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avl_tree.c
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avl_tree.c
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/* SPDX-License-Identifier: LGPL-3.0-or-later */
/* Copyright (C) 2020 Invisible Things Lab
* Borys Popławski <borysp@invisiblethingslab.com>
*/
#include "avl_tree.h"
#include <stddef.h>
#include "api.h"
#include "assert.h"
static void avl_tree_init_node(struct avl_tree_node* node) {
node->left = NULL;
node->right = NULL;
node->parent = NULL;
node->balance = 0;
}
/* Inserts a node into tree, but leaves it unbalanced, i.e. all nodes on path from root to newly
* inserted node could have their balance field off by +1/-1 */
static void avl_tree_insert_unbalanced(struct avl_tree* tree,
struct avl_tree_node* node_to_insert) {
assert(tree);
assert(tree->root);
assert(node_to_insert);
struct avl_tree_node* node = tree->root;
while (1) {
if (tree->cmp(node_to_insert, node)) {
if (!node->left) {
node->left = node_to_insert;
node_to_insert->parent = node;
return;
} else {
node = node->left;
}
} else {
if (!node->right) {
node->right = node_to_insert;
node_to_insert->parent = node;
return;
} else {
node = node->right;
}
}
}
}
/* Replaces `old_node` with `new_node` fixing all necessary links. `parent` must be the parent of
* `old_node` before call to this. */
static void fixup_link(struct avl_tree_node* old_node, struct avl_tree_node* new_node,
struct avl_tree_node* parent) {
if (parent) {
if (parent->left == old_node) {
parent->left = new_node;
} else {
assert(parent->right == old_node);
parent->right = new_node;
}
}
if (new_node) {
new_node->parent = parent;
}
}
/*
* The next 4 functions do rotations (rot1 - single, rot2 - double, which is a concatenation of two
* single rotations). L stands for left (counterclockwise) rotation and R for right (clockwise).
* The naming convention is: `p` is topmost node and parent of `q`, which in turn is parent of `r`.
*/
static void rot1L(struct avl_tree_node* q, struct avl_tree_node* p) {
assert(q->parent == p);
assert(p->right == q);
assert(q->balance == 1 || q->balance == 0);
assert(p->balance == 2);
fixup_link(/*old_node=*/p, /*new_node=*/q, /*parent=*/p->parent);
p->right = q->left;
if (q->left) {
q->left->parent = p;
}
q->left = p;
p->parent = q;
if (q->balance == 1) {
p->balance = 0;
q->balance = 0;
} else { // q->balance == 0
p->balance = 1;
q->balance = -1;
}
}
static void rot1R(struct avl_tree_node* q, struct avl_tree_node* p) {
assert(q->parent == p);
assert(p->left == q);
assert(q->balance == -1 || q->balance == 0);
assert(p->balance == -2);
fixup_link(/*old_node=*/p, /*new_node=*/q, /*parent=*/p->parent);
p->left = q->right;
if (q->right) {
q->right->parent = p;
}
q->right = p;
p->parent = q;
if (q->balance == -1) {
p->balance = 0;
q->balance = 0;
} else { // q->balance == 0
p->balance = -1;
q->balance = 1;
}
}
static void rot2RL(struct avl_tree_node* r, struct avl_tree_node* q, struct avl_tree_node* p) {
assert(q->parent == p);
assert(p->right == q);
assert(q->balance == -1);
assert(p->balance == 2);
assert(r->parent == q);
assert(q->left == r);
assert(-1 <= r->balance && r->balance <= 1);
fixup_link(/*old_node=*/p, /*new_node=*/r, /*parent=*/p->parent);
p->right = r->left;
if (r->left) {
r->left->parent = p;
}
q->left = r->right;
if (r->right) {
r->right->parent = q;
}
r->left = p;
p->parent = r;
r->right = q;
q->parent = r;
if (r->balance == -1) {
p->balance = 0;
