// 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).
#ifndef ABSL_CONTAINER_INTERNAL_BTREE_H_
#define ABSL_CONTAINER_INTERNAL_BTREE_H_
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <cstring>
#include <functional>
#include <iterator>
#include <limits>
#include <new>
#include <string>
#include <type_traits>
#include <utility>
#include "absl/base/macros.h"
#include "absl/container/internal/common.h"
#include "absl/container/internal/compressed_tuple.h"
#include "absl/container/internal/container_memory.h"
#include "absl/container/internal/layout.h"
#include "absl/memory/memory.h"
#include "absl/meta/type_traits.h"
#include "absl/strings/cord.h"
#include "absl/strings/string_view.h"
#include "absl/types/compare.h"
#include "absl/utility/utility.h"
namespace absl {
ABSL_NAMESPACE_BEGIN
namespace container_internal {
// A helper class that indicates if the Compare parameter is a key-compare-to
// comparator.
template <typename Compare, typename T>
using btree_is_key_compare_to =
std::is_convertible<absl::result_of_t<Compare(const T &, const T &)>,
absl::weak_ordering>;
struct StringBtreeDefaultLess {
using is_transparent = void;
StringBtreeDefaultLess() = default;
// Compatibility constructor.
StringBtreeDefaultLess(std::less<std::string>) {} // NOLINT
StringBtreeDefaultLess(std::less<string_view>) {} // NOLINT
absl::weak_ordering operator()(absl::string_view lhs,
absl::string_view rhs) const {
return compare_internal::compare_result_as_ordering(lhs.compare(rhs));
}
StringBtreeDefaultLess(std::less<absl::Cord>) {} // NOLINT
absl::weak_ordering operator()(const absl::Cord &lhs,
const absl::Cord &rhs) const {
return compare_internal::compare_result_as_ordering(lhs.Compare(rhs));
}
absl::weak_ordering operator()(const absl::Cord &lhs,
absl::string_view rhs) const {
return compare_internal::compare_result_as_ordering(lhs.Compare(rhs));
}
absl::weak_ordering operator()(absl::string_view lhs,
const absl::Cord &rhs) const {
return compare_internal::compare_result_as_ordering(-rhs.Compare(lhs));
}
};
struct StringBtreeDefaultGreater {
using is_transparent = void;
StringBtreeDefaultGreater() = default;
StringBtreeDefaultGreater(std::greater<std::string>) {} // NOLINT
StringBtreeDefaultGreater(std::greater<string_view>) {} // NOLINT
absl::weak_ordering operator()(absl::string_view lhs,
absl::string_view rhs) const {
return compare_internal::compare_result_as_ordering(rhs.compare(lhs));
}
StringBtreeDefaultGreater(std::greater<absl::Cord>) {} // NOLINT
absl::weak_ordering operator()(const absl::Cord &lhs,
const absl::Cord &rhs) const {
return compare_internal::compare_result_as_ordering(rhs.Compare(lhs));
}
absl::weak_ordering operator()(const absl::Cord &lhs,
absl::string_view rhs) const {
return compare_internal::compare_result_as_ordering(-lhs.Compare(rhs));
}
absl::weak_ordering operator()(absl::string_view lhs,
const absl::Cord &rhs) const {
return compare_internal::compare_result_as_ordering(rhs.Compare(lhs));
}
};
// A helper class to convert a boolean comparison into a three-way "compare-to"
// comparison that returns an `absl::weak_ordering`. This helper
// class is specialized for less<std::string>, greater<std::string>,
// less<string_view>, greater<string_view>, less<absl::Cord>, and
// greater<absl::Cord>.
//
// key_compare_to_adapter is provided so that btree users
// automatically get the more efficient compare-to code when using common
// Abseil string types with common comparison functors.
// These string-like specializations also turn on heterogeneous lookup by
// default.
template <typename Compare>
struct key_compare_to_adapter {
using type = Compare;
};
template <>
struct key_compare_to_adapter<std::less<std::string>> {
using type = StringBtreeDefaultLess;
};
template <>
struct key_compare_to_adapter<std::greater<std::string>> {
using type = StringBtreeDefaultGreater;
};
template <>
struct key_compare_to_adapter<std::less<absl::string_view>> {
using type = StringBtreeDefaultLess;
};
template <>
struct key_compare_to_adapter<std::greater<absl::string_view>> {
using type = StringBtreeDefaultGreater;
};
template <>
struct key_compare_to_adapter<std::less<absl::Cord>> {
using type = StringBtreeDefaultLess;
};
template <>
struct key_compare_to_adapter<std::greater<absl::Cord>> {
using type = StringBtreeDefaultGreater;
};
// Detects an 'absl_btree_prefer_linear_node_search' member. This is
// a protocol used as an opt-in or opt-out of linear search.
//
// For example, this would be useful for key types that wrap an integer
// and define their own cheap operator<(). For example:
//
// class K {
// public:
// using absl_btree_prefer_linear_node_search = std::true_type;
// ...
// private:
// friend bool operator<(K a, K b) { return a.k_ < b.k_; }
// int k_;
// };
//
// btree_map<K, V> m; // Uses linear search
//
// If T has the preference tag, then it has a preference.
// Btree will use the tag's truth value.
template <typename T, typename = void>
struct has_linear_node_search_preference : std::false_type {};
template <typename T, typename = void>
struct prefers_linear_node_search : std::false_type {};
template <typename T>
struct has_linear_node_search_preference<
T, absl::void_t<typename T::absl_btree_prefer_linear_node_search>>
: std::true_type {};
template <typename T>
struct prefers_linear_node_search<
T, absl::void_t<typename T::absl_btree_prefer_linear_node_search>>
: T::absl_btree_prefer_linear_node_search {};
template <typename Key, typename Compare, typename Alloc, int TargetNodeSize,
bool Multi, typename SlotPolicy>
struct common_params {
// If Compare is a common comparator for a 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;
// True when key_compare has been adapted to StringBtreeDefault{Less,Greater}.
using is_key_compare_adapted =
absl::negation<std::is_same<key_compare, Compare>>;
// 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>;
using slot_policy = SlotPolicy;
using slot_type = typename slot_policy::slot_type;
using value_type = typename slot_policy::value_type;
using init_type = typename slot_policy::mutable_value_type;
using pointer = value_type *;
using const_pointer = const value_type *;
using reference = value_type &;
using const_reference = const value_type &;
enum {
kTargetNodeSize = TargetNodeSize,
// Upper bound for the available space for values. This is largest for leaf
// nodes, which have overhead of at least a pointer + 4 bytes (for storing
// 3 field_types and an enum).
