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bptree.h
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bptree.h
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// SPDX-License-Identifier: GPL-2.0-or-later
/*
* Author: Abby Cin
* Mail: [email protected]
* Create Time: 2023-11-02 14:50:25
*/
#include <cassert>
#include <cstddef>
#include <cstdio>
#include <cstring>
#include <tuple>
#ifndef BPTREE_1698907825_H_
#define BPTREE_1698907825_H_
namespace nm
{
template<typename Key>
concept BpTreeLess = requires(Key l, Key r) {
{
l <=> r
} -> std::same_as<std::strong_ordering>;
};
template<typename Policy, int M = 3>
requires BpTreeLess<typename Policy::key_type>
class BpTree {
public:
using key_t = typename Policy::key_type;
using val_t = typename Policy::value_type;
private:
static_assert(M >= 3, "order must greater than 2");
enum node_type {
LEAF_NODE = 1,
INTL_NODE = 2
};
struct node_t;
struct kc_t {
key_t key;
node_t *child;
};
struct node_t {
int type;
// it's count of keys for leaf node, count of children for
// internal node
int count;
node_t *parent;
node_t *prev, *next;
};
struct leaf_t : node_t {
val_t data[M];
};
// NOTE: key count is count - 1
struct intl_t : node_t {
// one extra space for simplify `split` procedure
kc_t kc[M + 1];
};
static node_t *to_node(void *x)
{
return static_cast<node_t *>(x);
}
static leaf_t *to_leaf(void *x)
{
return static_cast<leaf_t *>(x);
}
static intl_t *to_intl(void *x)
{
return static_cast<intl_t *>(x);
}
public:
class iter {
public:
iter(leaf_t *beg, leaf_t *end, short b, short e)
: off_ { b }
, b_off_ { b }
, e_off_ { e }
, cursor_ { beg }
, head_ { beg }
, tail_ { end }
{
assert(b_off_ <= head_->count);
assert(e_off_ <= tail_->count);
if (e_off_ == tail_->count) {
assert(tail_->count > 0);
e_off_ -= 1;
}
}
iter()
: off_ {}
, b_off_ {}
, e_off_ {}
, cursor_ { nullptr }
, head_ { nullptr }
, tail_ { nullptr }
{
}
val_t &data()
{
return cursor_->data[off_];
}
explicit operator bool()
{
if (!cursor_)
return false;
if (cursor_ == head_ && off_ < b_off_)
return false;
if (cursor_ == tail_ && off_ > e_off_)
return false;
return true;
}
iter &operator++()
{
off_ += 1;
if (off_ >= cursor_->count && cursor_ != tail_) {
cursor_ = to_leaf(cursor_->next);
off_ = 0;
}
return *this;
}
iter &operator--()
{
off_ -= 1;
if (off_ < 0 && cursor_ != head_) {
cursor_ = to_leaf(cursor_->prev);
assert(cursor_);
off_ = cursor_->count - 1;
}
return *this;
}
void seek_beg()
{
cursor_ = head_;
off_ = b_off_;
}
void seek_end()
{
cursor_ = tail_;
off_ = e_off_;
}
private:
int off_;
short b_off_;
short e_off_;
leaf_t *cursor_;
leaf_t *head_;
leaf_t *tail_;
};
BpTree() : root_ { nullptr }
{
}
~BpTree()
{
clear();
}
void put(val_t key)
{
if (!root_) {
auto leaf = new leaf_t {};
leaf->data[0] = std::move(key);
leaf->count += 1;
leaf->type = LEAF_NODE;
root_ = to_node(leaf);
} else {
auto l = search(root_, Policy::key(key));
if (l)
leaf_put(l, std::move(key));
}
}
val_t *get(key_t key)
{
auto l = search(root_, key);
if (l) {
auto [ok, pos] = leaf_search(l, key);
if (ok)
return &l->data[pos];
}
return nullptr;
}
void del(key_t key)
{
auto l = search(root_, key);
if (l)
leaf_del(l, key);
}
// return exactly range [from, to] when found, or else return
// sub-range
iter range(key_t from, key_t to)
{
if (from > to)
std::swap(from, to);
auto l = search(root_, from);
auto r = search(root_, to);
auto [_b, beg] = leaf_search(l, from);
auto [_e, end] = leaf_search(r, to);
if (!_b && !_e && l == r) {
// both `from` and `to` are not found in same leaft
if (beg == l->count && end == r->count)
return {};
}
// adjust left boundary
if (!_b) {
if (beg == l->count) {
l = to_leaf(l->next);
if (!l)
