_type *node) { + using aligned_alloc_t = + AlignedAlloc<node_type::Alignment(), allocator_type>; + aligned_alloc_t::deallocate(mutable_allocator(), node, size); + } + + void delete_internal_node(node_type *node) { + node->destroy(mutable_allocator()); + deallocate(node_type::InternalSize(), node); + } + void delete_leaf_node(node_type *node) { + node->destroy(mutable_allocator()); + deallocate(node_type::LeafSize(node->max_count()), node); + } + + // Rebalances or splits the node iter points to. + void rebalance_or_split(iterator *iter); + + // Merges the values of left, right and the delimiting key on their parent + // onto left, removing the delimiting key and deleting right. + void merge_nodes(node_type *left, node_type *right); + + // Tries to merge node with its left or right sibling, and failing that, + // rebalance with its left or right sibling. Returns true if a merge + // occurred, at which point it is no longer valid to access node. Returns + // false if no merging took place. + bool try_merge_or_rebalance(iterator *iter); + + // Tries to shrink the height of the tree by 1. + void try_shrink(); + + iterator internal_end(iterator iter) { + return iter.node != nullptr ? iter : end(); + } + const_iterator internal_end(const_iterator iter) const { + return iter.node != nullptr ? iter : end(); + } + + // Emplaces a value into the btree immediately before iter. Requires that + // key(v) <= iter.key() and (--iter).key() <= key(v). + template <typename... Args> + iterator internal_emplace(iterator iter, Args &&... args); + + // Returns an iterator pointing to the first value >= the value "iter" is + // pointing at. Note that "iter" might be pointing to an invalid location as + // iter.position == iter.node->count(). This routine simply moves iter up in + // the tree to a valid location. + // Requires: iter.node is non-null. + template <typename IterType> + static IterType internal_last(IterType iter); + + // Returns an iterator pointing to the leaf position at which key would + // reside in the tree. We provide 2 versions of internal_locate. The first + // version uses a less-than comparator and is incapable of distinguishing when + // there is an exact match. The second version is for the key-compare-to + // specialization and distinguishes exact matches. The key-compare-to + // specialization allows the caller to avoid a subsequent comparison to + // determine if an exact match was made, which is important for keys with + // expensive comparison, such as strings. + template <typename K> + SearchResult<iterator, is_key_compare_to::value> internal_locate( + const K &key) const; + + template <typename K> + SearchResult<iterator, false> internal_locate_impl( + const K &key, std::false_type /* IsCompareTo */) const; + + template <typename K> + SearchResult<iterator, true> internal_locate_impl( + const K &key, std::true_type /* IsCompareTo */) const; + + // Internal routine which implements lower_bound(). + template <typename K> + iterator internal_lower_bound(const K &key) const; + + // Internal routine which implements upper_bound(). + template <typename K> + iterator internal_upper_bound(const K &key) const; + + // Internal routine which implements find(). + template <typename K> + iterator internal_find(const K &key) const; + + // Deletes a node and all of its children. + void internal_clear(node_type *node); + + // Verifies the tree structure of node. + int internal_verify(const node_type *node, + const key_type *lo, const key_type *hi) const; + + node_stats internal_stats(const node_type *node) const { + // The root can be a static empty node. + if (node == nullptr || (node == root() && empty())) { + return node_stats(0, 0); + } + if (node->leaf()) { + return node_stats(1, 0); + } + node_stats res(0, 1); + for (int i = 0; i <= node->count(); ++i) { + res += internal_stats(node->child(i)); + } + return res; + } + + private: + empty_base_handle<key_compare, allocator_type, node_type*> root_; + + // A pointer to the rightmost node. Note that the leftmost node is stored as + // the root's parent. + node_type *rightmost_; + + // Number of values. + size_type size_; +}; + +//// +// btree_node methods +template <typename P> +template <typename... Args> +inline void btree_node<P>::emplace_value(const size_type i, + allocator_type *alloc, + Args &&... args) { + assert(i <= count()); + // Shift old values to create space for new value and then construct it in + // place. + if (i < count()) { + value_init(count(), alloc, slot(count() - 1)); + std::copy_backward(std::make_move_iterator(slot(i)), + std::make_move_iterator(slot(count() - 1)), + slot(count())); + value_destroy(i, alloc); + } + value_init(i, alloc, std::forward<Args>(args)...); + set_count(count() + 1); + + if (!leaf() && count() > i + 1) { + for (int j = count(); j > i + 1; --j) { + set_child(j, child(j - 1)); + } + clear_child(i + 1); + } +} + +template <typename P> +inline void