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 =
absl::conditional_t<(kNodeValueSpace / sizeof(value_type) >
(std::numeric_limits<uint8_t>::max)()),
uint16_t, uint8_t>; // NOLINT
// The following methods are necessary for passing this struct as PolicyTraits
// for node_handle and/or are used within btree.
static value_type &element(slot_type *slot) {
return slot_policy::element(slot);
}
static const value_type &element(const slot_type *slot) {
return slot_policy::element(slot);
}
template <class... Args>
static void construct(Alloc *alloc, slot_type *slot, Args &&... args) {
slot_policy::construct(alloc, slot, std::forward<Args>(args)...);
}
static void construct(Alloc *alloc, slot_type *slot, slot_type *other) {
slot_policy::construct(alloc, slot, other);
}
static void destroy(Alloc *alloc, slot_type *slot) {
slot_policy::destroy(alloc, slot);
}
static void transfer(Alloc *alloc, slot_type *new_slot, slot_type *old_slot) {
construct(alloc, new_slot, old_slot);
destroy(alloc, old_slot);
}
static void swap(Alloc *alloc, slot_type *a, slot_type *b) {
slot_policy::swap(alloc, a, b);
}
static void move(Alloc *alloc, slot_type *src, slot_type *dest) {
slot_policy::move(alloc, src, dest);
}
};
// 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, Multi,
map_slot_policy<Key, Data>> {
using super_type = typename map_params::common_params;
using mapped_type = Data;
// This type allows us to move keys when it is safe to do so. It is safe
// for maps in which value_type and mutable_value_type are layout compatible.
using slot_policy = typename super_type::slot_policy;
using slot_type = typename super_type::slot_type;
using value_type = typename super_type::value_type;
using init_type = typename super_type::init_type;
using key_compare = typename super_type::key_compare;
// 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;
template <typename V>
static auto key(const V &value) -> decltype(value.first) {
return value.first;
}
static const Key &key(const slot_type *s) { return slot_policy::key(s); }
static const Key &key(slot_type *s) { return slot_policy::key(s); }
// For use in node handle.
static auto mutable_key(slot_type *s)
-> decltype(slot_policy::mutable_key(s)) {
return slot_policy::mutable_key(s);
}
static mapped_type &value(value_type *value) { return value->second; }
};
// This type implements the necessary functions from the
// absl::container_internal::slot_type interface.
template <typename Key>
struct set_slot_policy {
using slot_type = Key;
using value_type = Key;
using mutable_value_type = Key;
static value_type &element(slot_type *slot) { return *slot; }
static const value_type &element(const slot_type *slot) { return *slot; }
template <typename Alloc, class... Args>
static void construct(Alloc *alloc, slot_type *slot, Args &&... args) {
absl::allocator_traits<Alloc>::construct(*alloc, slot,
std::forward<Args>(args)...);
}
template <typename Alloc>
static void construct(Alloc *alloc, slot_type *slot, slot_type *other) {
absl::allocator_traits<Alloc>::construct(*alloc, slot, std::move(*other));
}
template <typename Alloc>
static void destroy(Alloc *alloc, slot_type *slot) {
absl::allocator_traits<Alloc>::destroy(*alloc, slot);
}
template <typename Alloc>
static void swap(Alloc * /*alloc*/, slot_type *a, slot_type *b) {
using std::swap;
swap(*a, *b);
}
template <typename Alloc>
static void move(Alloc * /*alloc*/, slot_type *src, slot_type *dest) {
*dest = std::move(*src);
}
};
// A parameters structure for holding the type parameters for a btree_set.
// Compare and Alloc should be nothrow copy-constructible.
template <typename Key, typename Compare, typename Alloc, int TargetNodeSize,
bool Multi>
struct set_params : common_params<Key, Compare, Alloc, TargetNodeSize, Multi,
set_slot_policy<Key>> {
using value_type = Key;
using slot_type = typename set_params::common_params::slot_type;
using value_compare = typename set_params::common_params::key_compare;
using is_map_container = std::false_type;
template <typename V>
static const V &key(const V &value) { return value; }
static const Key &key(const slot_type *slot) { return *slot; }
static const Key &key(slot_type *slot) { return *slot; }
};
// 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 K1, typename K2>
bool operator()(const K1 &a, const K2 &b) const {
// Returns true when a is not greater than b.
return !compare_internal::compare_result_as_less_than(comp(b, a));
}
private:
Compare comp;
};
enum class MatchKind : uint8_t { kEq, kNe };
template <typename V, bool IsCompareTo>
struct SearchResult {
V value;
MatchKind match;
static constexpr bool HasMatch() { return 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> {
SearchResult() {}
explicit SearchResult(V value) : value(value) {}
SearchResult(V value, MatchKind /*match*/) : value(value) {}
V value;
static constexpr bool HasMatch() { return 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 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 comparator expresses a preference, use that.
// - If the key expresses a preference, use that.
// - 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,
has_linear_node_search_preference<key_compare>::value
? prefers_linear_node_search<key_compare>::value
: has_linear_node_search_preference<key_type>::value
? prefers_linear_node_search<key_type>::value
: std::is_arithmetic<key_type>::value &&
(std::is_same<std::less<key_type>, key_compare>::value ||
std::is_same<std::greater<key_type>,
key_compare>::value)>;
// This class is organized by gtl::Layout as if it had the following
// structure:
// // A pointer to the node's parent.
// btree_node *parent;
//
// // The position of the node in the node's parent.
// field_type position;
// // The index of the first populated value in `values`.
// // TODO(ezb): right now, `start` is always 0. Update insertion/merge
// // logic to allow for floating storage within nodes.
// field_type start;
// // The index after the last populated value in `values`. Currently, this
// // is the same as the count of values.
