// Copyright 2023, Roman Gershman.  All rights reserved.
// See LICENSE for licensing terms.
//

#pragma once

#include <array>
#include <cassert>
#include <cstring>

namespace dfly {

template <typename T, typename Policy> class BPTree;

namespace detail {

// Internal classes related to B+tree implementation. The design is largely based on the
// implementation of absl::bPtree_map/set.
// The motivation for replacing zskiplist - significant size reduction:
//   we reduce the metadata overhead per record from 45 bytes in zskiplist to just a
//   few bytes with b-tree. The trick is using significantly large nodes (256 bytes) so that
//   their overhead is negligible compared to the items they store.
//   Why not use absl::bPtree_set? We must support Rank tree functionality that
//   absl does not supply.
//   Hacking into absl is not a simple task, implementing our own tree is easier.
// Below some design decisions:
// 1. We use predefined node size of 256 bytes and derive number of items in each node from it.
//    Inner nodes have less items than leaf nodes because they also need to store child pointers.
// 2. BPTreeNode does not predeclare fields besides the 8 bytes metadata - everything else is
//    calculated at run-time and has dedicated accessors (similarly to absl). This allows
//    dense and efficient representation of tree nodes.
// 3. We assume that we store small items (8, 16 bytes) which will have a large branching
//    factor (248/16), meaning the tree will stay shallow even for sizes reaching billion nodes.
// 4. We do not store parent pointer like in absl tree. Instead we use BPTreePath to store
//    hierarchy of parent nodes. That should reduce our overhead even further by few bits per item.
// 5. We assume we store trivially copyable types - this reduces the
//    complexity of the generics in the code.
// 6. We support pmr memory resource. This allows us to use pluggable heaps.
//
// TODO: (all the ideas taken from absl implementation)
//       1. to introduce slices when removing items from the tree (avoid shifts).
//       2. to avoid merging/rebalancing when removing max/min items from the tree.
//       3. Small tree optimization: when the tree is small with a single root node, we can
//          allocate less then 256 bytes (special case) to avoid relative blowups in memory for
//          small trees.

constexpr uint16_t kBPNodeSize = 256;

/**
 * @brief The BPNodeLayout class is a helper class that defines the layout of the B+tree node.
 *        The inner node looks like this:
 *        | 4 bytes metadata | keys ... | 4 bytes tree-count | children nodes |
 *        The leaf node looks like this:
 *        | 4 bytes metadata | keys ... |
 *
 * @tparam T
 */
template <typename T> class BPNodeLayout {
  static_assert(std::is_trivially_copyable<T>::value, "KeyT must be triviall copyable");

  static constexpr uint16_t kKeyOffset = 4;                  // 4 bytes for metadata
  static constexpr uint16_t kSubTreeLen = sizeof(uint32_t);  // 4 bytes for count.
 public:
  static constexpr uint16_t kKeySize = sizeof(T);
  static constexpr uint16_t kMaxLeafKeys = (kBPNodeSize - kKeyOffset) / kKeySize;
  static constexpr uint16_t kMinLeafKeys = kMaxLeafKeys / 2;

  // internal node:
  // x slots, (x+1) children: x * kKeySize + (x+1) * sizeof(BPTreeNode*) = x * (kKeySize + 8) + 8
  // x = (kBPNodeSize - kInnerKeyOffset - 8) / (kKeySize + 8)
  static constexpr uint16_t kMaxInnerKeys =
      (kBPNodeSize - sizeof(void*) - kKeyOffset - kSubTreeLen) / (kKeySize + sizeof(void*));
  static constexpr uint16_t kMinInnerKeys = kMaxInnerKeys / 2;

  using KeyT = T;