return {};
beg = 0;
}
}
// adjust right boundary
if (!_e) {
if (end == 0) {
r = to_leaf(r->prev);
if (!r)
return {};
end = r->count - 1;
} else {
end -= 1;
}
}
return { l, r, (short)beg, (short)end };
}
[[nodiscard]] size_t size() const
{
size_t n = 0;
auto cur = root_;
if (cur) {
while (cur->type != LEAF_NODE) {
auto it = to_intl(cur);
cur = it->kc[0].child;
}
while (cur) {
n += cur->count;
cur = cur->next;
}
}
return n;
}
[[nodiscard]] size_t height() const
{
size_t h = 0;
auto cur = root_;
if (cur) {
h += 1;
while (cur->type != LEAF_NODE) {
h += 1;
auto it = to_intl(cur);
cur = it->kc[0].child;
}
}
return h;
}
void clear()
{
if (root_) {
while (root_->type != LEAF_NODE) {
auto it = to_intl(root_);
auto next = it->kc[0].child;
list_clear(root_);
root_ = next;
}
list_clear(root_);
root_ = nullptr;
}
}
private:
node_t *root_;
static leaf_t *search(node_t *cur, key_t key)
{
while (cur) {
switch (cur->type) {
case LEAF_NODE: {
auto l = to_leaf(cur);
return l;
}
case INTL_NODE: {
auto n = to_intl(cur);
auto [ok, pos] = intl_search(n, key);
if (ok)
pos += 1;
cur = n->kc[pos].child;
}
}
}
return nullptr;
}
// there are 4 cases:
// 1. if leaf is not full, insert and return
// 2. if leaf is full, split into two, the old holds floor half and the
// new holds ceil half
// 3. if in `2.` cause the parent full, split parent recursively
// 4. if the key is larger than any key in `root_`, insert to last child
// of `root_` and repeat `2.` and `3.`
void leaf_put(leaf_t *leaf, val_t &&val)
{
auto [ok, pos] = leaf_search(leaf, Policy::key(val));
// update old value
if (ok) {
leaf->data[pos] = val;
return;
}
if (!leaf_is_full(leaf)) {
// make a space for new key val pair
rshift(leaf->data, leaf->count, pos);
leaf->data[pos] = val;
leaf->count += 1;
return;
}
auto &v = leaf_split(leaf, pos, val);
insert_fixup(leaf, leaf->next, Policy::key(v));
}
// we reserve a space for insert, and then split
static val_t &leaf_split(leaf_t *leaf, int pos, val_t val)
{
auto mid = leaf->count / 2;
auto node = new leaf_t {};
node->type = LEAF_NODE;
list_append(leaf, node);
rshift(leaf->data, leaf->count, pos);
leaf->data[pos] = val;
leaf->count += 1;
// copy to node
node->count = leaf->count - mid;
copy(node->data, leaf->data + mid, node->count);
leaf->count -= node->count;
return node->data[0];
}
void insert_fixup(void *l, void *r, key_t key)
{
auto lhs = to_node(l);
auto rhs = to_node(r);
if (!lhs->parent && !rhs->parent) {
auto parent = new intl_t {};
parent->type = INTL_NODE;
parent->count = 2;
parent->kc[0].key = key;
parent->kc[0].child = lhs;
parent->kc[1].child = rhs;
lhs->parent = to_node(parent);
rhs->parent = to_node(parent);
root_ = to_node(parent);
} else {
// since we always split the new node in right
assert(lhs->parent);
rhs->parent = lhs->parent;
intl_put(to_intl(rhs->parent), rhs, key);
}
}
void intl_put(intl_t *parent, node_t *child, key_t key)
{
auto [ok, pos] = intl_search(parent, key);
assert(!ok);
if (!intl_is_full(parent)) {
// NOTE: the old child remain unchanged, since rshift is
// copying not moving, so we only need to set pos + 1 to
// the new child
rshift(parent->kc, parent->count, pos);
parent->kc[pos].key = key;
parent->kc[pos + 1].child = child;
parent->count += 1;
return;
}
key = intl_split(parent, child, pos, key);
auto right_sibling = to_intl(parent->next);
insert_fixup(parent, right_sibling, key);
}
static key_t intl_split(intl_t *node, node_t *child, int pos, key_t key)
{
// the ceil half
int mid = (node->count + 1) / 2;
auto rhs = new intl_t {};
rhs->type = INTL_NODE;
list_append(node, rhs);
// for example:
// | 1 | 2 | 3 | |
// | c | c1 | p2 | c3 |
// we need copy the last two keys and children, the middle key 2