// field_type finish;
// // The maximum number of values the node can hold. This is an integer in
// // [1, kNodeValues] for root leaf nodes, kNodeValues for non-root leaf
// // nodes, and kInternalNodeMaxCount (as a sentinel value) for internal
// // nodes (even though there are still kNodeValues values in the node).
// // TODO(ezb): make max_count use only 4 bits and record log2(capacity)
// // to free extra bits for is_root, etc.
// field_type max_count;
//
// // The array of values. The capacity is `max_count` for leaf nodes and
// // kNodeValues for internal nodes. Only the values in
// // [start, finish) have been initialized and are valid.
// slot_type values[max_count];
//
// // 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 0 children for leaf nodes and kNodeValues + 1 children for
// // internal nodes.
// btree_node *children[kNodeValues + 1];
//
// This class is only constructed by EmptyNodeType. Normally, pointers to the
// layout above are allocated, cast to btree_node*, and de-allocated within
// the btree implementation.
~btree_node() = default;
btree_node(btree_node const &) = delete;
btree_node &operator=(btree_node const &) = delete;
// Public for EmptyNodeType.
constexpr static size_type Alignment() {
static_assert(LeafLayout(1).Alignment() == InternalLayout().Alignment(),
"Alignment of all nodes must be equal.");
return InternalLayout().Alignment();
}
protected:
btree_node() = default;
private:
using layout_type = absl::container_internal::Layout<btree_node *, field_type,
slot_type, btree_node *>;
constexpr static size_type SizeWithNValues(size_type n) {
return layout_type(/*parent*/ 1,
/*position, start, finish, max_count*/ 4,
/*values*/ n,
/*children*/ 0)
.AllocSize();
}
// 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);
}
enum {
kTargetNodeSize = params_type::kTargetNodeSize,
kNodeTargetValues = NodeTargetValues(0, params_type::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).
kNodeValues = kNodeTargetValues >= 3 ? kNodeTargetValues : 3,
// The node is internal (i.e. is not a leaf node) if and only if `max_count`
// has this value.
kInternalNodeMaxCount = 0,
};
// Leaves can have less than kNodeValues values.
constexpr static layout_type LeafLayout(const int max_values = kNodeValues) {
return layout_type(/*parent*/ 1,
/*position, start, finish, max_count*/ 4,
/*values*/ max_values,
/*children*/ 0);
}
constexpr static layout_type InternalLayout() {
return layout_type(/*parent*/ 1,
/*position, start, finish, max_count*/ 4,
/*values*/ kNodeValues,
/*children*/ kNodeValues + 1);
}
constexpr static size_type LeafSize(const int max_values = kNodeValues) {
return LeafLayout(max_values).AllocSize();
}
constexpr static size_type InternalSize() {
return InternalLayout().AllocSize();
}
// N is the index of the type in the Layout definition.
// ElementType<N> is the Nth type in the Layout definition.
template <size_type N>
inline typename layout_type::template ElementType<N> *GetField() {
// We assert that we don't read from values that aren't there.
assert(N < 3 || !leaf());
return InternalLayout().template Pointer<N>(reinterpret_cast<char *>(this));
}
template <size_type N>
inline const typename layout_type::template ElementType<N> *GetField() const {
assert(N < 3 || !leaf());
return InternalLayout().template Pointer<N>(
reinterpret_cast<const char *>(this));
}
void set_parent(btree_node *p) { *GetField<0>() = p; }
field_type &mutable_finish() { return GetField<1>()[2]; }
slot_type *slot(int i) { return &GetField<2>()[i]; }
slot_type *start_slot() { return slot(start()); }
slot_type *finish_slot() { return slot(finish()); }
const slot_type *slot(int i) const { return &GetField<2>()[i]; }
void set_position(field_type v) { GetField<1>()[0] = v; }
void set_start(field_type v) { GetField<1>()[1] = v; }
void set_finish(field_type v) { GetField<1>()[2] = v; }
// This method is only called by the node init methods.
void set_max_count(field_type v) { GetField<1>()[3] = v; }
public:
// Whether this is a leaf node or not. This value doesn't change after the
// node is created.
bool leaf() const { return GetField<1>()[3] != kInternalNodeMaxCount; }
// Getter for the position of this node in its parent.
field_type position() const { return GetField<1>()[0]; }
// Getter for the offset of the first value in the `values` array.
field_type start() const {
// TODO(ezb): when floating storage is implemented, return GetField<1>()[1];
assert(GetField<1>()[1] == 0);
return 0;
}
// Getter for the offset after the last value in the `values` array.
field_type finish() const { return GetField<1>()[2]; }
// Getters for the number of values stored in this node.
field_type count() const {
assert(finish() >= start());
return finish() - start();
}
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<1>()[3];
return max_count == field_type{kInternalNodeMaxCount}
? field_type{kNodeValues}
: max_count;
}
// Getter for the parent of this node.
btree_node *parent() const { return *GetField<0>(); }
// 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<3>()[i]; }
btree_node *start_child() const { return child(start()); }
btree_node *&mutable_child(int i) { return GetField<3>()[i]; }
void clear_child(int i) {
absl::container_internal::SanitizerPoisonObject(&mutable_child(i));
}
void set_child(int i, btree_node *c) {
absl::container_internal::SanitizerUnpoisonObject(&mutable_child(i));
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, start(), finish(), 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, start(), finish(), 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 SearchResult<int, false>{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 absl::weak_ordering 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 SearchResult<int, false>{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 (is_multi_container::value) {
MatchKind exact_match = MatchKind::kNe;
while (s != e) {
const int mid = (s + e) >> 1;
const absl::weak_ordering 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 absl::weak_ordering 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 values at positions [i, i + to_erase), shifting all existing
// values and children after that range to the left by to_erase. Clears all
// children between [i, i + to_erase).
void remove_values(field_type i, field_type to_erase, allocator_type *alloc);
// Rebalances a node with its right sibling.
void rebalance_right_to_left(int to_move, btree_node *right,
allocator_type *alloc);
void rebalance_left_to_right(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(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, and deleting the src node.
void merge(btree_node *src, allocator_type *alloc);
// Node allocation/deletion routines.
