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sandbox: btree: add documentation and license

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max 🍓
2023-01-30 20:57:55 +00:00
parent 07e2e5099d
commit caf4d2b969
2 changed files with 480 additions and 6 deletions
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275
sandbox/btree/btree.c
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@@ -1,3 +1,62 @@
/*
The Clear BSD License
Copyright (c) 2023 Max Wash
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted (subject to the limitations in the disclaimer
below) provided that the following conditions are met:
- Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
- Neither the name of the copyright holder nor the names of its
contributors may be used to endorse or promote products derived from this
software without specific prior written permission.
*/
/* templated AVL binary tree implementation
this file implements an extensible AVL binary tree data structure.
the primary rule of an AVL binary tree is that for a given node N,
the heights of N's left and right subtrees can differ by at most 1.
the height of a subtree is the length of the longest path between
the root of the subtree and a leaf node, including the root node itself.
the height of a leaf node is 1.
when a node is inserted into or deleted from the tree, this rule may
be broken, in which the tree must be rotated to restore the balance.
no more than one rotation is required for any insert operations,
while multiple rotations may be required for a delete operation.
there are four types of rotations that can be applied to a tree:
- left rotation
- right rotation
- double left rotations
- double right rotations
by enforcing the balance rule, for a tree with n nodes, the worst-case
performance for insert, delete, and search operations is guaranteed
to be O(log n).
this file intentionally excludes any kind of search function implementation.
it is up to the programmer to implement their own tree node type
using btree_node_t, and their own search function using btree_t.
this allows the programmer to define their own node types with complex
non-integer key types. btree.h contains a number of macros to help
define these functions. the macros do all the work, you just have to
provide a comparator function.
*/
#include <socks/btree.h>
#include <stddef.h>
#include <stdlib.h>
@@ -43,6 +102,32 @@ static inline int bf(btree_node_t *x)
return bf;
}
/* perform a left rotation on a subtree
if you have a tree like this:
Z
/ \
X .
/ \
. Y
/ \
. .
and you perform a left rotation on node X,
you will get the following tree:
Z
/ \
Y .
/ \
X .
/ \
. .
note that this function does NOT update b_height for the rotated
nodes. it is up to you to call update_height_to_root().
*/
static void rotate_left(btree_t *tree, btree_node_t *x)
{
assert(x != NULL);
@@ -84,6 +169,32 @@ static void update_height_to_root(btree_node_t *x)
}
}
/* perform a right rotation on a subtree
if you have a tree like this:
Z
/ \
. X
/ \
Y .
/ \
. .
and you perform a right rotation on node X,
you will get the following tree:
Z
/ \
. Y
/ \
. X
/ \
. .
note that this function does NOT update b_height for the rotated
nodes. it is up to you to call update_height_to_root().
*/
static void rotate_right(btree_t *tree, btree_node_t *y)
{
assert(y);
@@ -117,6 +228,33 @@ static void rotate_right(btree_t *tree, btree_node_t *y)
x->b_parent = p;
}
/* for a given node Z, perform a right rotation on Z's right child,
followed by a left rotation on Z itself.
if you have a tree like this:
Z
/ \
. X
/ \
Y .
/ \
. .
and you perform a double-left rotation on node Z,
you will get the following tree:
Y
/ \
/ \
Z X
/ \ / \
. . . .
note that, unlike rotate_left and rotate_right, this function
DOES update b_height for the rotated nodes (since it needs to be
done in a certain order).
*/
static void rotate_double_left(btree_t *tree, btree_node_t *z)
{
btree_node_t *x = z->b_right;
@@ -134,6 +272,33 @@ static void rotate_double_left(btree_t *tree, btree_node_t *z)
}
}
/* for a given node Z, perform a left rotation on Z's left child,
followed by a right rotation on Z itself.
if you have a tree like this:
Z
/ \
X .
/ \
. Y
/ \
. .
and you perform a double-right rotation on node Z,
you will get the following tree:
Y
/ \
/ \
X Z
/ \ / \
. . . .
note that, unlike rotate_left and rotate_right, this function
DOES update b_height for the rotated nodes (since it needs to be
done in a certain order).
