text:
// 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 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>, 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
// google 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;
};

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;
  // 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);
  }
  static void move(Alloc *alloc, slot_type *first, slot_type *last,
                   slot_type *result) {
    slot_policy::move(alloc, first, last, result);
  }
};

// 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;

  static const Key &key(const value_type &value) { return value.first; }
  static const Key &key(const init_type &init) { return init.first; }
  static const Key &key(const slot_type *s) { return slot_policy::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);
  }

  template <typename Alloc>
  static void move(Alloc *alloc, slot_type *first, slot_type *last,
                   slot_type *result) {
    for (slot_type *src = first, *dest = result; src != last; ++src, ++dest)
      move(alloc, src, dest);
  }
};

// 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;

  static const Key &key(const value_type &value) { return value; }
  static const Key &key(const 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> {
  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 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<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 {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 {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 value at position i, shifting all existing values and children
  // at positions > i to the left by 1.
  void remove_value(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(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.
  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 *));
  }
  void destroy(allocator_type *alloc) {
    for (int i = start(); i < finish(); ++i) {
      value_destroy(i, alloc);
    }
  }

 public:
  // Exposed only for tests.
  static bool testonly_uses_linear_node_search() {
    return use_linear_search::value;
  }

 private:
  template <typename... Args>
  void value_init(const size_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 size_type i, allocator_type *alloc) {
    params_type::destroy(alloc, slot(i));
    absl::container_internal::SanitizerPoisonObject(slot(i));
  }

  // Transfers value from slot `src_i` in `src` to slot `dest_i` in `this`.
  void transfer(const size_type dest_i, const size_type src_i, btree_node *src,
                allocator_type *alloc) {
    absl::container_internal::SanitizerUnpoisonObject(slot(dest_i));
    params_type::transfer(alloc, slot(dest_i), src->slot(src_i));
    absl::container_internal::SanitizerPoisonObject(src->slot(src_i));
  }

  // Move n values starting at value i in this node into the values starting at
  // value j in dest_node.
  void uninitialized_move_n(const size_type n, const size_type i,
                            const size_type j, btree_node *dest_node,
                            allocator_type *alloc) {
    absl::container_internal::SanitizerUnpoisonMemoryRegion(
        dest_node->slot(j), n * sizeof(slot_type));
    for (slot_type *src = slot(i), *end = src + n, *dest = dest_node->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);
    }
  }

  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;

  // 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 {
    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);

  btree(const btree &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() {
    // 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));
  }
  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_range(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();

  // 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.
  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) {
    absl::container_internal::Deallocate<node_type::Alignment()>(
        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 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. 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 = node->start(); i <= node->finish(); ++i) {
      res += internal_stats(node->child(i));
    }
    return res;
  }

 public:
  // Exposed only for tests.
  static bool testonly_uses_linear_node_search() {
    return node_type::testonly_uses_linear_node_search();
  }

 private:
  // 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()) {
    value_init(finish(), alloc, slot(finish() - 1));
    for (size_type j = finish() - 1; j > i; --j)
      params_type::move(alloc, slot(j - 1), slot(j));
    value_destroy(i, 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_value(const int i, allocator_type *alloc) {
  if (!leaf() && finish() > i + 1) {
    assert(child(i + 1)->count() == 0);
    for (size_type j = i + 1; j < finish(); ++j) {
      set_child(j, child(j + 1));
    }
    clear_child(finish());
  }

  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) {
  params_type::move(alloc, slot(i + to_erase), finish_slot(), slot(i));
  value_destroy_n(finish() - to_erase, to_erase, alloc);
  set_finish(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.
  value_init(finish(), 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, right->start(), finish() + 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.
  params_type::move(alloc, right->slot(to_move), right->finish_slot(),
                    right->start_slot());

  // 5) Destroy the now-empty to_move entries in the right node.
  right->value_destroy_n(right->finish() - 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(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.

  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->finish() - to_move,
                                right->finish(), right, alloc);
    for (slot_type *src = right->slot(right->finish() - to_move - 1),
                   *dest = right->slot(right->finish() - 1),
                   *end = right->start_slot();
         src >= end; --src, --dest) {
      params_type::move(alloc, src, dest);
    }

    // 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.
    params_type::move(alloc, slot(finish() - (to_move - 1)), finish_slot(),
                      right->start_slot());
  } 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(), right->start(),
                                right->start() + 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,
                         finish() - uninitialized_remaining, right->finish(),
                         right, alloc);
    params_type::move(alloc, slot(finish() - (to_move - 1)),
                      slot(finish() - uninitialized_remaining),
                      right->start_slot());
  }

  // 4) Move the new delimiting value to the parent from the left node.
  params_type::move(alloc, slot(finish() - to_move),
                    parent()->slot(position()));

  // 5) Destroy the now-empty to_move entries in the left node.
  value_destroy_n(finish() - to_move, to_move, 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.
  uninitialized_move_n(dest->count(), finish(), dest->start(), dest, alloc);