void init_leaf(btree_node *parent, int max_count) {
set_parent(parent);
set_position(0);
set_start(0);
set_finish(0);
set_max_count(max_count);
absl::container_internal::SanitizerPoisonMemoryRegion(
start_slot(), max_count * sizeof(slot_type));
}
void init_internal(btree_node *parent) {
init_leaf(parent, kNodeValues);
// Set `max_count` to a sentinel value to indicate that this node is
// internal.
set_max_count(kInternalNodeMaxCount);
absl::container_internal::SanitizerPoisonMemoryRegion(
&mutable_child(start()), (kNodeValues + 1) * sizeof(btree_node *));
}
static void deallocate(const size_type size, btree_node *node,
allocator_type *alloc) {
absl::container_internal::Deallocate<Alignment()>(alloc, node, size);
}
// Deletes a node and all of its children.
static void clear_and_delete(btree_node *node, allocator_type *alloc);
private:
template <typename... Args>
void value_init(const field_type i, allocator_type *alloc, Args &&... args) {
absl::container_internal::SanitizerUnpoisonObject(slot(i));
params_type::construct(alloc, slot(i), std::forward<Args>(args)...);
}
void value_destroy(const field_type i, allocator_type *alloc) {
params_type::destroy(alloc, slot(i));
absl::container_internal::SanitizerPoisonObject(slot(i));
}
void value_destroy_n(const field_type i, const field_type n,
allocator_type *alloc) {
for (slot_type *s = slot(i), *end = slot(i + n); s != end; ++s) {
params_type::destroy(alloc, s);
absl::container_internal::SanitizerPoisonObject(s);
}
}
static void transfer(slot_type *dest, slot_type *src, allocator_type *alloc) {
absl::container_internal::SanitizerUnpoisonObject(dest);
params_type::transfer(alloc, dest, src);
absl::container_internal::SanitizerPoisonObject(src);
}
// Transfers value from slot `src_i` in `src_node` to slot `dest_i` in `this`.
void transfer(const size_type dest_i, const size_type src_i,
btree_node *src_node, allocator_type *alloc) {
transfer(slot(dest_i), src_node->slot(src_i), alloc);
}
// Transfers `n` values starting at value `src_i` in `src_node` into the
// values starting at value `dest_i` in `this`.
void transfer_n(const size_type n, const size_type dest_i,
const size_type src_i, btree_node *src_node,
allocator_type *alloc) {
for (slot_type *src = src_node->slot(src_i), *end = src + n,
*dest = slot(dest_i);
src != end; ++src, ++dest) {
transfer(dest, src, alloc);
}
}
// Same as above, except that we start at the end and work our way to the
// beginning.
void transfer_n_backward(const size_type n, const size_type dest_i,
const size_type src_i, btree_node *src_node,
allocator_type *alloc) {
for (slot_type *src = src_node->slot(src_i + n - 1), *end = src - n,
*dest = slot(dest_i + n - 1);
src != end; --src, --dest) {
transfer(dest, src, alloc);
}
}
template <typename P>
friend class btree;
template <typename N, typename R, typename P>
friend struct btree_iterator;
friend class BtreeNodePeer;
};
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() : node(nullptr), position(-1) {}
explicit btree_iterator(Node *n) : node(n), position(n->start()) {}
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,
absl::enable_if_t<
std::is_same<btree_iterator<N, R, P>, iterator>::value &&
std::is_same<btree_iterator, const_iterator>::value,
int> = 0>
btree_iterator(const btree_iterator<N, R, P> &other) // NOLINT
: node(other.node), position(other.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,
absl::enable_if_t<
std::is_same<btree_iterator<N, R, P>, const_iterator>::value &&
std::is_same<btree_iterator, iterator>::value,
int> = 0>
explicit btree_iterator(const btree_iterator<N, R, P> &other)
: node(const_cast<node_type *>(other.node)), position(other.position) {}
// Increment/decrement the iterator.
void increment() {
if (node->leaf() && ++position < node->finish()) {
return;
}
increment_slow();
}
void increment_slow();
void decrement() {
if (node->leaf() && --position >= node->start()) {
return;
}
decrement_slow();
}
void decrement_slow();
public:
bool operator==(const iterator &other) const {
return node == other.node && position == other.position;
}
bool operator==(const const_iterator &other) const {
return node == other.node && position == other.position;
}
bool operator!=(const iterator &other) const {
return node != other.node || position != other.position;
}
bool operator!=(const const_iterator &other) const {
return node != other.node || position != other.position;
}
// Accessors for the key/value the iterator is pointing at.
reference operator*() const {
ABSL_HARDENING_ASSERT(node != nullptr);
ABSL_HARDENING_ASSERT(node->start() <= position);
ABSL_HARDENING_ASSERT(node->finish() > position);
return node->value(position);
}
pointer operator->() const { return &operator*(); }
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;
template <typename TreeType, typename CheckerType>
friend class base_checker;
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;
// The position within the node of the tree the iterator is pointing at.
// NOTE: this is an int rather than a field_type because iterators can point
// to invalid positions (such as -1) in certain circumstances.
int position;
};
template <typename Params>
class btree {
using node_type = btree_node<Params>;
using is_key_compare_to = typename Params::is_key_compare_to;
using init_type = typename Params::init_type;
using field_type = typename node_type::field_type;
using is_multi_container = typename Params::is_multi_container;
using is_key_compare_adapted = typename Params::is_key_compare_adapted;
// 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 start = 0;
field_type finish = 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;
#ifdef _MSC_VER
// MSVC has constexpr code generations bugs here.