// is going to move to parent
// NOTE: we reserved a space for insert, then split
rshift(node->kc, node->count, pos);
node->kc[pos].key = key;
node->kc[pos + 1].child = child;
node->count += 1;
// the old child at `pos` is not overwritten, do nothing
// the key transfer to parent
key_t rkey = node->kc[mid - 1].key;
// split node
rhs->count = node->count - mid;
for (int i = mid, j = 0; j < rhs->count; ++i, ++j) {
rhs->kc[j] = node->kc[i];
if (rhs->kc[j].child)
rhs->kc[j].child->parent = to_node(rhs);
}
node->count -= rhs->count;
return rkey;
}
static void list_append(node_t *node, node_t *x)
{
x->next = node->next;
if (node->next)
node->next->prev = x;
x->prev = node;
node->next = x;
}
static void list_del(node_t *node)
{
auto prev = node->prev;
auto next = node->next;
if (prev)
prev->next = next;
if (next)
next->prev = prev;
if (node->type == LEAF_NODE)
delete to_leaf(node);
else
delete to_intl(node);
}
void list_clear(node_t *head)
{
node_t *next;
while (head) {
next = head->next;
if (head->type == LEAF_NODE)
delete to_leaf(head);
else
delete to_intl(head);
head = next;
}
}
static bool leaf_overhalf(leaf_t *leaf)
{
return leaf->count > (M + 1) / 2;
}
static bool intl_overhalf(intl_t *it)
{
return it->count > (M + 1) / 2;
}
// NOTE: the `M - 1` slot is reserved for new key-value pairs before
// performing split, this simplifies the split procedure
static bool leaf_is_full(leaf_t *leaf)
{
return leaf->count == M - 1;
}
// NOTE: when the child count == M then key count is M - 1
static bool intl_is_full(intl_t *it)
{
return it->count == M;
}
template<typename T>
static void rshift(T *arr, int size, int pos)
{
size -= pos;
if (size > 0)
memmove(arr + pos + 1, arr + pos, size * sizeof(T));
}
template<typename T>
static void lshift(T *arr, int size, int pos)
{
size -= (pos + 1);
if (size > 0)
memmove(arr + pos, arr + pos + 1, size * sizeof(T));
}
template<typename T>
static void copy(T *dst, T *src, int count)
{
memcpy(dst, src, count * sizeof(T));
}
static const key_t &key_of(val_t &v)
{
return Policy::key(v);
}
static const key_t &key_of(kc_t &v)
{
return v.key;
}
template<typename T>
static int bsearch(T arr[], int n, key_t key)
{
int l = 0;
int r = n - 1;
while (l <= r) {
int m = l + (r - l) / 2;
if (key_of(arr[m]) >= key)
r = m - 1;
else
l = m + 1;
}
return l;
}
static std::tuple<bool, int> leaf_search(leaf_t *leaf, key_t key)
{
auto pos = bsearch(leaf->data, leaf->count, key);
if (pos < leaf->count && Policy::key(leaf->data[pos]) == key)
return { true, pos };
return { false, pos };
}
// find child index, when found, the index is `pos` or else it should be
// `pos+1`, for example:
// the root is [9, 11] and it has 3 leaves [1, 4] [9, 10] and [11, 12]
// when `key = 5` the pos will be `0` which less than key_count, and we
// know the 5 may exist in `kc[pos].child`
// when the `key = 10` the pos will be `1` which equal to key_count, and
// we know the 10 may exist in `kc[pos+1].child`
static std::tuple<bool, int> intl_search(intl_t *it, key_t key)
{
// NOTE: we are search by keys, and the keys' count is one less
// than child count
assert(it->count > 0);
auto key_count = it->count - 1;
auto pos = bsearch(it->kc, key_count, key);
if (pos < key_count && it->kc[pos].key == key)
return { true, pos };
// NOTE: here the pos may less than or equal to key_count, which
// is the insert pos of the given key
return { false, pos };
}
// find the key's index in parent, since `intl_search` return the insert
// position of child and key index equal to child index - 1, so when not
// found, the key's index should subtract 1
//
// the index is used for rotation when perform borrow or merge operation
// for example:
// borrow a kv from right sibling, before that the node itself, parent
// and right sibling have order node < parent < right, to not violate
// that order, we need move key of parent down to node's last slot and
// then move right first key to parent, and finally shift all slots in
// right to left
//
// it's more efficient to track the index in `node_t`, but on the other
// hand, the code will be more complex and error-prone
static int key_index_in_parent(intl_t *parent, key_t key)
{
auto [ok, pos] = intl_search(parent, key);
if (!ok)
pos -= 1;
return pos;
}
// idx is key's index in parent, since the child's insert position is in
// range [0, p->count-1], then key's index is in range [-1, p->count-2]
// return 1 for operate on right, 0 for the left, we prefer operate on
// left side
static int which_side(intl_t *p, int idx, node_t *l, node_t *r)
{
if (idx == -1)
return 1;
if (idx == p->count - 2)
return 0;
return l->count >= r->count ? 0 : 1;
}
// there are 3 cases:
// 1. leaf count overhalf, simple remove elem and return
// 2. if in step 1. the key to be deleted is the first one, then the
// parent's key should be updated
// 3. leaf count too low, borrow one from left or right if possible:
// - if leaf is first node, merge right to leaf, delete right
// - if leaf is last node, merge leaf to left, delete leaf
// - if both left and right exist, borrow from the larger count one
// 4. no borrow can be made, merge sibling nodes
void leaf_del(leaf_t *leaf, key_t key)
{
auto [ok, pos] = leaf_search(leaf, key);
if (!ok)
return;
if (leaf_overhalf(leaf))
return leaf_simple_del(leaf, pos);
auto parent = to_intl(leaf->parent);
if (!parent) {
if (leaf->count == 1) {
list_del(leaf);
root_ = nullptr;
} else {
leaf_simple_del(leaf, pos);
}
return;
}
auto idx =
key_index_in_parent(parent, Policy::key(leaf->data[0]));
int right = which_side(parent, idx, leaf->prev, leaf->next);
auto l = to_leaf(leaf->prev);
auto r = to_leaf(leaf->next);
leaf_simple_del(leaf, pos);
// NOTE: the operation direction is always from right to left
// borrow or merge right operate on right's parent, so idx + 1
// while borrow or merge to left operate on node's parent, idx
// remain unchanged
if (right) {
idx += 1;
if (leaf_overhalf(r)) {
leaf_borrow_rhs(parent, leaf, r, idx);
} else {
leaf_merge_rhs(leaf, r);
intl_del(parent, idx);
}
} else {
assert(idx >= 0);
if (leaf_overhalf(l)) {
leaf_borrow_lhs(parent, leaf, l, idx);
} else {
leaf_merge_lhs(leaf, l);
intl_del(parent, idx);
}
}
}
static void
leaf_borrow_rhs(intl_t *parent, leaf_t *leaf, leaf_t *r, int idx)
{
// borrow one to the end of leaf
leaf->data[leaf->count] = r->data[0];
leaf->count += 1;
// remove the borrowed one
leaf_simple_del(r, 0);
parent->kc[idx].key = Policy::key(r->data[0]);
}
static void
leaf_borrow_lhs(intl_t *parent, leaf_t *leaf, leaf_t *l, int idx)
{
rshift(leaf->data, leaf->count, 0);
leaf->data[0] = l->data[l->count - 1];
leaf->count += 1;
l->count -= 1;
parent->kc[idx].key = Policy::key(leaf->data[0]);
}
static void leaf_merge_rhs(leaf_t *leaf, leaf_t *r)
{
copy(leaf->data + leaf->count, r->data, r->count);
leaf->count += r->count;
list_del(r);
}
static void leaf_merge_lhs(leaf_t *leaf, leaf_t *l)
{
copy(l->data + l->count, leaf->data, leaf->count);
l->count += leaf->count;
list_del(leaf);
}
static void leaf_simple_del(leaf_t *leaf, int pos)
{
lshift(leaf->data, leaf->count, pos);
leaf->count -= 1;
}
void intl_del(intl_t *node, int pos)
{
if (intl_overhalf(node))
return intl_simple_del(node, pos);
auto parent = to_intl(node->parent);
if (!parent) {
// the last one, reduce tree height
if (node->count == 2) {
node->kc[0].child->parent = nullptr;