*/
static void rotate_double_right(btree_t *tree, btree_node_t *z)
{
btree_node_t *x = z->b_left;
@@ -151,9 +316,20 @@ static void rotate_double_right(btree_t *tree, btree_node_t *z)
}
}
/* run after an insert operation. checks that the balance factor
of the local subtree is within the range -1 <= BF <= 1. if it
is not, rotate the subtree to restore balance.
note that at most one rotation should be required after a node
is inserted into the tree.
this function depends on all nodes in the tree having
correct b_height values.
@param w the node that was just inserted into the tree
*/
static void insert_fixup(btree_t *tree, btree_node_t *w)
{
int nr_rotations = 0;
btree_node_t *z = NULL, *y = NULL, *x = NULL;
z = w;
@@ -181,7 +357,6 @@ static void insert_fixup(btree_t *tree, btree_node_t *w)
update_height_to_root(z);
}
}
nr_rotations++;
next_ancestor:
x = y;
@@ -190,19 +365,35 @@ next_ancestor:
}
}
/* run after a delete operation. checks that the balance factor
of the local subtree is within the range -1 <= BF <= 1. if it
is not, rotate the subtree to restore balance.
note that, unlike insert_fixup, multiple rotations may be required
to restore balance after a node is deleted.
this function depends on all nodes in the tree having
correct b_height values.
@param w one of the following:
- the parent of the node that was deleted if the node
had no children.
- the parent of the node that replaced the deleted node
if the deleted node had two children.
- the node that replaced the node that was deleted, if
the node that was deleted had one child.
*/
static void delete_fixup(btree_t *tree, btree_node_t *w)
{
btree_node_t *z = w;
int nr_rotations = 0;
while (z) {
if (bf(z) > 1) {
if (bf(z->b_right) >= 0) {
rotate_left(tree, z);
update_height_to_root(z);
} else {
rotate_double_left(tree, z); // <==
rotate_double_left(tree, z);
}
} else if (bf(z) < -1) {
if (bf(z->b_left) <= 0) {
@@ -214,10 +405,14 @@ static void delete_fixup(btree_t *tree, btree_node_t *w)
}
z = z->b_parent;
nr_rotations++;
}
}
/* updates b_height for all nodes between the inserted node and the root
of the tree, and calls insert_fixup.
@param node the node that was just inserted into the tree.
*/
void btree_insert_fixup(btree_t *tree, btree_node_t *node)
{
node->b_height = 0;
@@ -231,6 +426,15 @@ void btree_insert_fixup(btree_t *tree, btree_node_t *node)
insert_fixup(tree, node);
}
/* remove a node from a tree.
this function assumes that `node` has no children, and therefore
doesn't need to be replaced.
updates b_height for all nodes between `node` and the tree root.
@param node the node to delete.
*/
static btree_node_t *remove_node_with_no_children(btree_t *tree, btree_node_t *node)
{
btree_node_t *w = node->b_parent;
@@ -253,6 +457,16 @@ static btree_node_t *remove_node_with_no_children(btree_t *tree, btree_node_t *n
return w;
}
/* remove a node from a tree.
this function assumes that `node` has one child.
the child of `node` is inherited by `node`'s parent, and `node` is removed.
updates b_height for all nodes between the node that replaced
`node` and the tree root.
@param node the node to delete.
*/
static btree_node_t *replace_node_with_one_subtree(btree_t *tree, btree_node_t *node)
{
btree_node_t *p = node->b_parent;
@@ -286,6 +500,20 @@ static btree_node_t *replace_node_with_one_subtree(btree_t *tree, btree_node_t *
return w;
}
/* remove a node from a tree.
this function assumes that `node` has two children.
find the in-order successor Y of `node` (the largest node in `node`'s left sub-tree),
removes `node` from the tree and moves Y to where `node` used to be.
if Y has a child (it will never have more than one), have Y's parent inherit
Y's child.
updates b_height for all nodes between the deepest node that was modified
and the tree root.
@param z the node to delete.