  // The class is constructed inside a block of memory of size kBPNodeSize.
  // Only BPTree can create it, hence it can access the memory outside its fields.
  static uint8_t* KeyPtr(unsigned index, void* node) {
    return reinterpret_cast<uint8_t*>(node) + kKeyOffset + kKeySize * index;
  }

  static const uint8_t* KeyPtr(unsigned index, const void* node) {
    return reinterpret_cast<const uint8_t*>(node) + kKeyOffset + kKeySize * index;
  }

  static uint8_t* TreeCountPtr(void* node) {
    return reinterpret_cast<uint8_t*>(node) + kKeyOffset + kKeySize * kMaxInnerKeys;
  }

  static const uint8_t* TreeCountPtr(const void* node) {
    return reinterpret_cast<const uint8_t*>(node) + kKeyOffset + kKeySize * kMaxInnerKeys;
  }

  static uint8_t* ChildrenStart(void* node) {
    return TreeCountPtr(node) + kSubTreeLen;
  }

  static const uint8_t* ChildrenStart(const void* node) {
    return TreeCountPtr(node) + kSubTreeLen;
  }

  static_assert(kMaxLeafKeys < 128);
};

template <typename T> class BPTreeNode {
  template <typename K, typename Policy> friend class ::dfly::BPTree;

  BPTreeNode(const BPTreeNode&) = delete;
  BPTreeNode& operator=(const BPTreeNode&) = delete;

  BPTreeNode(bool leaf) : num_items_(0), leaf_(leaf) {
  }

  using Layout = BPNodeLayout<T>;

 public:
  using KeyT = T;

  void InitSingle(T key) {
    SetKey(0, key);
    num_items_ = 1;
  }

  KeyT Key(unsigned index) const {
    KeyT res;
    memcpy(&res, Layout::KeyPtr(index, this), sizeof(KeyT));
    return res;
  }

  void SetKey(size_t index, KeyT item) {
    uint8_t* slot = Layout::KeyPtr(index, this);
    memcpy(slot, &item, sizeof(KeyT));
  }

  bool IsLeaf() const {
    return leaf_;
  }

  struct SearchResult {
    uint16_t index;
    bool found;
  };

  // Searches for key in the node using binary search.
  // Returns SearchResult with index of the smallest key for which comp(key) >=0.
  // comp: is a three way comparator.
  template <typename Comp> SearchResult BSearch(Comp&& comp) const;

  void Split(BPTreeNode* right, KeyT* median);

  unsigned NumItems() const {
    return num_items_;
  }

  unsigned AvailableSlotCount() const {
    return MaxItems() - num_items_;
  }

  unsigned MaxItems() const {
    return IsLeaf() ? Layout::kMaxLeafKeys : Layout::kMaxInnerKeys;
  }

  unsigned MinItems() const {
    return IsLeaf() ? Layout::kMinLeafKeys : Layout::kMinInnerKeys;
  }

  // Returns the overall number of iterms for a subtree rooted at this node.
  // Equals to NumItems() for leaf nodes and GetInnerTreeCount() for inner nodes.
  uint32_t TreeCount() const {
    return IsLeaf() ? NumItems() : GetInnerTreeCount();
  }

  void ShiftRight(unsigned index);
  void ShiftLeft(unsigned index, bool child_step_right = false);

  void LeafEraseRight() {
    assert(IsLeaf() && num_items_ > 0);
    --num_items_;
  }

  // Inserts item into a leaf node.
  // Assumes: the node is IsLeaf() and has some space.
  void LeafInsert(unsigned index, KeyT item) {
    assert(IsLeaf() && NumItems() < MaxItems());
    InsertItem(index, item);
  }

  void Validate(KeyT upper_bound) const;

  //
  // Below is the inner node API
  //

  BPTreeNode* Child(unsigned i) {
    BPTreeNode* res;
    memcpy(&res, Layout::ChildrenStart(this) + sizeof(BPTreeNode*) * i, sizeof(BPTreeNode*));
    return res;
  }

  const BPTreeNode* Child(unsigned i) const {
    BPTreeNode* res;
    memcpy(&res, Layout::ChildrenStart(this) + sizeof(BPTreeNode*) * i, sizeof(BPTreeNode*));
    return res;
  }

  void SetChild(unsigned i, BPTreeNode* child) {
    memcpy(Layout::ChildrenStart(this) + sizeof(BPTreeNode*) * i, &child, sizeof(BPTreeNode*));
  }