btree_node<P>::remove_value(const int i, allocator_type *alloc) { + if (!leaf() && count() > i + 1) { + assert(child(i + 1)->count() == 0); + for (size_type j = i + 1; j < count(); ++j) { + set_child(j, child(j + 1)); + } + clear_child(count()); + } + + remove_values_ignore_children(i, /*to_erase=*/1, alloc); +} + +template <typename P> +inline void btree_node<P>::remove_values_ignore_children( + const int i, const int to_erase, allocator_type *alloc) { + assert(to_erase >= 0); + std::copy(std::make_move_iterator(slot(i + to_erase)), + std::make_move_iterator(slot(count())), + slot(i)); + value_destroy_n(count() - to_erase, to_erase, alloc); + set_count(count() - to_erase); +} + +template <typename P> +void btree_node<P>::rebalance_right_to_left(const int to_move, + btree_node *right, + allocator_type *alloc) { + assert(parent() == right->parent()); + assert(position() + 1 == right->position()); + assert(right->count() >= count()); + assert(to_move >= 1); + assert(to_move <= right->count()); + + // 1) Move the delimiting value in the parent to the left node. + value_init(count(), alloc, parent()->slot(position())); + + // 2) Move the (to_move - 1) values from the right node to the left node. + right->uninitialized_move_n(to_move - 1, 0, count() + 1, this, alloc); + + // 3) Move the new delimiting value to the parent from the right node. + params_type::move(alloc, right->slot(to_move - 1), + parent()->slot(position())); + + // 4) Shift the values in the right node to their correct position. + std::copy(std::make_move_iterator(right->slot(to_move)), + std::make_move_iterator(right->slot(right->count())), + right->slot(0)); + + // 5) Destroy the now-empty to_move entries in the right node. + right->value_destroy_n(right->count() - to_move, to_move, alloc); + + if (!leaf()) { + // Move the child pointers from the right to the left node. + for (int i = 0; i < to_move; ++i) { + init_child(count() + i + 1, right->child(i)); + } + for (int i = 0; i <= right->count() - to_move; ++i) { + assert(i + to_move <= right->max_count()); + right->init_child(i, right->child(i + to_move)); + right->clear_child(i + to_move); + } + } + + // Fixup the counts on the left and right nodes. + set_count(count() + to_move); + right->set_count(right->count() - to_move); +} + +template <typename P> +void btree_node<P>::rebalance_left_to_right(const int to_move, + btree_node *right, + allocator_type *alloc) { + assert(parent() == right->parent()); + assert(position() + 1 == right->position()); + assert(count() >= right->count()); + assert(to_move >= 1); + assert(to_move <= count()); + + // Values in the right node are shifted to the right to make room for the + // new to_move values. Then, the delimiting value in the parent and the + // other (to_move - 1) values in the left node are moved into the right node. + // Lastly, a new delimiting value is moved from the left node into the + // parent, and the remaining empty left node entries are destroyed. + + if (right->count() >= to_move) { + // The original location of the right->count() values are sufficient to hold + // the new to_move entries from the parent and left node. + + // 1) Shift existing values in the right node to their correct positions. + right->uninitialized_move_n(to_move, right->count() - to_move, + right->count(), right, alloc); + std::copy_backward(std::make_move_iterator(right->slot(0)), + std::make_move_iterator(right->slot(right->count() - to_move)), + right->slot(right->count())); + + // 2) Move the delimiting value in the parent to the right node. + params_type::move(alloc, parent()->slot(position()), + right->slot(to_move - 1)); + + // 3) Move the (to_move - 1) values from the left node to the right node. + std::copy(std::make_move_iterator(slot(count() - (to_move - 1))), + std::make_move_iterator(slot(count())), + right->slot(0)); + } else { + // The right node does not have enough initialized space to hold the new + // to_move entries, so part of them will move to uninitialized space. + + // 1) Shift existing values in the right node to their correct positions. + right->uninitialized_move_n(right->count(), 0, to_move, right, alloc); + + // 2) Move the delimiting value in the parent to the right node. + right->value_init(to_move - 1, alloc, parent()->slot(position())); + + // 3) Move the (to_move - 1) values from the left node to the right node. + const size_type uninitialized_remaining = to_move - right->count() - 1; + uninitialized_move_n(uninitialized_remaining, + count() - uninitialized_remaining, right->count(), + right, alloc); + std::copy(std::make_move_iterator(slot(count() - (to_move - 1))), + std::make_move_iterator(slot(count() - uninitialized_remaining)), + right->slot(0)); + } + + // 4) Move the new delimiting value to the parent from the left node. + params_type::move(alloc, slot(count() - to_move), parent()->slot(position())); + + // 5) Destroy the now-empty to_move entries in the left