  // Destroy the now-empty entries in the left node.
  value_destroy_n(finish(), dest->count(), 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.
  src->uninitialized_move_n(src->count(), src->start(), finish() + 1, this,
                            alloc);

  // Destroy the now-empty entries in the right node.
  src->value_destroy_n(src->start(), src->count(), 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.
  parent()->remove_value(position(), alloc);
}

////
// 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>
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 &other)
    : btree(other.key_comp(), other.allocator()) {
  copy_or_move_values_in_order(&other);
}

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 (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... 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())) {
      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>
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)) {
      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_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->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) {
    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->finish() - 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->finish();
         ++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->finish() > begin.position);
  assert(begin.position + to_erase <= node->finish());

  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_range(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 &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 < kNodeValues));
        to_move = (std::max)(1, to_move);

        if (insert_position - to_move >= node->start() ||
            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 < 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 = (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 < 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 (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() > parent->start()) {
    // 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->finish()) {
    // 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 > 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() {
  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() = rightmost_ = EmptyNode();
  } else {
    node_type *child = root()->start_child();
    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->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 int 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;
      for (int i = old_root->start(), f = old_root->finish(); i < f; ++i) {
        new_root->transfer(i, i, old_root, alloc);
      }
      new_root->set_finish(old_root->finish());
      old_root->set_finish(old_root->start());
      delete_leaf_node(old_root);
      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> {
  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()));
  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()));
  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()));
  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()));
  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 (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>
void btree<P>::internal_clear(node_type *node) {
  if (!node->leaf()) {
    for (int i = node->start(); i <= node->finish(); ++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(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_


text:
.. _revent_files_creation:

revent
======

revent utility can be used to record and later play back a sequence of user
input events, such as key presses and touch screen taps. This is an alternative
to Android UI Automator for providing automation for workloads. ::

        usage:
                revent [record time file|replay file|info] [verbose]
                        record: stops after either return on stdin
                                or time (in seconds)
                                and stores in file
                        replay: replays eventlog from file
                        info:shows info about each event char device
                        any additional parameters make it verbose

Recording
---------

To record, transfer the revent binary to the device, then invoke ``revent
record``, giving it the time (in seconds) you want to record for, and the
file you want to record to (WA expects these files to have .revent
extension)::

        host$  adb push revent /data/local/revent
        host$  adb shell
        device#  cd /data/local
        device#  ./revent record 1000 my_recording.revent

The recording has now started and button presses, taps, etc you perform on the
device will go into the .revent file. The recording will stop after the
specified time period, and you can also stop it by hitting return in the adb
shell.

Replaying
---------

To replay a recorded file, run ``revent replay`` on the device, giving it the
file you want to replay::

        device#  ./revent replay my_recording.revent

Using revent With Workloads
---------------------------

Some workloads (pretty much all games) rely on recorded revents for their
execution. :class:`wlauto.common.GameWorkload`-derived workloads expect two
revent files -- one for performing the initial setup (navigating menus,
selecting game modes, etc), and one for the actual execution of the game.
Because revents are very device-specific\ [*]_, these two files would need to
be recorded for each device.

The files must be called ``<device name>.(setup|run).revent``, where
``<device name>`` is the name of your device (as defined by the ``name``
attribute of your device's class). WA will look for these files in two
places: ``<install dir>/wlauto/workloads/<workload name>/revent_files``
and ``~/.workload_automation/dependencies/<workload name>``. The first
location is primarily intended for revent files that come with WA (and if
you did a system-wide install, you'll need sudo to add files there), so it's
probably easier to use the second location for the files you record. Also,
if revent files for a workload exist in both locations, the files under
``~/.workload_automation/dependencies`` will be used in favor of those
installed with WA.

For example, if you wanted to run angrybirds workload on "Acme" device, you would
record the setup and run revent files using the method outlined in the section
above and then pull them for the devices into the following locations::

        ~/workload_automation/dependencies/angrybirds/Acme.setup.revent
        ~/workload_automation/dependencies/angrybirds/Acme.run.revent

(you may need to create the intermediate directories if they don't already
exist).

.. [*] It's not just about screen resolution -- the event codes may be different
       even if devices use the same screen.

revent vs. UiAutomator
----------------------

In general, Android UI Automator is the preferred way of automating user input
for workloads because, unlike revent, UI Automator does not depend on a
particular screen resolution, and so is more portable across different devices.
It also gives better control and can potentially be faster for ling UI
manipulations, as input events are scripted based on the available UI elements,
rather than generated by human input.

On the other hand, revent can be used to manipulate pretty much any workload,
where as UI Automator only works for Android UI elements (such as text boxes or
radio buttons), which makes the latter useless for things like games. Recording
revent sequence is also faster than writing automation code (on the other hand,
one would need maintain a different revent log for each screen resolution).

redpajama_set_name: RedPajamaGithub