EmptyNodeType() : parent(this) {}
#else
constexpr EmptyNodeType(node_type *p) : parent(p) {}
#endif
};
static node_type *EmptyNode() {
#ifdef _MSC_VER
static EmptyNodeType *empty_node = new EmptyNodeType;
// This assert fails on some other construction methods.
assert(empty_node->parent == empty_node);
return empty_node;
#else
static constexpr EmptyNodeType empty_node(
const_cast<EmptyNodeType *>(&empty_node));
return const_cast<EmptyNodeType *>(&empty_node);
#endif
}
enum : uint32_t {
kNodeValues = node_type::kNodeValues,
kMinNodeValues = kNodeValues / 2,
};
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 &other) {
leaf_nodes += other.leaf_nodes;
internal_nodes += other.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>;
using node_handle_type = node_handle<Params, Params, allocator_type>;
// Internal types made public for use by btree_container types.
using params_type = Params;
using slot_type = typename Params::slot_type;
private:
// For use in copy_or_move_values_in_order.
const value_type &maybe_move_from_iterator(const_iterator it) { return *it; }
value_type &&maybe_move_from_iterator(iterator it) { return std::move(*it); }
// Copies or moves (depending on the template parameter) the values in
// other into this btree in their order in other. 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 &other);
// 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)
: root_(comp, alloc, EmptyNode()), rightmost_(EmptyNode()), size_(0) {}
btree(const btree &other) : btree(other, other.allocator()) {}
btree(const btree &other, const allocator_type &alloc)
: btree(other.key_comp(), alloc) {
copy_or_move_values_in_order(other);
}
btree(btree &&other) noexcept
: root_(std::move(other.root_)),
rightmost_(absl::exchange(other.rightmost_, EmptyNode())),
size_(absl::exchange(other.size_, 0)) {
other.mutable_root() = EmptyNode();
}
btree(btree &&other, const allocator_type &alloc)
: btree(other.key_comp(), alloc) {
if (alloc == other.allocator()) {
swap(other);
} else {
// Move values from `other` one at a time when allocators are different.
copy_or_move_values_in_order(other);
}
}
~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 other to *this.
btree &operator=(const btree &other);
btree &operator=(btree &&other) noexcept;
iterator begin() { return iterator(leftmost()); }
const_iterator begin() const { return const_iterator(leftmost()); }
iterator end() { return iterator(rightmost_, rightmost_->finish()); }
const_iterator end() const {
return const_iterator(rightmost_, rightmost_->finish());
}
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).value);
}
template <typename K>
const_iterator lower_bound(const K &key) const {
return internal_end(internal_lower_bound(key).value);
}
// 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 of the
// pair is equal to upper_bound(key).
template <typename K>
std::pair<iterator, iterator> equal_range(const K &key);
template <typename K>
std::pair<const_iterator, const_iterator> equal_range(const K &key) const {
return const_cast<btree *>(this)->equal_range(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 K, typename... Args>
std::pair<iterator, bool> insert_unique(const K &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 K, typename... Args>
std::pair<iterator, bool> insert_hint_unique(iterator position,
const K &key,
Args &&... args);
// Insert a range of values into the btree.
// Note: the first overload avoids constructing a value_type if the key
// already exists in the btree.
template <typename InputIterator,
typename = decltype(std::declval<const key_compare &>()(
params_type::key(*std::declval<InputIterator>()),
std::declval<const key_type &>()))>
void insert_iterator_unique(InputIterator b, InputIterator e, int);
// We need the second overload for cases in which we need to construct a
// value_type in order to compare it with the keys already in the btree.
template <typename InputIterator>
void insert_iterator_unique(InputIterator b, InputIterator e, char);
// 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_range(iterator begin, iterator end);
// 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));
}
// Clear the btree, deleting all of the values it contains.
void clear();
// Swaps the contents of `this` and `other`.
void swap(btree &other);
const key_compare &key_comp() const noexcept {
return root_.template get<0>();
}
template <typename K1, typename K2>
bool compare_keys(const K1 &a, const K2 &b) const {
return compare_internal::compare_result_as_less_than(key_comp()(a, b));
}
value_compare value_comp() const { return value_compare(key_comp()); }
// 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_.template get<2>(); }
const node_type *root() const { return root_.template get<2>(); }
node_type *&mutable_root() noexcept { return root_.template get<2>(); }
key_compare *mutable_key_comp() noexcept { return &root_.template get<0>(); }
// The leftmost node is stored as the parent of the root node.
node_type *leftmost() { return root()->parent(); }
const node_type *leftmost() const { return root()->parent(); }
// Allocator routines.
allocator_type *mutable_allocator() noexcept {
return &root_.template get<1>();
}
const allocator_type &allocator() const noexcept {
return root_.template get<1>();
}
// Allocates a correctly aligned node of at least size bytes using the
// allocator.
node_type *allocate(const size_type size) {
return reinterpret_cast<node_type *>(
absl::container_internal::Allocate<node_type::Alignment()>(
mutable_allocator(), size));
}
// Node creation/deletion routines.
node_type *new_internal_node(node_type *parent) {
node_type *n = allocate(node_type::InternalSize());
n->init_internal(parent);
return n;
}
node_type *new_leaf_node(node_type *parent) {
node_type *n = allocate(node_type::LeafSize());
n->init_leaf(parent, kNodeValues);
return n;
}
node_type *new_leaf_root_node(const int max_count) {
node_type *n = allocate(node_type::LeafSize(max_count));
n->init_leaf(/*parent=*/n, max_count);
return n;
}
// Deletion helper routines.
iterator rebalance_after_delete(iterator iter);
// 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 such
// as iter.position == iter.node->finish(). 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, unless there is an exact match - in which case, the
// result may not be on a leaf. When there's a three-way comparator, we can
// return whether there was an exact match. This 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;
// Internal routine which implements lower_bound().
template <typename K>
SearchResult<iterator, is_key_compare_to::value> 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;
// 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 = node->start(); i <= node->finish(); ++i) {
res += internal_stats(node->child(i));
}
return res;
}
// We use compressed tuple in order to save space because key_compare and
// allocator_type are usually empty.
absl::container_internal::CompressedTuple<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 >= start());
assert(i <= finish());
// Shift old values to create space for new value and then construct it in
// place.
if (i < finish()) {
transfer_n_backward(finish() - i, /*dest_i=*/i + 1, /*src_i=*/i, this,
alloc);
}
value_init(i, alloc, std::forward<Args>(args)...);
set_finish(finish() + 1);
if (!leaf() && finish() > i + 1) {
for (int j = finish(); j > i + 1; --j) {
set_child(j, child(j - 1));
}
clear_child(i + 1);
}
}
template <typename P>
inline void btree_node<P>::remove_values(const field_type i,
const field_type to_erase,
allocator_type *alloc) {
// Transfer values after the removed range into their new places.