*/
static btree_node_t *replace_node_with_two_subtrees(btree_t *tree, btree_node_t *z)
{
/* x will replace z */
@@ -349,6 +577,7 @@ static btree_node_t *replace_node_with_two_subtrees(btree_t *tree, btree_node_t
return w;
}
/* delete a node from the tree and re-balance it afterwards */
void btree_delete(btree_t *tree, btree_node_t *node)
{
btree_node_t *w = NULL;
@@ -370,6 +599,8 @@ void btree_delete(btree_t *tree, btree_node_t *node)
btree_node_t *btree_first(btree_t *tree)
{
/* the first node in the tree is the node with the smallest key.
we keep moving left until we can't go any further */
btree_node_t *cur = tree->b_root;
if (!cur) {
return NULL;
@@ -384,6 +615,8 @@ btree_node_t *btree_first(btree_t *tree)
btree_node_t *btree_last(btree_t *tree)
{
/* the first node in the tree is the node with the largest key.
we keep moving right until we can't go any further */
btree_node_t *cur = tree->b_root;
if (!cur) {
return NULL;
@@ -402,7 +635,18 @@ btree_node_t *btree_next(btree_node_t *node)
return NULL;
}
/* there are two possibilities for the next node:
1. if `node` has a right sub-tree, every node in this sub-tree is bigger
than node. the in-order successor of `node` is the smallest node in
this subtree.
2. if `node` has no right sub-tree, we've reached the largest node in
the sub-tree rooted at `node`. we need to go back to our parent
and continue the search elsewhere.
*/
if (node->b_right) {
/* case 1: step into `node`'s right sub-tree and keep going
left to find the smallest node */
btree_node_t *cur = node->b_right;
while (cur->b_left) {
cur = cur->b_left;
@@ -411,6 +655,10 @@ btree_node_t *btree_next(btree_node_t *node)
return cur;
}
/* case 2: keep stepping back up towards the root of the tree.
if we encounter a step where we are our parent's left child,
we've found a parent with a value larger than us. this parent
is the in-order successor of `node` */
while (node->b_parent && node->b_parent->b_left != node) {
node = node->b_parent;
}
@@ -424,7 +672,18 @@ btree_node_t *btree_prev(btree_node_t *node)
return NULL;
}
/* there are two possibilities for the previous node:
1. if `node` has a left sub-tree, every node in this sub-tree is smaller
than `node`. the in-order predecessor of `node` is the largest node in
this subtree.
2. if `node` has no left sub-tree, we've reached the smallest node in
the sub-tree rooted at `node`. we need to go back to our parent
and continue the search elsewhere.
*/
if (node->b_left) {
/* case 1: step into `node`'s left sub-tree and keep going
right to find the largest node */
btree_node_t *cur = node->b_left;
while (cur->b_right) {
cur = cur->b_right;
@@ -433,6 +692,10 @@ btree_node_t *btree_prev(btree_node_t *node)
return cur;
}
/* case 2: keep stepping back up towards the root of the tree.
if we encounter a step where we are our parent's right child,
we've found a parent with a value smaller than us. this parent
is the in-order predecessor of `node`. */
while (node->b_parent && node->b_parent->b_right != node) {
node = node->b_parent;
}

211
sandbox/btree/include/socks/btree.h
View File

@@ -1,10 +1,63 @@
/*
The Clear BSD License
Copyright (c) 2023 Max Wash
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted (subject to the limitations in the disclaimer
below) provided that the following conditions are met:
- Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
- Neither the name of the copyright holder nor the names of its
contributors may be used to endorse or promote products derived from this
software without specific prior written permission.
*/
#ifndef SOCKS_BTREE_H_
#define SOCKS_BTREE_H_
#include <stdint.h>
/* if your custom structure contains a btree_node_t (i.e. it can be part of a btree),
you can use this macro to convert a btree_node_t* to a your_type*
@param t the name of your custom type (something that can be passed to offsetof)
@param m the name of the btree_node_t member variable within your custom type.
@param v the btree_node_t pointer that you wish to convert. if this is NULL, NULL will be returned.