node. + value_destroy_n(count() - to_move, to_move, alloc); + + if (!leaf()) { + // Move the child pointers from the left to the right node. + for (int i = right->count(); i >= 0; --i) { + right->init_child(i + to_move, right->child(i)); + right->clear_child(i); + } + for (int i = 1; i <= to_move; ++i) { + right->init_child(i - 1, child(count() - to_move + i)); + clear_child(count() - to_move + i); + } + } + + // Fixup the counts on the left and right nodes. + set_count(count() - to_move); + right->set_count(right->count() + to_move); +} + +template <typename P> +void btree_node<P>::split(const int insert_position, btree_node *dest, + allocator_type *alloc) { + assert(dest->count() == 0); + assert(max_count() == kNodeValues); + + // We bias the split based on the position being inserted. If we're + // inserting at the beginning of the left node then bias the split to put + // more values on the right node. If we're inserting at the end of the + // right node then bias the split to put more values on the left node. + if (insert_position == 0) { + dest->set_count(count() - 1); + } else if (insert_position == kNodeValues) { + dest->set_count(0); + } else { + dest->set_count(count() / 2); + } + set_count(count() - dest->count()); + assert(count() >= 1); + + // Move values from the left sibling to the right sibling. + uninitialized_move_n(dest->count(), count(), 0, dest, alloc); + + // Destroy the now-empty entries in the left node. + value_destroy_n(count(), dest->count(), alloc); + + // The split key is the largest value in the left sibling. + set_count(count() - 1); + parent()->emplace_value(position(), alloc, slot(count())); + value_destroy(count(), alloc); + parent()->init_child(position() + 1, dest); + + if (!leaf()) { + for (int i = 0; i <= dest->count(); ++i) { + assert(child(count() + i + 1) != nullptr); + dest->init_child(i, child(count() + i + 1)); + clear_child(count() + i + 1); + } + } +} + +template <typename P> +void btree_node<P>::merge(btree_node *src, allocator_type *alloc) { + assert(parent() == src->parent()); + assert(position() + 1 == src->position()); + + // Move the delimiting value to the left node. + value_init(count(), alloc, parent()->slot(position())); + + // Move the values from the right to the left node. + src->uninitialized_move_n(src->count(), 0, count() + 1, this, alloc); + + // Destroy the now-empty entries in the right node. + src->value_destroy_n(0, src->count(), alloc); + + if (!leaf()) { + // Move the child pointers from the right to the left node. + for (int i = 0; i <= src->count(); ++i) { + init_child(count() + i + 1, src->child(i)); + src->clear_child(i); + } + } + + // Fixup the counts on the src and dest nodes. + set_count(1 + count() + src->count()); + src->set_count(0); + + // Remove the value on the parent node. + parent()->remove_value(position(), alloc); +} + +template <typename P> +void btree_node<P>::swap(btree_node *x, allocator_type *alloc) { + using std::swap; + assert(leaf() == x->leaf()); + + // Determine which is the smaller/larger node. + btree_node *smaller = this, *larger = x; + if (smaller->count() > larger->count()) { + swap(smaller, larger); + } + + // Swap the values. + std::swap_ranges(smaller->slot(0), smaller->slot(smaller->count()), + larger->slot(0)); + + // Move values that can't be swapped. + const size_type to_move = larger->count() - smaller->count(); + larger->uninitialized_move_n(to_move, smaller->count(), smaller->count(), + smaller, alloc); + larger->value_destroy_n(smaller->count(), to_move, alloc); + + if (!leaf()) { + // Swap the child pointers. + std::swap_ranges(&smaller->mutable_child(0), + &smaller->mutable_child(smaller->count() + 1), + &larger->mutable_child(0)); + // Update swapped children's parent pointers. + int i = 0; + for (; i <= smaller->count(); ++i) { + smaller->child(i)->set_parent(smaller); + larger->child(i)->set_parent(larger); + } + // Move the child pointers that couldn't be swapped. + for (; i <= larger->count(); ++i) { + smaller->init_child(i, larger->child(i)); + larger->clear_child(i); + } + } + + // Swap the counts. + swap(mutable_count(), x->mutable_count()); +} + +//// +// btree_iterator methods +template <typename N, typename R, typename P> +void btree_iterator<N, R, P>::increment_slow() { + if (node->leaf()) { + assert(position >= node->count()); + btree_iterator save(*this); + while (position == node->count() && !node->is_root()) { + assert(node->parent()->child(node->position()) == node); + position = node->position(); + node = node->parent(); + } + if (position == node->count()) { + *this = save; + } + } else { + assert(position < node->count()); + node = node->child(position + 1); + while (!node->leaf()) { + node = node->child(0); + } + position = 0; + } +} + +template <typename N, typename R, typename P> +void btree_iterator<N, R, P>::decrement_slow() { + if (node->leaf()) { + assert(position <= -1); + btree_iterator save(*this); + while (position < 0 && !node->is_root()) { + assert(node->parent()->child(node->position()) == node); + position = node->position() - 1; + node = node->parent(); + } + if (position < 0) { + *this = save; + } + } else { + assert(position >= 0); + node = node->child(position); + while (!node->leaf()) { + node = node->child(node->count()); + } + position = node->count() - 1; + } +} + +//// +// btree methods +template <typename P> +template <typename Btree> +void btree<P>::copy_or_move_values_in_order(Btree *x) { + static_assert(std::is_same_v<btree, Btree>|| + std::is_same_v<const btree, Btree>, + "Btree type must be same or const."); + assert(empty()); + + // We can avoid key comparisons because we know the order of the + // values is the same order we'll store them in. + auto iter = x->begin(); + if (iter == x->end()) return; + insert_multi(maybe_move_from_iterator(iter)); + ++iter; + for (; iter != x->end(); ++iter) { + // If the btree is not empty, we can just insert the new value at the end + // of the tree. + internal_emplace(end(), maybe_move_from_iterator(iter)); + } +} + +template <typename P> +constexpr bool btree<P>::static_assert_validation() { + static_assert(std::is_nothrow_copy_constructible_v<key_compare>, + "Key comparison must be nothrow copy constructible"); + static_assert(std::is_nothrow_copy_constructible_v<allocator_type>, + "Allocator must be nothrow copy constructible"); + static_assert(std::is_trivially_copyable_v<iterator>, + "iterator not trivially copyable."); + + // Note: We assert that kTargetValues, which is computed from + // Params::kTargetNodeSize, must fit the base_fields::field_type. + static_assert( + kNodeValues < (1 << (8 * sizeof(typename node_type::field_type))), + "target node size too large"); + + // Verify that key_compare returns an absl::{weak,strong}_ordering or bool. + using compare_result_type = + std::invoke_result_t<key_compare, key_type, key_type>; + static_assert( + std::is_same_v<compare_result_type, bool> || + std::is_signed_v<compare_result_type>, + "key comparison function must return a signed value or " + "bool."); + + // Test the assumption made in setting kNodeValueSpace. + static_assert(node_type::MinimumOverhead() >= sizeof(void *) + 4, + "node space assumption incorrect"); + + return true; +} + +template <typename P> +btree<P>::btree(const key_compare &comp, const allocator_type &alloc) + : root_(comp, alloc, EmptyNode()), rightmost_(EmptyNode()), size_(0) {} + +template <typename P> +btree<P>::btree(const btree &x) : btree(x.key_comp(), x.allocator()) { + copy_or_move_values_in_order(&x); +} + +template <typename P> +template <typename... Args> +auto btree<P>::insert_unique(const key_type &key, Args &&... args) + -> std::pair<iterator, bool> { + if (empty()) { + mutable_root() = rightmost_ = new_leaf_root_node(1); + } + + auto res = internal_locate(key); + iterator &iter = res.value; + + if constexpr (res.has_match) { + if (res.IsEq()) { + // The key already exists in the tree, do nothing. + return {iter, false}; + } + } else { + iterator last = internal_last(iter); + if (last.node && !compare_keys(key, last.key())) { + // The key already exists in the tree, do nothing. + return {last, false}; + } + } + return {internal_emplace(iter, std::forward<Args>(args)...), true}; +} + +template <typename P> +template <typename... Args> +inline auto btree<P>::insert_hint_unique(iterator position, const key_type &key, + Args &&... args) + -> std::pair<iterator, bool> { + if (!empty()) { + if (position == end() || compare_keys(key, position.key())) { + iterator prev = position; + if (position == begin() || compare_keys((--prev).key(), key)) { + // prev.key() < key < position.key() + return {internal_emplace(position, std::forward<Args>(args)...), true}; + } + } else if (compare_keys(position.key(), key)) { + ++position; + if (position == end() || compare_keys(key, position.key())) { + // {original `position`}.key() < key < {current `position`}.key() + return {internal_emplace(position, std::forward<Args>(args)...), true}; + } + } else { + // position.key() == key + return {position, false}; + } + } + return insert_unique(key, std::forward<Args>(args)...); +} + +template <typename P> +template <typename InputIterator> +void btree<P>::insert_iterator_unique(InputIterator b, InputIterator e) { + for (; b != e; ++b) { + insert_hint_unique(end(), params_type::key(*b), *b); + } +} + +template <typename P> +template <typename ValueType> +auto btree<P>::insert_multi(const key_type &key, ValueType&& v) -> iterator { + if (empty()) { + mutable_root() = rightmost_ = new_leaf_root_node(1); + } + + iterator iter = internal_upper_bound(key); + if (iter.node == nullptr) { + iter = end(); + } + return internal_emplace(iter, std::forward<ValueType>(v)); +} + +template <typename P> +template <typename ValueType> +auto btree<P>::insert_hint_multi(iterator position, ValueType &&v) -> iterator { + if (!empty()) { + const key_type &key = params_type::key(v); + if (position == end() || !compare_keys(position.key(), key)) { + iterator prev = position; + if (position == begin() || !compare_keys(key, (--prev).key())) { + // prev.key() <= key <= position.key() + return internal_emplace(position, std::forward<ValueType>(v)); + } + } else { + iterator next = position; + ++next; + if (next == end() || !compare_keys(next.key(), key)) { + // position.key() < key <= next.key() + return internal_emplace(next, std::forward<ValueType>(v)); + } + } + } + return insert_multi(std::forward<ValueType>(v)); +} + +template <typename P> +template <typename InputIterator> +void btree<P>::insert_iterator_multi(InputIterator b, InputIterator e) { + for (; b != e; ++b) { + insert_hint_multi(end(), *b); + } +} + +template <typename P> +auto btree<P>::operator=(const btree &x) -> btree & { + if (this != &x) { + clear(); + + *mutable_key_comp() = x.key_comp(); + if constexpr (std::allocator_traits< + allocator_type>::propagate_on_container_copy_assignment::value) { + *mutable_allocator() = x.allocator(); + } + + copy_or_move_values_in_order(&x); + } + return *this; +} + +template <typename P> +auto btree<P>::operator=(btree &&x) noexcept -> btree & { + if (this != &x) { + clear(); + + using std::swap; + if constexpr (std::allocator_traits< + allocator_type>::propagate_on_container_copy_assignment::value) { + // Note: `root_` also contains the allocator and the key comparator. + swap(root_, x.root_); + swap(rightmost_, x.rightmost_); + swap(size_, x.size_); + } else { + if (allocator() == x.allocator()) { + swap(mutable_root(), x.mutable_root()); + swap(*mutable_key_comp(), *x.mutable_key_comp()); + swap(rightmost_, x.rightmost_); + swap(size_, x.size_); + } else { + // We aren't allowed to propagate the allocator and the allocator is + // different so we can't take over its memory. We must move each element + // individually. We need both `x` and `this` to have `x`s key comparator + // while moving the values so we can't swap the key comparators. + *mutable_key_comp() = x.key_comp(); + copy_or_move_values_in_order(&x); + } + } + } + return *this; +} + +template <typename P> +auto btree<P>::erase(iterator iter) -> iterator { + bool internal_delete = false; + if (!iter.node->leaf()) { + // Deletion of a value on an internal node. First, move the largest value + // from our left child here, then delete that position (in remove_value() + // below). We can get to the largest value from our left child by + // decrementing iter. + iterator internal_iter(iter); + --iter; + assert(iter.node->leaf()); + params_type::move(mutable_allocator(), iter.node->slot(iter.position), + internal_iter.node->slot(internal_iter.position)); + internal_delete = true; + } + + // Delete the key from the leaf. + iter.node->remove_value(iter.position, mutable_allocator()); + --size_; + + // We want to return the next value after the one we just erased. If we + // erased from an internal node (internal_delete == true), then the next + // value is ++(++iter). If we erased from a leaf node (internal_delete == + // false) then the next value is ++iter. Note that ++iter may point to an + // internal node and the value in the internal node may move to a leaf node + // (iter.node) when rebalancing is performed at the leaf level. + + iterator res = rebalance_after_delete(iter); + + // If we erased from an internal node, advance the iterator. + if (internal_delete) { + ++res; + } + return res; +} + +template <typename P> +auto btree<P>::rebalance_after_delete(iterator iter) -> iterator { + // Merge/rebalance as we walk back up the tree. + iterator res(iter); + bool first_iteration = true; + for (;;) { + if (iter.node == root()) { + try_shrink(); + if (empty()) { + return end(); + } + break; + } + if (iter.node->count() >= kMinNodeValues) { + break; + } + bool merged = try_merge_or_rebalance(&iter); + // On the first iteration, we should update `res` with `iter` because `res` + // may have been invalidated. + if (first_iteration) { + res = iter; + first_iteration = false; + } + if (!merged) { + break; + } + iter.position = iter.node->position(); + iter.node = iter.node->parent(); + } + + // Adjust our return value. If we're pointing at the end of a node, advance + // the iterator. + if (res.position == res.node->count()) { + res.position = res.node->count() - 1; + ++res; + } + + return res; +} + +template <typename P> +auto btree<P>::erase(iterator begin, iterator end) + -> std::pair<size_type, iterator> { + difference_type count = std::distance(begin, end); + assert(count >= 0); + + if (count == 0) { + return {0, begin}; + } + + if (count == size_) { + clear(); + return {count, this->end()}; + } + + if (begin.node == end.node) { + erase_same_node(begin, end); + size_ -= count; + return {count, rebalance_after_delete(begin)}; + } + + const size_type target_size = size_ - count; + while (size_ > target_size) { + if (begin.node->leaf()) { + const size_type remaining_to_erase = size_ - target_size; + const size_type remaining_in_node = begin.node->count() - begin.position; + begin = erase_from_leaf_node( + begin, std::min(remaining_to_erase, remaining_in_node)); + } else { + begin = erase(begin); + } + } + return {count, begin}; +} + +template <typename P> +void btree<P>::erase_same_node(iterator begin, iterator end) { + assert(begin.node == end.node); + assert(end.position > begin.position); + + node_type *node = begin.node; + size_type to_erase = end.position - begin.position; + if (!node->leaf()) { + // Delete all children between begin and end. + for (size_type i = 0; i < to_erase; ++i) { + internal_clear(node->child(begin.position + i + 1)); + } + // Rotate children after end into new positions. + for (size_type i = begin.position + to_erase + 1; i <= node->count(); ++i) { + node->set_child(i - to_erase, node->child(i)); + node->clear_child(i); + } + } + node->remove_values_ignore_children(begin.position, to_erase, + mutable_allocator()); + + // Do not need to update rightmost_, because + // * either end == this->end(), and therefore node == rightmost_, and still + // exists + // * or end != this->end(), and therefore rightmost_ hasn't been erased, since + // it wasn't covered in [begin, end) +} + +template <typename P> +auto btree<P>::erase_from_leaf_node(iterator begin, size_type to_erase) + -> iterator { + node_type *node = begin.node; + assert(node->leaf()); + assert(node->count() > begin.position); + assert(begin.position + to_erase <= node->count()); + + node->remove_values_ignore_children(begin.position, to_erase, + mutable_allocator()); + + size_ -= to_erase; + + return rebalance_after_delete(begin); +} + +template <typename P> +template <typename K> +auto btree<P>::erase_unique(const K &key) -> size_type { + const iterator iter = internal_find(key); + if (iter.node == nullptr) { + // The key doesn't exist in the tree, return nothing done. + return 0; + } + erase(iter); + return 1; +} + +template <typename P> +template <typename K> +auto btree<P>::erase_multi(const K &key) -> size_type { + const iterator begin = internal_lower_bound(key); + if (begin.node == nullptr) { + // The key doesn't exist in the tree, return nothing done. + return 0; + } + // Delete all of the keys between begin and upper_bound(key). + const iterator end = internal_end(internal_upper_bound(key)); + return erase(begin, end).first; +} + +template <typename P> +void btree<P>::clear() { + if (!empty()) { + internal_clear(root()); + } + mutable_root() = EmptyNode(); + rightmost_ = EmptyNode(); + size_ = 0; +} + +template <typename P> +void btree<P>::swap(btree &x) { + using std::swap; + if (std::allocator_traits< + allocator_type>::propagate_on_container_swap::value) { + // Note: `root_` also contains the allocator and the key comparator. + swap(root_, x.root_); + } else { + // It's undefined behavior if the allocators are unequal here. + assert(allocator() == x.allocator()); + swap(mutable_root(), x.mutable_root()); + swap(*mutable_key_comp(), *x.mutable_key_comp()); + } + swap(rightmost_, x.rightmost_); + swap(size_, x.size_); +} + +template <typename P> +void btree<P>::verify() const { + assert(root() != nullptr); + assert(leftmost() != nullptr); + assert(rightmost_ != nullptr); + assert(empty() || size() == internal_verify(root(), nullptr, nullptr)); + assert(leftmost() == (++const_iterator(root(), -1)).node); + assert(rightmost_ == (--const_iterator(root(), root()->count())).node); + assert(leftmost()->leaf()); + assert(rightmost_->leaf()); +} + +template <typename P> +void btree<P>::rebalance_or_split(iterator *iter) { + node_type *&node = iter->node; + int &insert_position = iter->position; + assert(node->count() == node->max_count()); + assert(kNodeValues == node->max_count()); + + // First try to make room on the node by rebalancing. + node_type *parent = node->parent(); + if (node != root()) { + if (node->position() > 0) { + // Try rebalancing with our left sibling. + node_type *left = parent->child(node->position() - 1); + assert(left->max_count() == kNodeValues); + if (left->count() < kNodeValues) { + // We bias rebalancing based on the position being inserted. If we're + // inserting at the end of the right node then we bias rebalancing to + // fill up the left node. + int to_move = (kNodeValues - left->count()) / + (1 + (insert_position < kNodeValues)); + to_move = std::max(1, to_move); + + if (((insert_position - to_move) >= 0) || + ((left->count() + to_move) < kNodeValues)) { + left->rebalance_right_to_left(to_move, node, mutable_allocator()); + + assert(node->max_count() - node->count() == to_move); + insert_position = insert_position - to_move; + if (insert_position < 0) { + insert_position = insert_position + left->count() + 1; + node = left; + } + + assert(node->count() < node->max_count()); + return; + } + } + } + + if (node->position() < parent->count()) { + // Try rebalancing with our right sibling. + node_type *right = parent->child(node->position() + 1); + assert(right->max_count() == kNodeValues); + if (right->count() < kNodeValues) { + // We bias rebalancing based on the position being inserted. If we're + // inserting at the beginning of the left node then we bias rebalancing + // to fill up the right node. + int to_move = + (kNodeValues - right->count()) / (1 + (insert_position > 0)); + to_move = (std::max)(1, to_move); + + if ((insert_position <= (node->count() - to_move)) || + ((right->count() + to_move) < kNodeValues)) { + node->rebalance_left_to_right(to_move, right, mutable_allocator()); + + if (insert_position > node->count()) { + insert_position = insert_position - node->count() - 1; + node = right; + } + + assert(node->count() < node->max_count()); + return; + } + } + } + + // Rebalancing failed, make sure there is room on the parent node for a new + // value. + assert(parent->max_count() == kNodeValues); + if (parent->count() == kNodeValues) { + iterator parent_iter(node->parent(), node->position()); + rebalance_or_split(&parent_iter); + } + } else { + // Rebalancing not possible because this is the root node. + // Create a new root node and set the current root node as the child of the + // new root. + parent = new_internal_node(parent); + parent->init_child(0, root()); + mutable_root() = parent; + // If the former root was a leaf node, then it's now the rightmost node. + assert(!parent->child(0)->leaf() || parent->child(0) == rightmost_); + } + + // Split the node. + node_type *split_node; + if (node->leaf()) { + split_node = new_leaf_node(parent); + node->split(insert_position, split_node, mutable_allocator()); + if (rightmost_ == node) rightmost_ = split_node; + } else { + split_node = new_internal_node(parent); + node->split(insert_position, split_node, mutable_allocator()); + } + + if (insert_position > node->count()) { + insert_position = insert_position - node->count() - 1; + node = split_node; + } +} + +template <typename P> +void btree<P>::merge_nodes(node_type *left, node_type *right) { + left->merge(right, mutable_allocator()); + if (right->leaf()) { + if (rightmost_ == right) rightmost_ = left; + delete_leaf_node(right); + } else { + delete_internal_node(right); + } +} + +template <typename P> +bool btree<P>::try_merge_or_rebalance(iterator *iter) { + node_type *parent = iter->node->parent(); + if (iter->node->position() > 0) { + // Try merging with our left sibling. + node_type *left = parent->child(iter->node->position() - 1); + assert(left->max_count() == kNodeValues); + if ((1 + left->count() + iter->node->count()) <= kNodeValues) { + iter->position += 1 + left->count(); + merge_nodes(left, iter->node); + iter->node = left; + return true; + } + } + if (iter->node->position() < parent->count()) { + // Try merging with our right sibling. + node_type *right = parent->child(iter->node->position() + 1); + assert(right->max_count() == kNodeValues); + if ((1 + iter->node->count() + right->count()) <= kNodeValues) { + merge_nodes(iter->node, right); + return true; + } + // Try rebalancing with our right sibling. We don't perform rebalancing if + // we deleted the first element from iter->node and the node is not + // empty. This is a small optimization for the common pattern of deleting + // from the front of the tree. + if ((right->count() > kMinNodeValues) && + ((iter->node->count() == 0) || + (iter->position > 0))) { + int to_move = (right->count() - iter->node->count()) / 2; + to_move = std::min(to_move, right->count() - 1); + iter->node->rebalance_right_to_left(to_move, right, mutable_allocator()); + return false; + } + } + if (iter->node->position() > 0) { + // Try rebalancing with our left sibling. We don't perform rebalancing if + // we deleted the last element from iter->node and the node is not + // empty. This is a small optimization for the common pattern of deleting + // from the back of the tree. + node_type *left = parent->child(iter->node->position() - 1); + if ((left->count() > kMinNodeValues) && + ((iter->node->count() == 0) || + (iter->position < iter->node->count()))) { + int to_move = (left->count() - iter->node->count()) / 2; + to_move = std::min(to_move, left->count() - 1); + left->rebalance_left_to_right(to_move, iter->node, mutable_allocator()); + iter->position += to_move; + return false; + } + } + return false; +} + +template <typename P> +void btree<P>::try_shrink() { + if (root()->count() > 0) { + return; + } + // Deleted the last item on the root node, shrink the height of the tree. + if (root()->leaf()) { + assert(size() == 0); + delete_leaf_node(root()); + mutable_root() = EmptyNode(); + rightmost_ = EmptyNode(); + } else { + node_type *child = root()->child(0); + child->make_root(); + delete_internal_node(root()); + mutable_root() = child; + } +} + +template <typename P> +template <typename IterType> +inline IterType btree<P>::internal_last(IterType iter) { + assert(iter.node != nullptr); + while (iter.position == iter.node->count()) { + iter.position = iter.node->position(); + iter.node = iter.node->parent(); + if (iter.node->leaf()) { + iter.node = nullptr; + break; + } + } + return iter; +} + +template <typename P> +template <typename... Args> +inline auto btree<P>::internal_emplace(iterator iter, Args &&... args) + -> iterator { + if (!iter.node->leaf()) { + // We can't insert on an internal node. Instead, we'll insert after the + // previous value which is guaranteed to be on a leaf node. + --iter; + ++iter.position; + } + const int max_count = iter.node->max_count(); + if (iter.node->count() == max_count) { + // Make room in the leaf for the new item. + if (max_count < kNodeValues) { + // Insertion into the root where the root is smaller than the full node + // size. Simply grow the size of the root node. + assert(iter.node == root()); + iter.node = + new_leaf_root_node(std::min(kNodeValues, 2 * max_count)); + iter.node->swap(root(), mutable_allocator()); + delete_leaf_node(root()); + mutable_root() = iter.node; + rightmost_ = iter.node; + } else { + rebalance_or_split(&iter); + } + } + iter.node->emplace_value(iter.position, mutable_allocator(), + std::forward<Args>(args)...); + ++size_; + return iter; +} + +template <typename P> +template <typename K> +inline auto btree<P>::internal_locate(const K &key) const + -> SearchResult<iterator, is_key_compare_to::value> { + return internal_locate_impl(key, is_key_compare_to()); +} + +template <typename P> +template <typename K> +inline auto btree<P>::internal_locate_impl( + const K &key, std::false_type /* IsCompareTo */) const + -> SearchResult<iterator, false> { + iterator iter(const_cast<node_type *>(root()), 0); + for (;;) { + iter.position = iter.node->lower_bound(key, key_comp()).value; + // NOTE: we don't need to walk all the way down the tree if the keys are + // equal, but determining equality would require doing an extra comparison + // on each node on the way down, and we will need to go all the way to the + // leaf node in the expected case. + if (iter.node->leaf()) { + break; + } + iter.node = iter.node->child(iter.position); + } + return {iter}; +} + +template <typename P> +template <typename K> +inline auto btree<P>::internal_locate_impl( + const K &key, std::true_type /* IsCompareTo */) const + -> SearchResult<iterator, true> { + iterator iter(const_cast<node_type *>(root()), 0); + for (;;) { + SearchResult<int, true> res = iter.node->lower_bound(key, key_comp()); + iter.position = res.value; + if (res.match == MatchKind::kEq) { + return {iter, MatchKind::kEq}; + } + if (iter.node->leaf()) { + break; + } + iter.node = iter.node->child(iter.position); + } + return {iter, MatchKind::kNe}; +} + +template <typename P> +template <typename K> +auto btree<P>::internal_lower_bound(const K &key) const -> iterator { + iterator iter(const_cast<node_type *>(root()), 0); + for (;;) { + iter.position = iter.node->lower_bound(key, key_comp()).value; + if (iter.node->leaf()) { + break; + } + iter.node = iter.node->child(iter.position); + } + return internal_last(iter); +} + +template <typename P> +template <typename K> +auto btree<P>::internal_upper_bound(const K &key) const -> iterator { + iterator iter(const_cast<node_type *>(root()), 0); + for (;;) { + iter.position = iter.node->upper_bound(key, key_comp()); + if (iter.node->leaf()) { + break; + } + iter.node = iter.node->child(iter.position); + } + return internal_last(iter); +} + +template <typename P> +template <typename K> +auto btree<P>::internal_find(const K &key) const -> iterator { + auto res = internal_locate(key); + if constexpr (res.has_match) { + if (res.IsEq()) { + return res.value; + } + } else { + const iterator iter = internal_last(res.value); + if (iter.node != nullptr && !compare_keys(key, iter.key())) { + return iter; + } + } + return {nullptr, 0}; +} + +template <typename P> +void btree<P>::internal_clear(node_type *node) { + if (!node->leaf()) { + for (int i = 0; i <= node->count(); ++i) { + internal_clear(node->child(i)); + } + delete_internal_node(node); + } else { + delete_leaf_node(node); + } +} + +template <typename P> +int btree<P>::internal_verify( + const node_type *node, const key_type *lo, const key_type *hi) const { + assert(node->count() > 0); + assert(node->count() <= node->max_count()); + if (lo) { + assert(!compare_keys(node->key(0), *lo)); + } + if (hi) { + assert(!compare_keys(*hi, node->key(node->count() - 1))); + } + for (int i = 1; i < node->count(); ++i) { + assert(!compare_keys(node->key(i), node->key(i - 1))); + } + int count = node->count(); + if (!node->leaf()) { + for (int i = 0; i <= node->count(); ++i) { + assert(node->child(i) != nullptr); + assert(node->child(i)->parent() == node); + assert(node->child(i)->position() == i); + count += internal_verify( + node->child(i), + (i == 0) ? lo : &node->key(i - 1), + (i == node->count()) ? hi : &node->key(i)); + } + } + return count; +} + +} // namespace btree::internal |