value_destroy_n(i, to_erase, alloc);
const field_type orig_finish = finish();
const field_type src_i = i + to_erase;
transfer_n(orig_finish - src_i, i, src_i, this, alloc);
if (!leaf()) {
// Delete all children between begin and end.
for (int j = 0; j < to_erase; ++j) {
clear_and_delete(child(i + j + 1), alloc);
}
// Rotate children after end into new positions.
for (int j = i + to_erase + 1; j <= orig_finish; ++j) {
set_child(j - to_erase, child(j));
clear_child(j);
}
}
set_finish(orig_finish - 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.
transfer(finish(), position(), parent(), alloc);
// 2) Move the (to_move - 1) values from the right node to the left node.
transfer_n(to_move - 1, finish() + 1, right->start(), right, alloc);
// 3) Move the new delimiting value to the parent from the right node.
parent()->transfer(position(), right->start() + to_move - 1, right, alloc);
// 4) Shift the values in the right node to their correct positions.
right->transfer_n(right->count() - to_move, right->start(),
right->start() + to_move, right, alloc);
if (!leaf()) {
// Move the child pointers from the right to the left node.
for (int i = 0; i < to_move; ++i) {
init_child(finish() + i + 1, right->child(i));
}
for (int i = right->start(); i <= right->finish() - 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 `finish` on the left and right nodes.
set_finish(finish() + to_move);
right->set_finish(right->finish() - 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.
// 1) Shift existing values in the right node to their correct positions.
right->transfer_n_backward(right->count(), right->start() + to_move,
right->start(), right, alloc);
// 2) Move the delimiting value in the parent to the right node.
right->transfer(right->start() + to_move - 1, position(), parent(), alloc);
// 3) Move the (to_move - 1) values from the left node to the right node.
right->transfer_n(to_move - 1, right->start(), finish() - (to_move - 1), this,
alloc);
// 4) Move the new delimiting value to the parent from the left node.
parent()->transfer(position(), finish() - to_move, this, alloc);
if (!leaf()) {
// Move the child pointers from the left to the right node.
for (int i = right->finish(); i >= right->start(); --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(finish() - to_move + i));
clear_child(finish() - to_move + i);
}
}
// Fixup the counts on the left and right nodes.
set_finish(finish() - to_move);
right->set_finish(right->finish() + 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 == start()) {
dest->set_finish(dest->start() + finish() - 1);
} else if (insert_position == kNodeValues) {
dest->set_finish(dest->start());
} else {
dest->set_finish(dest->start() + count() / 2);
}
set_finish(finish() - dest->count());
assert(count() >= 1);
// Move values from the left sibling to the right sibling.
dest->transfer_n(dest->count(), dest->start(), finish(), this, alloc);
// The split key is the largest value in the left sibling.
--mutable_finish();
parent()->emplace_value(position(), alloc, finish_slot());
value_destroy(finish(), alloc);
parent()->init_child(position() + 1, dest);
if (!leaf()) {
for (int i = dest->start(), j = finish() + 1; i <= dest->finish();
++i, ++j) {
assert(child(j) != nullptr);
dest->init_child(i, child(j));
clear_child(j);
}
}
}
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(finish(), alloc, parent()->slot(position()));
// Move the values from the right to the left node.
transfer_n(src->count(), finish() + 1, src->start(), src, alloc);
if (!leaf()) {
// Move the child pointers from the right to the left node.
for (int i = src->start(), j = finish() + 1; i <= src->finish(); ++i, ++j) {
init_child(j, src->child(i));
src->clear_child(i);
}
}
// Fixup `finish` on the src and dest nodes.
set_finish(start() + 1 + count() + src->count());
src->set_finish(src->start());
// Remove the value on the parent node and delete the src node.
parent()->remove_values(position(), /*to_erase=*/1, alloc);
}
template <typename P>
void btree_node<P>::clear_and_delete(btree_node *node, allocator_type *alloc) {
if (node->leaf()) {
node->value_destroy_n(node->start(), node->count(), alloc);
deallocate(LeafSize(node->max_count()), node, alloc);
return;
}
if (node->count() == 0) {
deallocate(InternalSize(), node, alloc);
return;
}
// The parent of the root of the subtree we are deleting.
btree_node *delete_root_parent = node->parent();
// Navigate to the leftmost leaf under node, and then delete upwards.
while (!node->leaf()) node = node->start_child();
// Use `int` because `pos` needs to be able to hold `kNodeValues+1`, which
// isn't guaranteed to be a valid `field_type`.
int pos = node->position();
btree_node *parent = node->parent();
for (;;) {
// In each iteration of the next loop, we delete one leaf node and go right.
assert(pos <= parent->finish());
do {
node = parent->child(pos);
if (!node->leaf()) {
// Navigate to the leftmost leaf under node.
while (!node->leaf()) node = node->start_child();
pos = node->position();
parent = node->parent();
}
node->value_destroy_n(node->start(), node->count(), alloc);
deallocate(LeafSize(node->max_count()), node, alloc);
++pos;
} while (pos <= parent->finish());
// Once we've deleted all children of parent, delete parent and go up/right.
assert(pos > parent->finish());
do {
node = parent;
pos = node->position();
parent = node->parent();
node->value_destroy_n(node->start(), node->count(), alloc);
deallocate(InternalSize(), node, alloc);
if (parent == delete_root_parent) return;
++pos;
} while (pos > parent->finish());
}
}
////
// btree_iterator methods
template <typename N, typename R, typename P>
void btree_iterator<N, R, P>::increment_slow() {
if (node->leaf()) {
assert(position >= node->finish());
btree_iterator save(*this);
while (position == node->finish() && !node->is_root()) {
assert(node->parent()->child(node->position()) == node);
position = node->position();
node = node->parent();
}
// TODO(ezb): assert we aren't incrementing end() instead of handling.
if (position == node->finish()) {
*this = save;
}
} else {
assert(position < node->finish());
node = node->child(position + 1);
while (!node->leaf()) {
node = node->start_child();
}
position = node->start();
}
}
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 < node->start() && !node->is_root()) {
assert(node->parent()->child(node->position()) == node);
position = node->position() - 1;
node = node->parent();
}
// TODO(ezb): assert we aren't decrementing begin() instead of handling.