// it's why we prefer merge into left
root_ = node->kc[0].child;
list_del(node);
} else {
intl_simple_del(node, pos);
}
return;
}
auto idx = key_index_in_parent(parent, node->kc[0].key);
int right = which_side(parent, idx, node->prev, node->next);
auto l = to_intl(node->prev);
auto r = to_intl(node->next);
if (right) {
idx += 1;
intl_simple_del(node, pos);
if (intl_overhalf(r)) {
intl_borrow_rhs(parent, node, r, idx);
} else {
intl_merge_rhs(parent, node, r, idx);
intl_del(parent, idx);
}
} else {
assert(idx >= 0);
// skipp the key and child at pos while shifting instead
// of delete, it's more simple and efficient than invoke
// intl_simple_del and then move all data, since the key
// and child are not correspond one-to-one
if (intl_overhalf(l)) {
intl_borrow_lhs(parent, node, l, pos, idx);
} else {
intl_merge_lhs(parent, node, l, pos, idx);
intl_del(parent, idx);
}
}
}
static void intl_borrow_rhs(intl_t *p, intl_t *node, intl_t *r, int idx)
{
// left rotation, put the parent key to the left, and then put
// the right key to the parent, and finally left shift the right
// to keep the order lhs < parent < rhs
node->kc[node->count - 1].key = p->kc[idx].key;
// update parent key to larger one
p->kc[idx].key = r->kc[0].key;
// borrow first child from right
node->kc[node->count].child = r->kc[0].child;
node->kc[node->count].child->parent = to_node(node);
node->count += 1;
// remove borrowed kc from right
for (int i = 0; i < r->count - 2; ++i)
r->kc[i].key = r->kc[i + 1].key;
for (int i = 0; i < r->count - 1; ++i)
r->kc[i].child = r->kc[i + 1].child;
r->count -= 1;
}
static void
intl_borrow_lhs(intl_t *p, intl_t *node, intl_t *l, int pos, int idx)
{
// reserve one slot at 0 for borrowing key and child
for (int i = pos; i > 0; --i)
node->kc[i].key = node->kc[i - 1].key;
for (int i = pos + 1; i > 0; --i)
node->kc[i].child = node->kc[i - 1].child;
// right rotation, put the parent key to the right, and then put
// the left key to the parent, and finally remove the last key
// from left (simply reduce its size) to keep the order
// left last < parent at `idx` < node first
node->kc[0].key = p->kc[idx].key;
p->kc[idx].key = l->kc[l->count - 2].key;
node->kc[0].child = l->kc[l->count - 1].child;
node->kc[0].child->parent = to_node(node);
l->count -= 1;
}
static void intl_merge_rhs(intl_t *p, intl_t *node, intl_t *r, int idx)
{
// the key is corresponding to the child of `r` in first slot
node->kc[node->count - 1].key = p->kc[idx].key;
for (int i = node->count, j = 0; j < r->count - 1; ++i, ++j)
node->kc[i].key = r->kc[j].key;
for (int i = node->count, j = 0; j < r->count; ++i, ++j) {
node->kc[i].child = r->kc[j].child;
if (node->kc[i].child)
node->kc[i].child->parent = to_node(node);
}
node->count += r->count;
list_del(r);
}
static void
intl_merge_lhs(intl_t *p, intl_t *node, intl_t *l, int pos, int idx)
{
// the key is corresponding to the child of `node` in first slot
l->kc[l->count - 1].key = p->kc[idx].key;
for (int i = l->count, j = 0; j < node->count - 1; ++j) {
if (j != pos) {
l->kc[i].key = node->kc[j].key;
i += 1;
}
}
for (int i = l->count, j = 0; j < node->count; ++j) {
if (j == pos + 1)
continue;
l->kc[i].child = node->kc[j].child;
if (l->kc[i].child)
l->kc[i].child->parent = to_node(l);
i += 1;
}
l->count += node->count - 1;
list_del(node);
}
// NOTE: pos is the key's index, child index should be pos + 1
static void intl_simple_del(intl_t *node, int pos)
{
assert(node->count >= 2);
for (int i = pos; i < node->count - 2; ++i) {
node->kc[i].key = node->kc[i + 1].key;
// we have one extra space, so i + 2 is valid
node->kc[i + 1].child = node->kc[i + 2].child;
}
node->count -= 1;
}
};
}
#endif // BPTREE_1698907825_H_