  // TODO: instead of storing counts at nodes we could keep at parent level
  //       along the children array. Unfortunately, this complicates implementation of the tree,
  //       so we will do it after the whole functionality is completed.
  uint32_t GetChildTreeCount(unsigned i) {
    return Child(i)->TreeCount();
  }

  void SetChildTreeCount(unsigned i, uint32_t cnt) {
    Child(i)->SetTreeCount(cnt);
  }

  void IncreaseTreeCount(int32_t delta) {
    uint32_t cnt = GetInnerTreeCount();
    cnt += delta;
    memcpy(Layout::TreeCountPtr(this), &cnt, sizeof(uint32_t));
  }

  // Rebalance a full child at position pos, at which we tried to insert at insert_pos.
  // Returns the node and the position to insert into if rebalancing succeeded.
  // Returns nullptr if rebalancing did not succeed.
  std::pair<BPTreeNode*, unsigned> RebalanceChild(unsigned pos, unsigned insert_pos);

  // We do not update tree count and it is done on the caller side.
  // Inserts item into a inner node at position pos and adds `child` at position pos+1.
  void InnerInsert(unsigned index, KeyT item, BPTreeNode* child) {
    InsertItem(index, item);
    SetChild(index + 1, child);
  }

  // Tries to merge the child at position pos with its sibling.
  // If we did not succeed to merge, we try to rebalance.
  // Returns retired BPTreeNode* if children got merged and this parent node's children
  // count decreased, otherwise, we return nullptr (rebalanced).
  BPTreeNode* MergeOrRebalanceChild(unsigned pos);

  uint32_t DEBUG_TreeCount() const {
    uint32_t res = NumItems();
    if (!IsLeaf()) {
      for (unsigned i = 0; i <= NumItems(); ++i) {
        res += Child(i)->DEBUG_TreeCount();
      }
    }
    return res;
  }

 private:
  void SetTreeCount(uint32_t cnt) {
    assert(!IsLeaf());
    memcpy(Layout::TreeCountPtr(this), &cnt, sizeof(uint32_t));
  }

  void RebalanceChildToLeft(unsigned child_pos, unsigned count);
  void RebalanceChildToRight(unsigned child_pos, unsigned count);

  void MergeFromRight(KeyT key, BPTreeNode* right);

  void InsertItem(unsigned index, KeyT item) {
    assert(index <= num_items_);

    ShiftRight(index);
    SetKey(index, item);
  }

  uint32_t GetInnerTreeCount() const {
    assert(!IsLeaf());
    uint32_t res;
    memcpy(&res, Layout::TreeCountPtr(this), sizeof(uint32_t));
    return res;
  }

  struct {
    uint32_t num_items_ : 7;
    uint32_t leaf_ : 1;
    uint32_t : 24;
  };
};

// Contains parent/index pairs. Meaning that node0->Child(index0) == node1.
template <typename T> class BPTreePath {
  static constexpr unsigned kMaxDepth = 16;

 public:
  void Push(BPTreeNode<T>* node, unsigned pos) {
    assert(depth_ < kMaxDepth);
    assert(depth_ == 0 || !record_[depth_ - 1].node->IsLeaf());
    record_[depth_].node = node;
    record_[depth_].pos = pos;
    depth_++;
  }

  unsigned Depth() const {
    return depth_;
  }

  void Clear() {
    depth_ = 0;
  }

  bool Empty() const {
    return depth_ == 0;
  }

  std::pair<BPTreeNode<T>*, unsigned> Last() const {
    assert(depth_ > 0u);
    return {record_[depth_ - 1].node, record_[depth_ - 1].pos};
  }

  BPTreeNode<T>* Node(unsigned i) const {
    assert(i < depth_);
    return record_[i].node;
  }

  unsigned Position(unsigned i) const {
    assert(i < depth_);
    return record_[i].pos;
  }

  void Pop() {
    assert(depth_ > 0u);
    depth_--;
  }

  bool HasValidTerminal() const {
    return depth_ > 0u && Last().second < Last().first->NumItems();
  }

  T Terminal() const {
    assert(Last().second < Last().first->NumItems());
    return Last().first->Key(Last().second);
  }

  /// @brief Returns the rank of the path's terminal item.
  /// Requires that the path is valid and has a terminal item.
  uint32_t Rank() const;