if (position < node->start()) {
*this = save;
}
} else {
assert(position >= node->start());
node = node->child(position);
while (!node->leaf()) {
node = node->child(node->finish());
}
position = node->finish() - 1;
}
}
////
// btree methods
template <typename P>
template <typename Btree>
void btree<P>::copy_or_move_values_in_order(Btree &other) {
static_assert(std::is_same<btree, Btree>::value ||
std::is_same<const btree, Btree>::value,
"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 = other.begin();
if (iter == other.end()) return;
insert_multi(maybe_move_from_iterator(iter));
++iter;
for (; iter != other.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<key_compare>::value,
"Key comparison must be nothrow copy constructible");
static_assert(std::is_nothrow_copy_constructible<allocator_type>::value,
"Allocator must be nothrow copy constructible");
static_assert(type_traits_internal::is_trivially_copyable<iterator>::value,
"iterator not trivially copyable.");
// Note: We assert that kTargetValues, which is computed from
// Params::kTargetNodeSize, must fit the node_type::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 =
absl::result_of_t<key_compare(key_type, key_type)>;
static_assert(
std::is_same<compare_result_type, bool>::value ||
std::is_convertible<compare_result_type, absl::weak_ordering>::value,
"key comparison function must return absl::{weak,strong}_ordering 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>
template <typename K>
auto btree<P>::equal_range(const K &key) -> std::pair<iterator, iterator> {
const SearchResult<iterator, is_key_compare_to::value> res =
internal_lower_bound(key);
const iterator lower = internal_end(res.value);
if (res.HasMatch() ? !res.IsEq()
: lower == end() || compare_keys(key, lower.key())) {
return {lower, lower};
}
const iterator next = std::next(lower);
// When the comparator is heterogeneous, we can't assume that comparison with
// non-`key_type` will be equivalent to `key_type` comparisons so there
// could be multiple equivalent keys even in a unique-container. But for
// heterogeneous comparisons from the default string adapted comparators, we
// don't need to worry about this.
if (!is_multi_container::value &&
(std::is_same<K, key_type>::value || is_key_compare_adapted::value)) {
// The next iterator after lower must point to a key greater than `key`.
// Note: if this assert fails, then it may indicate that the comparator does
// not meet the equivalence requirements for Compare
// (see https://en.cppreference.com/w/cpp/named_req/Compare).
assert(next == end() || compare_keys(key, next.key()));
return {lower, next};
}
// Try once more to avoid the call to upper_bound() if there's only one
// equivalent key. This should prevent all calls to upper_bound() in cases of
// unique-containers with heterogeneous comparators in which all comparison
// operators have the same equivalence classes.
if (next == end() || compare_keys(key, next.key())) return {lower, next};
// In this case, we need to call upper_bound() to avoid worst case O(N)
// behavior if we were to iterate over equal keys.
return {lower, upper_bound(key)};
}
template <typename P>
template <typename K, typename... Args>
auto btree<P>::insert_unique(const K &key, Args &&... args)
-> std::pair<iterator, bool> {
if (empty()) {
mutable_root() = rightmost_ = new_leaf_root_node(1);
}
SearchResult<iterator, is_key_compare_to::value> res = internal_locate(key);
iterator iter = res.value;
if (res.HasMatch()) {
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 K, typename... Args>
inline auto btree<P>::insert_hint_unique(iterator position, const K &key,
Args &&... args)
-> std::pair<iterator, bool> {
if (!empty()) {
if (position == end() || compare_keys(key, position.key())) {
if (position == begin() || compare_keys(std::prev(position).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, typename>
void btree<P>::insert_iterator_unique(InputIterator b, InputIterator e, int) {
for (; b != e; ++b) {
insert_hint_unique(end(), params_type::key(*b), *b);
}
}
template <typename P>
template <typename InputIterator>
void btree<P>::insert_iterator_unique(InputIterator b, InputIterator e, char) {
for (; b != e; ++b) {
init_type value(*b);
insert_hint_unique(end(), params_type::key(value), std::move(value));
}
}
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)) {
if (position == begin() ||
!compare_keys(key, std::prev(position).key())) {
// prev.key() <= key <= position.key()
return internal_emplace(position, std::forward<ValueType>(v));
}
} else {
++position;
if (position == end() || !compare_keys(position.key(), key)) {
// {original `position`}.key() < key < {current `position`}.key()
return internal_emplace(position, 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 &other) -> btree & {
if (this != &other) {
clear();
*mutable_key_comp() = other.key_comp();
if (absl::allocator_traits<
allocator_type>::propagate_on_container_copy_assignment::value) {
*mutable_allocator() = other.allocator();
}
copy_or_move_values_in_order(other);
}
return *this;
}
template <typename P>
auto btree<P>::operator=(btree &&other) noexcept -> btree & {
if (this != &other) {
clear();
using std::swap;
if (absl::allocator_traits<
allocator_type>::propagate_on_container_copy_assignment::value) {
// Note: `root_` also contains the allocator and the key comparator.
swap(root_, other.root_);
swap(rightmost_, other.rightmost_);
swap(size_, other.size_);
} else {
if (allocator() == other.allocator()) {
swap(mutable_root(), other.mutable_root());
swap(*mutable_key_comp(), *other.mutable_key_comp());
swap(rightmost_, other.rightmost_);
swap(size_, other.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 `other` and `this` to have `other`s key
// comparator while moving the values so we can't swap the key
// comparators.