q->balance = 1;
} else if (r->balance == 0) {
p->balance = 0;
q->balance = 0;
} else { // r->balance == 1
p->balance = -1;
q->balance = 0;
}
r->balance = 0;
}
static void rot2LR(struct avl_tree_node* r, struct avl_tree_node* q, struct avl_tree_node* p) {
assert(q->parent == p);
assert(p->left == q);
assert(q->balance == 1);
assert(p->balance == -2);
assert(r->parent == q);
assert(q->right == r);
assert(-1 <= r->balance && r->balance <= 1);
fixup_link(/*old_node=*/p, /*new_node=*/r, /*parent=*/p->parent);
q->right = r->left;
if (r->left) {
r->left->parent = q;
}
p->left = r->right;
if (r->right) {
r->right->parent = p;
}
r->left = q;
q->parent = r;
r->right = p;
p->parent = r;
if (r->balance == -1) {
q->balance = 0;
p->balance = 1;
} else if (r->balance == 0) {
q->balance = 0;
p->balance = 0;
} else { // r->balance == 1
q->balance = -1;
p->balance = 0;
}
r->balance = 0;
}
/* Does appropriate rotation of node, which mush have disturbed balance (i.e. +2/-2).
* Returns whether height might have changed and sets `new_root_ptr` to root of this subtree after
* rotation. */
static bool avl_tree_do_balance(struct avl_tree_node* node, struct avl_tree_node** new_root_ptr) {
assert(node->balance == -2 || node->balance == 2);
struct avl_tree_node* child = NULL;
bool ret;
if (node->balance < 0) { // node->balance == -2
child = node->left;
if (child->balance == 1) {
assert(child->right);
*new_root_ptr = child->right;
rot2LR(child->right, child, node);
return true;
} else { // child->balance <= 0
*new_root_ptr = child;
ret = child->balance != 0;
rot1R(child, node);
return ret;
}
} else { // node->balance == 2
child = node->right;
if (child->balance >= 0) {
*new_root_ptr = child;
ret = child->balance != 0;
rot1L(child, node);
return ret;
} else { // child->balance == -1
assert(child->left);
*new_root_ptr = child->left;
rot2RL(child->left, child, node);
return true;
}
}
}
enum side {
LEFT,
RIGHT
};
/*
* Balances the tree going from `node` upwards, to the tree root, stopping if a subtree height
* did not change.
* `side` indicates which child of `node` had its height changed.
* `height_increased` is false if the subtree height decreased, true if increased.
*
* Returns the root of the subtree that balancing stopped at.
*/
static struct avl_tree_node* avl_tree_balance(struct avl_tree_node* node, enum side side,
bool height_increased) {
assert(node);
while (1) {
bool height_changed = true;
if (side == LEFT) {
if (height_increased) {
height_changed = node->balance <= 0;
node->balance -= 1;
} else {
height_changed = node->balance < 0;
node->balance += 1;
}
} else {
assert(side == RIGHT);
if (height_increased) {
height_changed = node->balance >= 0;
node->balance += 1;
} else {
height_changed = node->balance > 0;
node->balance -= 1;
}
}
assert(-2 <= node->balance && node->balance <= 2);
if (node->balance == -2 || node->balance == 2) {
height_changed = avl_tree_do_balance(node, &node);
/* On inserting height never changes. */
height_changed = height_increased ? false : height_changed;
}
/* This sub-tree is balanced, but its height might have changed. */
if (!height_changed || !node->parent) {
return node;
}
if (node->parent->left == node) {
side = LEFT;
} else {
assert(node->parent->right == node);
side = RIGHT;
}
node = node->parent;
}
}
void avl_tree_insert(struct avl_tree* tree, struct avl_tree_node* node) {
avl_tree_init_node(node);
/* Inserting into an empty tree. */
if (!tree->root) {
tree->root = node;
return;
}