  /// @brief Advances the path to the next item.
  /// @return true if succeeded, false if reached the end.
  bool Next();

  /// @brief Advances the path to the previous item.
  /// @return true if succeeded, false if reached the end.
  bool Prev();

  // Extend the path to the leaf by always taking the rightmost child.
  void DigRight();

 private:
  struct Record {
    BPTreeNode<T>* node;
    unsigned pos;
  };

  std::array<Record, kMaxDepth> record_;
  unsigned depth_ = 0;
};

// Returns the position of the first item whose key is greater or equal than key.
// if all items are smaller than key, returns num_items_.
template <typename T>
template <typename Comp>
auto BPTreeNode<T>::BSearch(Comp&& cmp_op) const -> SearchResult {
  uint16_t lo = 0;
  uint16_t hi = num_items_;
  assert(hi > 0);

  // optimization: check the last item first.
  int cmp_res = cmp_op(Key(hi - 1));
  if (cmp_res >= 0) {
    return cmp_res > 0 ? SearchResult{.index = hi, .found = false}
                       : SearchResult{.index = uint16_t(hi - 1), .found = true};
  }

  // key < Key(hi - 1)

  --hi;
  while (lo < hi) {
    uint16_t mid = (lo + hi) >> 1;
    assert(mid < hi);

    KeyT item = Key(mid);

    int cmp_res = cmp_op(item);
    if (cmp_res == 0) {
      return SearchResult{.index = mid, .found = true};
    }

    if (cmp_res < 0) {
      hi = mid;
    } else {
      lo = mid + 1;  // we never return indices upto mid because they are strictly less than key.
    }
  }
  assert(lo == hi);

  return {.index = hi, .found = false};
}

template <typename T> void BPTreeNode<T>::ShiftRight(unsigned index) {
  unsigned num_items_to_shift = num_items_ - index;
  if (num_items_to_shift > 0) {
    uint8_t* ptr = Layout::KeyPtr(index, this);
    memmove(ptr + Layout::kKeySize, ptr, num_items_to_shift * Layout::kKeySize);

    if (!IsLeaf()) {
      uint8_t* src = Layout::ChildrenStart(this) + index * sizeof(BPTreeNode*);
      uint8_t* dest = src + sizeof(BPTreeNode*);
      memmove(dest, src, (num_items_to_shift + 1) * sizeof(BPTreeNode*));
    }
  }
  num_items_++;
}

template <typename T> void BPTreeNode<T>::ShiftLeft(unsigned index, bool child_step_right) {
  assert(index < num_items_);

  unsigned num_items_to_shift = num_items_ - index - 1;
  if (num_items_to_shift > 0) {
    memmove(Layout::KeyPtr(index, this), Layout::KeyPtr(index + 1, this),
            num_items_to_shift * Layout::kKeySize);
    if (!leaf_) {
      index += unsigned(child_step_right);
      num_items_to_shift = num_items_ - index;
      if (num_items_to_shift > 0) {
        uint8_t* dest = Layout::ChildrenStart(this) + index * sizeof(BPTreeNode*);
        uint8_t* src = dest + sizeof(BPTreeNode*);
        memmove(dest, src, num_items_to_shift * sizeof(BPTreeNode*));
      }
    }
  }
  num_items_--;
}

/***
 *  Rebalances the (full) child at position pos with its sibling. `this` node is an inner node.
 *  It first tried to rebalance (move items) from the full child to its left sibling. If the left
 *  sibling does not have enough space, it tries to rebalance to the right sibling. The caller
 *  passes the original position of the item it tried to insert into the full child. In case the
 *  rebalance succeeds the function returns the new node and the position to insert into. Otherwise,
 *  it returns result.first == nullptr.
 */
template <typename T>
std::pair<BPTreeNode<T>*, unsigned> BPTreeNode<T>::RebalanceChild(unsigned pos,
                                                                  unsigned insert_pos) {
  unsigned to_move = 0;
  BPTreeNode* node = Child(pos);