*/
#define BTREE_CONTAINER(t, m, v) ((void *)((v) ? (uintptr_t)(v) - (offsetof(t, m)) : 0))
/* defines a simple node insertion function.
this function assumes that your nodes have simple integer keys that can be compared with the usual operators.
EXAMPLE:
if you have a tree node type like this:
struct my_tree_node {
int key;
btree_node_t base;
}
You would use the following call to generate an insert function for a tree with this node type:
BTREE_DEFINE_SIMPLE_INSERT(struct my_tree_node, base, key, my_tree_node_insert);
Which would emit a function defined like:
static void my_tree_node_insert(btree_t *tree, struct my_tree_node *node);
@param node_type your custom tree node type. usually a structure that contains a btree_node_t member.
@param container_node_member the name of the btree_node_t member variable within your custom type.
@param container_key_member the name of the key member variable within your custom type.
@param function_name the name of the function to generate.
*/
#define BTREE_DEFINE_SIMPLE_INSERT(node_type, container_node_member, container_key_member, function_name) \
static void function_name(btree_t *tree, node_type *node) \
{ \
@@ -43,6 +96,43 @@
btree_insert_fixup(tree, &node->container_node_member); \
}
/* defines a node insertion function.
this function should be used for trees with complex node keys that cannot be directly compared.
a comparator for your keys must be supplied.
EXAMPLE:
if you have a tree node type like this:
struct my_tree_node {
complex_key_t key;
btree_node_t base;
}
You would need to define a comparator function or macro with the following signature:
int my_comparator(struct my_tree_node *a, struct my_tree_node *b);
Which implements the following:
return -1 if a < b
return 0 if a == b
return 1 if a > b
You would use the following call to generate an insert function for a tree with this node type:
BTREE_DEFINE_INSERT(struct my_tree_node, base, key, my_tree_node_insert, my_comparator);
Which would emit a function defined like:
static void my_tree_node_insert(btree_t *tree, struct my_tree_node *node);
@param node_type your custom tree node type. usually a structure that contains a btree_node_t member.
@param container_node_member the name of the btree_node_t member variable within your custom type.
@param container_key_member the name of the key member variable within your custom type.
@param function_name the name of the function to generate.
@param comparator the name of a comparator function or functional-macro that conforms to the
requirements listed above.
*/
#define BTREE_DEFINE_INSERT(node_type, container_node_member, container_key_member, function_name, comparator) \
static void function_name(btree_t *tree, node_type *node) \
{ \
@@ -82,6 +172,32 @@
btree_insert_fixup(tree, &node->container_node_member); \
}
/* defines a simple tree search function.
this function assumes that your nodes have simple integer keys that can be compared with the usual operators.
EXAMPLE:
if you have a tree node type like this:
struct my_tree_node {
int key;
btree_node_t base;
}
You would use the following call to generate a search function for a tree with this node type:
BTREE_DEFINE_SIMPLE_GET(struct my_tree_node, int, base, key, my_tree_node_get);
Which would emit a function defined like:
static void my_tree_node_get(btree_t *tree, int key);
@param node_type your custom tree node type. usually a structure that contains a btree_node_t member.
@param key_type the type name of the key embedded in your custom tree node type. this type must be
compatible with the builtin comparison operators.
@param container_node_member the name of the btree_node_t member variable within your custom type.
@param container_key_member the name of the key member variable within your custom type.
@param function_name the name of the function to generate.
*/
#define BTREE_DEFINE_SIMPLE_GET(node_type, key_type, container_node_member, container_key_member, function_name) \
node_type *get(btree_t *tree, key_type key) \
{ \
@@ -100,60 +216,155 @@ node_type *get(btree_t *tree, key_type key) \
return NULL; \
}
/* perform an in-order traversal of a binary tree
If you have a tree defined like:
btree_t my_tree;
with nodes defined like:
struct my_tree_node {
int key;
btree_node_t base;
}
and you want to do something like:
foreach (struct my_tree_node *node : my_tree) { ... }
you should use this:
btree_foreach (struct my_tree_node, node, &my_tree, base) { ... }
@param iter_type the type name of the iterator variable. this should be the tree's node type, and shouldn't be a pointer.
@param iter_name the name of the iterator variable.