avl_tree_insert_unbalanced(tree, node);
assert(node->parent);
struct avl_tree_node* new_root;
if (node->parent->left == node) {
new_root = avl_tree_balance(node->parent, LEFT, /*height_increased=*/true);
} else {
assert(node->parent->right == node);
new_root = avl_tree_balance(node->parent, RIGHT, /*height_increased=*/true);
}
if (!new_root->parent) {
tree->root = new_root;
}
}
void avl_tree_swap_node(struct avl_tree* tree, struct avl_tree_node* old_node,
struct avl_tree_node* new_node) {
assert(tree->cmp(old_node, new_node) && tree->cmp(new_node, old_node));
avl_tree_init_node(new_node);
fixup_link(/*old_node=*/old_node, /*new_node=*/new_node, /*parent=*/old_node->parent);
new_node->left = old_node->left;
if (new_node->left) {
new_node->left->parent = new_node;
}
new_node->right = old_node->right;
if (new_node->right) {
new_node->right->parent = new_node;
}
new_node->balance = old_node->balance;
if (tree->root == old_node) {
tree->root = new_node;
}
}
struct avl_tree_node* avl_tree_prev(struct avl_tree_node* node) {
if (node->left) {
node = node->left;
while (node->right) {
node = node->right;
}
return node;
}
while (node->parent && node->parent->left == node) {
node = node->parent;
}
return node->parent;
}
struct avl_tree_node* avl_tree_next(struct avl_tree_node* node) {
if (node->right) {
node = node->right;
while (node->left) {
node = node->left;
}
return node;
}
while (node->parent && node->parent->right == node) {
node = node->parent;
}
return node->parent;
}
struct avl_tree_node* avl_tree_first(struct avl_tree* tree) {
struct avl_tree_node* node = tree->root;
if (!node) {
return NULL;
}
while (node->left) {
node = node->left;
}
return node;
}
struct avl_tree_node* avl_tree_last(struct avl_tree* tree) {
struct avl_tree_node* node = tree->root;
if (!node) {
return NULL;
}
while (node->right) {
node = node->right;
}
return node;
}
void avl_tree_delete(struct avl_tree* tree, struct avl_tree_node* node) {
/* If `node` has both children, swap it with the next node. This might temporarily disturb
* the tree order, but only between `node` and `next`, which is ok, since we are about to
* remove `node` from the tree completely.
* This is done so that `node` has 1 child at most (if a node has 2 children, then the next
* node cannot have its left child). */
if (node->left && node->right) {
struct avl_tree_node* next = avl_tree_next(node);
assert(next->balance == 0 || next->balance == 1);
if (next->right) {
assert(next->right->balance == 0);
assert(!next->right->left);
assert(!next->right->right);
}
assert(next->parent);
struct avl_tree_node* tmp_right = next->right;
struct avl_tree_node* tmp_parent = next->parent;
signed char tmp_balance = next->balance;
fixup_link(/*old_node=*/node, /*new_node=*/next, /*parent=*/node->parent);
/* In this order it works even if both next->left and next->right are NULL pointers,
* because node->left is not NULL here. */
fixup_link(/*old_node=*/next->left, /*new_node=*/node->left, /*parent=*/next);
if (next == node->right) {
next->right = node;
node->parent = next;
} else {
fixup_link(/*old_node=*/next->right, /*new_node=*/node->right, /*parent=*/next);
fixup_link(/*old_node=*/next, /*new_node=*/node, /*parent=*/tmp_parent);
}
node->left = NULL;
fixup_link(/*old_node=*/node->right, /*new_node=*/tmp_right, /*parent=*/node);
next->balance = node->balance;
node->balance = tmp_balance;
if (tree->root == node) {
tree->root = next;
}
}
assert(!(node->left && node->right));