  if (pos > 0) {
    BPTreeNode* left = Child(pos - 1);
    unsigned dest_free = left->AvailableSlotCount();
    if (dest_free > 0) {
      // 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.
      if (insert_pos == node->NumItems()) {
        to_move = dest_free;
        assert(to_move < node->NumItems());
      } else if (dest_free > 1) {
        // we move less than left free capacity which leaves as some space in the node.
        to_move = dest_free / 2;
      }

      if (to_move) {
        unsigned dest_old_count = left->NumItems();
        RebalanceChildToLeft(pos, to_move);
        assert(node->AvailableSlotCount() == to_move);
        if (insert_pos < to_move) {
          assert(left->AvailableSlotCount() > 0u);       // we did not fill up the left node.
          insert_pos = dest_old_count + insert_pos + 1;  // +1 because we moved the separator.
          node = left;
        } else {
          insert_pos -= to_move;
        }

        return {node, insert_pos};
      }
    }
  }

  if (pos < NumItems()) {
    BPTreeNode* right = Child(pos + 1);
    unsigned dest_free = right->AvailableSlotCount();
    if (dest_free > 0) {
      if (insert_pos == 0) {
        to_move = dest_free;
        assert(to_move < node->NumItems());
      } else if (dest_free > 1) {
        to_move = dest_free / 2;
      }

      if (to_move) {
        RebalanceChildToRight(pos, to_move);
        if (insert_pos > node->NumItems()) {
          insert_pos -= (node->NumItems() + 1);
          node = right;
        }
        return {node, insert_pos};
      }
    }
  }
  return {nullptr, 0};
}

template <typename T> void BPTreeNode<T>::RebalanceChildToLeft(unsigned child_pos, unsigned count) {
  assert(child_pos > 0u);
  BPTreeNode* src = Child(child_pos);
  BPTreeNode* dest = Child(child_pos - 1);
  assert(src->NumItems() >= count);
  assert(count >= 1u);
  assert(dest->AvailableSlotCount() >= count);

  unsigned dest_items = dest->NumItems();

  // Move the delimiting value to the left node.
  dest->SetKey(dest_items, Key(child_pos - 1));

  // Copy src keys [0, count-1] to dest keys [dest_items+1, dest_items+count].
  for (unsigned i = 1; i < count; ++i) {
    dest->SetKey(dest_items + i, src->Key(i - 1));
  }

  SetKey(child_pos - 1, src->Key(count - 1));

  // Shift the values in the right node to their correct position.
  for (unsigned i = count; i < src->NumItems(); ++i) {
    src->SetKey(i - count, src->Key(i));
  }

  if (!src->IsLeaf()) {
    // Move the child pointers from the right to the left node.
    uint32_t src_move_count = 0;
    for (unsigned i = 0; i < count; ++i) {
      src_move_count += src->GetChildTreeCount(i);
      dest->SetChild(1 + dest->NumItems() + i, src->Child(i));
    }

    uint32_t dest_tree_count = GetChildTreeCount(child_pos - 1);
    uint32_t src_tree_count = GetChildTreeCount(child_pos);
    SetChildTreeCount(child_pos - 1, dest_tree_count + src_move_count + count);
    SetChildTreeCount(child_pos, src_tree_count - src_move_count - count);

    for (unsigned i = count; i <= src->NumItems(); ++i) {
      src->SetChild(i - count, src->Child(i));
      src->SetChild(i, NULL);
    }
  }

  // Fixup the counts on the src and dest nodes.
  dest->num_items_ += count;
  src->num_items_ -= count;
}

template <typename T>
void BPTreeNode<T>::RebalanceChildToRight(unsigned child_pos, unsigned count) {
  assert(child_pos < NumItems());
  BPTreeNode* src = Child(child_pos);
  BPTreeNode* dest = Child(child_pos + 1);

  assert(src->NumItems() >= count);
  assert(count >= 1u);
  assert(dest->AvailableSlotCount() >= count);

  unsigned dest_items = dest->NumItems();

  assert(dest_items > 0u);

  // Shift the values in the right node to their correct position.
  for (int i = dest_items - 1; i >= 0; --i) {
    dest->SetKey(i + count, dest->Key(i));
  }