@param tree_name a pointer to the tree to traverse.
@param node_member the name of the btree_node_t member variable within the tree node type.
*/
#define btree_foreach(iter_type, iter_name, tree_name, node_member) \
for (iter_type *iter_name = BTREE_CONTAINER(iter_type, node_member, btree_first(tree_name)); \
iter_name; \
iter_name = BTREE_CONTAINER(iter_type, node_member, btree_next(&((iter_name)->node_member))))
/* perform an reverse in-order traversal of a binary tree
If you have a tree defined like:
btree_t my_tree;
with nodes defined like:
struct my_tree_node {
int key;
btree_node_t base;
}
and you want to do something like:
foreach (struct my_tree_node *node : reverse(my_tree)) { ... }
you should use this:
btree_foreach_r (struct my_tree_node, node, &my_tree, base) { ... }
@param iter_type the type name of the iterator variable. this should be the tree's node type, and shouldn't be a pointer.
@param iter_name the name of the iterator variable.
@param tree_name a pointer to the tree to traverse.
@param node_member the name of the btree_node_t member variable within the tree node type.
*/
#define btree_foreach_r(iter_type, iter_name, tree_name, node_member) \
for (iter_type *iter_name = BTREE_CONTAINER(iter_type, node_member, btree_last(tree_name)); \
iter_name; \
iter_name = BTREE_CONTAINER(iter_type, node_member, btree_prev(&((iter_name)->node_member))))
/* binary tree nodes. this *cannot* be used directly. you need to define a custom node type
that contains a member variable of type btree_node_t.
you would then use the supplied macros to define functions to manipulate your custom binary tree.
*/
typedef struct btree_node {
struct btree_node *b_parent, *b_left, *b_right;
unsigned short b_height;
} btree_node_t;
/* binary tree. unlike btree_node_t, you can define variables of type btree_t. */
typedef struct btree {
struct btree_node *b_root;
} btree_t;
/* re-balance a binary tree after an insertion operation.
NOTE that, if you define an insertion function using BTREE_DEFINE_INSERT or similar,
this function will automatically called for you.
@param tree the tree to re-balance.
@param node the node that was just inserted into the tree.
*/
extern void btree_insert_fixup(btree_t *tree, btree_node_t *node);
/* delete a node from a binary tree and re-balance the tree afterwards.
@param tree the tree to delete from
@param node the node to delete.
*/
extern void btree_delete(btree_t *tree, btree_node_t *node);
/* get the first node in a binary tree.
this will be the node with the smallest key (i.e. the node that is furthest-left from the root)
*/
extern btree_node_t *btree_first(btree_t *tree);
/* get the last node in a binary tree.
this will be the node with the largest key (i.e. the node that is furthest-right from the root)
*/
extern btree_node_t *btree_last(btree_t *tree);
/* for any binary tree node, this function returns the node with the next-largest key value */
extern btree_node_t *btree_next(btree_node_t *node);
/* for any binary tree node, this function returns the node with the next-smallest key value */
extern btree_node_t *btree_prev(btree_node_t *node);
/* sets `child` as the immediate left-child of `parent` */
static inline void btree_put_left(btree_node_t *parent, btree_node_t *child)
{
parent->b_left = child;
child->b_parent = parent;
}
/* sets `child` as the immediate right-child of `parent` */
static inline void btree_put_right(btree_node_t *parent, btree_node_t *child)
{
parent->b_right = child;
child->b_parent = parent;
}
/* get the immediate left-child of `node` */
static inline btree_node_t *btree_left(btree_node_t *node)
{
return node->b_left;
}
/* get the immediate right-child of `node` */
static inline btree_node_t *btree_right(btree_node_t *node)
{
return node->b_right;
}
/* get the immediate parent of `node` */
static inline btree_node_t *btree_parent(btree_node_t *node)
{
return node->b_parent;
}
/* get the height of `node`.
the height of a node is defined as the length of the longest path
between the node and a leaf node.
this count includes the node itself, so the height of a leaf node will be 1.
*/
static inline unsigned short btree_height(btree_node_t *node)
{
return node->b_height;