/* This initialization value has no meaning, it's just here to keep GCC happy. */
enum side side = LEFT;
if (node->parent) {
if (node->parent->left == node) {
side = LEFT;
} else {
assert(node->parent->right == node);
side = RIGHT;
}
}
struct avl_tree_node* new_root = NULL;
/* Remove `node` from the tree. */
if (!node->left && !node->right) {
new_root = NULL;
fixup_link(/*old_node=*/node, /*new_node=*/NULL, /*parent=*/node->parent);
} else if (node->left && !node->right) {
new_root = node->left;
fixup_link(/*old_node=*/node, /*new_node=*/node->left, /*parent=*/node->parent);
} else {
assert(!node->left && node->right);
new_root = node->right;
fixup_link(/*old_node=*/node, /*new_node=*/node->right, /*parent=*/node->parent);
}
/* After removal the tree might need balancing. */
if (node->parent) {
new_root = avl_tree_balance(node->parent, side, /*height_increased=*/false);
}
if ((new_root && !new_root->parent) || !node->parent) {
tree->root = new_root;
}
}
static struct avl_tree_node* avl_tree_find_fn_to(struct avl_tree* tree,
struct avl_tree_node* cmp_arg,
bool cmp(struct avl_tree_node*,
struct avl_tree_node*)) {
struct avl_tree_node* node = tree->root;
while (node) {
bool x = cmp(cmp_arg, node);
if (x) {
if (cmp(node, cmp_arg)) {
return node;
}
node = node->left;
} else {
node = node->right;
}
}
return NULL;
}
struct avl_tree_node* avl_tree_find(struct avl_tree* tree, struct avl_tree_node* node) {
return avl_tree_find_fn_to(tree, node, tree->cmp);
}
#ifdef UBSAN
/*
* Function pointer cmp is of type `bool (*)(void*, struct avl_tree_node*)` but the caller
* avl_tree_lower_bound() passes cmp as `bool (*)(struct avl_tree_node*, struct avl_tree_node*)`.
* UBSan complains about "Indirect call of a function through a function pointer of the wrong type"
* because of this mismatch. However, allowing the first argument to be a pointer to any type was
* done on purpose; see corresponding comment in avl_tree.h. So, silence this particular complaint.
*/
__attribute__((no_sanitize("function")))
#endif
struct avl_tree_node* avl_tree_lower_bound_fn(struct avl_tree* tree, void* cmp_arg,
bool cmp(void*, struct avl_tree_node*)) {
struct avl_tree_node* node = tree->root;
struct avl_tree_node* ret = NULL;
while (node) {
if (cmp(cmp_arg, node)) {
ret = node;
node = node->left;
} else {
node = node->right;
}
}
return ret;
}
struct avl_tree_node* avl_tree_lower_bound(struct avl_tree* tree, struct avl_tree_node* cmp_arg) {
static_assert(SAME_TYPE(tree->cmp, bool (*)(struct avl_tree_node*, struct avl_tree_node*)),
"If you change this function type, make sure the code below works properly!");
return avl_tree_lower_bound_fn(tree, cmp_arg,
(bool (*)(void*, struct avl_tree_node*))tree->cmp);
}
/* This function returns whether a tree with root in `node` is avl-balanced and updates `*size`
* with height of the tree. */
static bool avl_tree_is_balanced_size(struct avl_tree_node* node, size_t* size) {
if (!node) {
*size = 0;
return true;
}
size_t a = 0;
size_t b = 0;
bool ret = avl_tree_is_balanced_size(node->left, &a);
ret &= avl_tree_is_balanced_size(node->right, &b);
if (a < b) {
ret &= (b - a) == 1;
ret &= node->balance == 1;
*size = b;
} else if (a == b) {
ret &= node->balance == 0;
*size = a;
} else { // a > b
ret &= (a - b) == 1;
ret &= node->balance == -1;
*size = a;
}
*size += 1;
return ret;
}
bool debug_avl_tree_is_balanced(struct avl_tree* tree) {
size_t s;
return avl_tree_is_balanced_size(tree->root, &s);
}