  // Move the delimiting value to the left node and the new delimiting value
  // from the right node.
  KeyT new_delim = src->Key(src->NumItems() - count);
  for (unsigned i = 1; i < count; ++i) {
    unsigned src_id = src->NumItems() - count + i;
    dest->SetKey(i - 1, src->Key(src_id));
  }
  // Move parent's delimiter to destination and update it with new delimiter.
  dest->SetKey(count - 1, Key(child_pos));
  SetKey(child_pos, new_delim);

  if (!src->IsLeaf()) {
    // Shift child pointers in the right node to their correct position.
    for (int i = dest_items; i >= 0; --i) {
      dest->SetChild(i + count, dest->Child(i));
    }

    // Move child pointers from the left node to the right.
    uint32_t src_move_count = 0;
    for (unsigned i = 0; i < count; ++i) {
      unsigned src_id = src->NumItems() - (count - 1) + i;
      src_move_count += src->Child(src_id)->TreeCount();
      dest->SetChild(i, src->Child(src_id));
      src->SetChild(src_id, NULL);
    }

    uint32_t dest_tree_count = GetChildTreeCount(child_pos + 1);
    uint32_t src_tree_count = GetChildTreeCount(child_pos);
    SetChildTreeCount(child_pos + 1, dest_tree_count + src_move_count + count);
    SetChildTreeCount(child_pos, src_tree_count - src_move_count - count);
  }

  // Fixup the counts on the src and dest nodes.
  dest->num_items_ += count;
  src->num_items_ -= count;
}

template <typename T> BPTreeNode<T>* BPTreeNode<T>::MergeOrRebalanceChild(unsigned pos) {
  BPTreeNode* node = Child(pos);
  BPTreeNode* left = nullptr;

  assert(NumItems() >= 1u);
  assert(node->NumItems() < node->MinItems());

  if (pos > 0) {
    left = Child(pos - 1);
    if (left->NumItems() + 1 + node->NumItems() <= left->MaxItems()) {
      left->MergeFromRight(Key(pos - 1), node);
      ShiftLeft(pos - 1, true);
      return node;
    }
  }

  if (pos < NumItems()) {
    BPTreeNode* right = Child(pos + 1);
    if (node->NumItems() + 1 + right->NumItems() <= right->MaxItems()) {
      node->MergeFromRight(Key(pos), right);
      ShiftLeft(pos, true);
      return right;
    }

    // Try rebalancing with our right sibling.
    // TODO: don't perform rebalancing if
    // we deleted the first element from 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 (true) {
      unsigned to_move = (right->NumItems() - node->NumItems()) / 2;
      assert(to_move < right->NumItems());

      RebalanceChildToLeft(pos + 1, to_move);
      return nullptr;
    }
  }

  assert(left);

  if (left) {
    // Try rebalancing with our left sibling.
    // TODO: don't perform rebalancing if we deleted the last element from node and the
    // node is not empty. This is a small optimization for the common pattern of deleting
    // from the back of the tree.
    if (true) {
      unsigned to_move = (left->NumItems() - node->NumItems()) / 2;
      assert(to_move < left->NumItems());
      RebalanceChildToRight(pos - 1, to_move);
      return nullptr;
    }
  }
  return nullptr;
}

// splits the node into two nodes. The left node is the current node and the right node is
// is filled with the right half of the items. The median key is returned in *median.
template <typename T> void BPTreeNode<T>::Split(BPTreeNode<T>* right, T* median) {
  unsigned mid = num_items_ / 2;
  *median = Key(mid);
  right->leaf_ = leaf_;
  right->num_items_ = num_items_ - (mid + 1);
  memmove(Layout::KeyPtr(0, right), Layout::KeyPtr(mid + 1, this),
          right->num_items_ * Layout::kKeySize);
  if (!IsLeaf()) {
    uint32_t right_subtree_count = right->num_items_;
    for (size_t i = 0; i <= right->num_items_; i++) {
      BPTreeNode* child = Child(mid + 1 + i);
      right_subtree_count += child->TreeCount();
      right->SetChild(i, child);
    }
    right->SetTreeCount(right_subtree_count);
    IncreaseTreeCount(-(right_subtree_count + 1));
  }
  num_items_ = mid;
}