*mutable_key_comp() = other.key_comp();
copy_or_move_values_in_order(other);
}
}
}
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_values()
// 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_values(iter.position, /*to_erase=*/1, 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->finish()) {
res.position = res.node->finish() - 1;
++res;
}
return res;
}
template <typename P>
auto btree<P>::erase_range(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) {
assert(end.position > begin.position);
begin.node->remove_values(begin.position, end.position - begin.position,
mutable_allocator());
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->finish() - begin.position;
const size_type to_erase =
(std::min)(remaining_to_erase, remaining_in_node);
begin.node->remove_values(begin.position, to_erase, mutable_allocator());
size_ -= to_erase;
begin = rebalance_after_delete(begin);
} else {
begin = erase(begin);
}
}
return {count, begin};
}
template <typename P>
void btree<P>::clear() {
if (!empty()) {
node_type::clear_and_delete(root(), mutable_allocator());
}
mutable_root() = EmptyNode();
rightmost_ = EmptyNode();
size_ = 0;
}
template <typename P>
void btree<P>::swap(btree &other) {
using std::swap;
if (absl::allocator_traits<
allocator_type>::propagate_on_container_swap::value) {
// Note: `root_` also contains the allocator and the key comparator.
swap(root_, other.root_);
} else {
// It's undefined behavior if the allocators are unequal here.
assert(allocator() == other.allocator());
swap(mutable_root(), other.mutable_root());
swap(*mutable_key_comp(), *other.mutable_key_comp());
}
swap(rightmost_, other.rightmost_);
swap(size_, other.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()->finish())).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() > parent->start()) {
// 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 < static_cast<int>(kNodeValues)));
to_move = (std::max)(1, to_move);
if (insert_position - to_move >= node->start() ||
left->count() + to_move < static_cast<int>(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 < node->start()) {
insert_position = insert_position + left->count() + 1;
node = left;
}
assert(node->count() < node->max_count());
return;
}
}
}
if (node->position() < parent->finish()) {
// 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 = (static_cast<int>(kNodeValues) - right->count()) /
(1 + (insert_position > node->start()));
to_move = (std::max)(1, to_move);
if (insert_position <= node->finish() - to_move ||
right->count() + to_move < static_cast<int>(kNodeValues)) {
node->rebalance_left_to_right(to_move, right, mutable_allocator());
if (insert_position > node->finish()) {
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(parent->start(), root());
mutable_root() = parent;
// If the former root was a leaf node, then it's now the rightmost node.
assert(!parent->start_child()->leaf() ||
parent->start_child() == 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->finish()) {
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 (rightmost_ == right) rightmost_ = left;
}
template <typename P>
bool btree<P>::try_merge_or_rebalance(iterator *iter) {
node_type *parent = iter->node->parent();
if (iter->node->position() > parent->start()) {
// Try merging with our left sibling.
node_type *left = parent->child(iter->node->position() - 1);
assert(left->max_count() == kNodeValues);
if (1U + 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->finish()) {
// Try merging with our right sibling.
node_type *right = parent->child(iter->node->position() + 1);
assert(right->max_count() == kNodeValues);
if (1U + 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 > iter->node->start())) {
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() > parent->start()) {
// 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->finish())) {
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() {
node_type *orig_root = root();
if (orig_root->count() > 0) {
return;
}
// Deleted the last item on the root node, shrink the height of the tree.
if (orig_root->leaf()) {
assert(size() == 0);
mutable_root() = rightmost_ = EmptyNode();
} else {
node_type *child = orig_root->start_child();
child->make_root();
mutable_root() = child;
}
node_type::clear_and_delete(orig_root, mutable_allocator());
}
template <typename P>
template <typename IterType>
inline IterType btree<P>::internal_last(IterType iter) {
assert(iter.node != nullptr);
while (iter.position == iter.node->finish()) {
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 field_type max_count = iter.node->max_count();
allocator_type *alloc = mutable_allocator();
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<int>)(kNodeValues, 2 * max_count));
// Transfer the values from the old root to the new root.
node_type *old_root = root();
node_type *new_root = iter.node;
new_root->transfer_n(old_root->count(), new_root->start(),
old_root->start(), old_root, alloc);
new_root->set_finish(old_root->finish());
old_root->set_finish(old_root->start());
node_type::clear_and_delete(old_root, alloc);
mutable_root() = rightmost_ = new_root;
} else {
rebalance_or_split(&iter);
}
}
iter.node->emplace_value(iter.position, alloc, 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> {
iterator iter(const_cast<node_type *>(root()));
for (;;) {
SearchResult<int, is_key_compare_to::value> res =
iter.node->lower_bound(key, key_comp());
iter.position = res.value;
if (res.IsEq()) {
return {iter, MatchKind::kEq};
}
// Note: in the non-key-compare-to case, 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);
}
// Note: in the non-key-compare-to case, the key may actually be equivalent
// here (and the MatchKind::kNe is ignored).
return {iter, MatchKind::kNe};
}
template <typename P>
template <typename K>
auto btree<P>::internal_lower_bound(const K &key) const
-> SearchResult<iterator, is_key_compare_to::value> {
iterator iter(const_cast<node_type *>(root()));
SearchResult<int, is_key_compare_to::value> res;
bool seen_eq = false;
for (;;) {
res = iter.node->lower_bound(key, key_comp());
iter.position = res.value;
// TODO(ezb): we should be able to terminate early on IsEq() if there can't
// be multiple equivalent keys in container for this lookup type.
if (iter.node->leaf()) {
break;
}
seen_eq = seen_eq || res.IsEq();
iter.node = iter.node->child(iter.position);
}
if (res.IsEq()) return {iter, MatchKind::kEq};
return {internal_last(iter), seen_eq ? MatchKind::kEq : MatchKind::kNe};
}
template <typename P>
template <typename K>
auto btree<P>::internal_upper_bound(const K &key) const -> iterator {
iterator iter(const_cast<node_type *>(root()));
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 {
SearchResult<iterator, is_key_compare_to::value> res = internal_locate(key);
if (res.HasMatch()) {
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>
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(node->start()), *lo));
}
if (hi) {
assert(!compare_keys(*hi, node->key(node->finish() - 1)));
}
for (int i = node->start() + 1; i < node->finish(); ++i) {
assert(!compare_keys(node->key(i), node->key(i - 1)));
}
int count = node->count();
if (!node->leaf()) {
for (int i = node->start(); i <= node->finish(); ++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 == node->start() ? lo : &node->key(i - 1),
i == node->finish() ? hi : &node->key(i));
}
}
return count;
}
} // namespace container_internal
ABSL_NAMESPACE_END
} // namespace absl
#endif // ABSL_CONTAINER_INTERNAL_BTREE_H_