template <typename T> void BPTreeNode<T>::MergeFromRight(KeyT key, BPTreeNode<T>* right) {
  assert(NumItems() + 1 + right->NumItems() <= MaxItems());

  unsigned dest_items = NumItems();
  SetKey(dest_items, key);
  for (unsigned i = 0; i < right->NumItems(); ++i) {
    SetKey(dest_items + 1 + i, right->Key(i));
  }

  if (!IsLeaf()) {
    for (unsigned i = 0; i <= right->NumItems(); ++i) {
      SetChild(dest_items + 1 + i, right->Child(i));
    }
    IncreaseTreeCount(right->TreeCount() + 1);
  }
  num_items_ += 1 + right->NumItems();
  right->num_items_ = 0;
}

template <typename T> uint32_t BPTreePath<T>::Rank() const {
  uint32_t rank = 0;
  unsigned bound = Depth();

  for (unsigned i = 0; i < bound; ++i) {
    auto* node = Node(i);
    unsigned pos = Position(i);
    if (!node->IsLeaf()) {
      unsigned delta = (i == bound - 1) ? 1 : 0;
      for (unsigned j = 0; j < pos + delta; ++j) {
        rank += node->Child(j)->TreeCount();
      }
    }
    rank += pos;
  }

  return rank;
}

template <typename T> bool BPTreePath<T>::Next() {
  assert(depth_ > 0);
  BPTreeNode<T>* node = Last().first;

  // The data in BPTree is stored in both the leaf nodes and the inner nodes.
  if (node->IsLeaf()) {
    ++record_[depth_ - 1].pos;
    if (record_[depth_ - 1].pos < node->NumItems()) {
      return true;
    }

    // Advance to the next item, which is Key(i) in some ascendent of the subtree with
    // root Child(i). i in that case must be less than NumItems().
    // Note, that subtree Child(i) in a inner node is located before Key(i).
    do {
      Pop();
    } while (depth_ > 0 && Position(depth_ - 1) == Node(depth_ - 1)->NumItems());

    // we either point now on separator Key(i) in the parent node or we finished the tree.
    return depth_ > 0;
  }

  // We are in the inner node after the ascent from the leaf node. We need to advance to the next
  // Child and dig left.
  assert(!node->IsLeaf());
  assert(record_[depth_ - 1].pos < node->NumItems());

  // we are in the inner node pointing to the separator.
  // now we need to advance to the next child and dig to the leftmost leaf.
  record_[depth_ - 1].pos++;
  do {
    node = node->Child(record_[depth_ - 1].pos);
    Push(node, 0);
  } while (!node->IsLeaf());

  return true;
}

template <typename T> bool BPTreePath<T>::Prev() {
  assert(depth_ > 0);

  auto* node = record_[depth_ - 1].node;
  if (node->IsLeaf()) {
    /*
        node
        / \
       l   r

       We must go left (decrement pos), and if there is no left, we must go up until we can
       go left.
    */
    while (record_[depth_ - 1].pos == 0) {
      Pop();
      if (depth_ == 0) {
        return false;
      }
    }
    assert(depth_ > 0 && record_[depth_ - 1].pos > 0);

    // we finished backtracking from child(i+1) or stayed in the leaf.
    // either way stop at the next key on the left.
    --record_[depth_ - 1].pos;
    return true;
  }

  DigRight();
  return true;
}

template <typename T> void BPTreePath<T>::DigRight() {
  assert(depth_ > 0);
  BPTreeNode<T>* node = Last().first;

  assert(!node->IsLeaf());

  // we are in the inner node pointing to the separator.
  // we now must explore the left subtree which is located under the same index as the separator.
  // we go far-right in the left subtree.
  do {
    node = node->Child(record_[depth_ - 1].pos);
    Push(node, node->NumItems());
  } while (!node->IsLeaf());

  // we reached the leaf node, fix the position to point to the last key.
  assert(record_[depth_ - 1].node->IsLeaf());
  --record_[depth_ - 1].pos;
}

}  // namespace detail
}  // namespace dfly
