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use std::cmp::max;
use crate::RefCounter;
pub enum AVL<K, V = ()> {
Empty,
Node {
key: RefCounter<K>,
value: RefCounter<V>,
left: RefCounter<AVL<K, V>>,
right: RefCounter<AVL<K, V>>,
},
}
pub type OrderedMap<K, V> = AVL<K, V>;
pub type OrderedSet<K> = AVL<K>;
impl<K, V> Clone for AVL<K, V> {
fn clone(&self) -> Self {
match self {
Self::Empty => Self::Empty,
Self::Node {
key,
value,
left,
right,
} => Self::Node {
key: key.clone(),
value: value.clone(),
left: left.clone(),
right: right.clone(),
},
}
}
}
impl<K: Ord> AVL<K> {
pub fn insert(&self, value: K) -> Self {
self.put(value, ())
}
pub fn search(&self, value: &K) -> bool {
self.find(value).is_some()
}
}
impl<K: Ord, V> AVL<K, V> {
pub fn empty() -> AVL<K, V> {
AVL::Empty
}
pub fn is_empty(&self) -> bool {
matches!(self, AVL::Empty)
}
fn height(&self) -> i64 {
match self {
AVL::Empty => 0,
AVL::Node {
key: _,
value: _,
left,
right,
} => 1 + max(&left.height(), &right.height()),
}
}
fn diff(&self) -> i64 {
match self {
AVL::Empty => 0,
AVL::Node {
key: _,
value: _,
left,
right,
} => left.height() - right.height(),
}
}
pub fn find(&self, target_value: &K) -> Option<&V> {
match self {
AVL::Empty => Option::None,
AVL::Node {
key,
value,
left,
right,
} => match target_value.cmp(key) {
std::cmp::Ordering::Less => left.find(target_value),
std::cmp::Ordering::Equal => Option::Some(value.as_ref()),
std::cmp::Ordering::Greater => right.find(target_value),
},
}
}
fn right_rotation(&self) -> AVL<K, V> {
if let AVL::Node {
key: x,
value: vx,
left: lt,
right: t3,
} = self
{
if let AVL::Node {
key: y,
value: vy,
left: t1,
right: t2,
} = (*lt).as_ref()
{
return AVL::Node {
key: y.clone(),
left: t1.clone(),
value: vy.clone(),
right: RefCounter::new(AVL::Node {
key: x.clone(),
value: vx.clone(),
left: t2.clone(),
right: t3.clone(),
}),
};
}
}
self.clone()
}
fn right_fix(&self) -> AVL<K, V> {
if let AVL::Node {
key: x,
value: vx,
left: t1,
right: t2,
} = self
{
if t1.diff() == -1 {
return AVL::Node {
key: x.clone(),
value: vx.clone(),
left: RefCounter::new(t1.left_rotation()),
right: t2.clone(),
}
.right_rotation();
} else {
return self.right_rotation();
}
}
self.clone()
}
fn left_rotation(&self) -> AVL<K, V> {
if let AVL::Node {
key: x,
value: vx,
left: t1,
right: rt,
} = self
{
if let AVL::Node {
key: y,
value: vy,
left: t2,
right: t3,
} = (*rt).as_ref()
{
return AVL::Node {
key: y.clone(),
value: vy.clone(),
left: RefCounter::new(AVL::Node {
key: x.clone(),
value: vx.clone(),
left: t1.clone(),
right: t2.clone(),
}),
right: t3.clone(),
};
}
}
self.clone()
}
fn left_fix(&self) -> AVL<K, V> {
if let AVL::Node {
key: x,
value: vx,
left: t1,
right: t2,
} = self
{
if t2.diff() == 1 {
return AVL::Node {
key: x.clone(),
value: vx.clone(),
left: t1.clone(),
right: RefCounter::new(t2.right_rotation()),
}
.left_rotation();
} else {
return self.left_rotation();
}
}
self.clone()
}
fn fix(&self) -> AVL<K, V> {
match self.diff() {
2 => self.right_fix(),
-2 => self.left_fix(),
_ => self.clone(),
}
}
pub fn put(&self, key: K, value: V) -> AVL<K, V> {
self.put_rc(RefCounter::new(key), RefCounter::new(value))
}
fn put_rc(&self, key_rc: RefCounter<K>, value_rc: RefCounter<V>) -> AVL<K, V> {
match self {
AVL::Empty => AVL::Node {
key: key_rc,
value: value_rc,
left: RefCounter::new(AVL::Empty),
right: RefCounter::new(AVL::Empty),
},
AVL::Node {
key,
value,
left,
right,
} => match key_rc.cmp(key) {
std::cmp::Ordering::Less => AVL::Node {
key: key.clone(),
value: value.clone(),
left: RefCounter::new(left.put_rc(key_rc, value_rc)),
right: right.clone(),
}
.fix(),
std::cmp::Ordering::Equal => AVL::Node {
key: key_rc,
value: value_rc,
left: left.clone(),
right: right.clone(),
},
std::cmp::Ordering::Greater => AVL::Node {
key: key.clone(),
value: value.clone(),
left: left.clone(),
right: RefCounter::new(right.put_rc(key_rc, value_rc)),
}
.fix(),
},
}
}
pub fn delete(&self, target_key: &K) -> AVL<K, V> {
match self {
AVL::Empty => AVL::Empty,
AVL::Node {
key,
value,
left,
right,
} => {
match target_key.cmp(key) {
std::cmp::Ordering::Less => {
let left_deleted = left.delete(target_key);
AVL::Node {
key: key.clone(),
value: value.clone(),
left: RefCounter::new(left_deleted),
right: right.clone(),
}
.fix()
}
std::cmp::Ordering::Equal => {
// Node with only one child or no child
if left.is_empty() {
return right.as_ref().clone();
} else if right.is_empty() {
return left.as_ref().clone();
}
// Node with two children, get the inorder predecessor (maximum value in the left subtree)
let inorder_predecessor = left.find_max();
if let Some((pred_key, pred_value)) = inorder_predecessor {
let left_deleted = left.delete(&pred_key);
AVL::Node {
key: pred_key.clone(),
value: pred_value.clone(),
left: RefCounter::new(left_deleted),
right: right.clone(),
}
.fix()
} else {
self.clone()
}
}
std::cmp::Ordering::Greater => {
let right_deleted = right.delete(target_key);
AVL::Node {
key: key.clone(),
value: value.clone(),
left: left.clone(),
right: RefCounter::new(right_deleted),
}
.fix()
}
}
}
}
}
fn find_max(&self) -> Option<(RefCounter<K>, RefCounter<V>)> {
match self {
AVL::Empty => None,
AVL::Node {
key,
value,
left: _,
right,
} => {
if right.is_empty() {
Some((key.clone(), value.clone()))
} else {
right.find_max()
}
}
}
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_avl_set() {
let l = AVL::empty().insert(1).insert(2).insert(3).insert(4);
let l2 = l.clone().insert(5);
for i in 1..=4 {
assert!(l.search(&i));
assert!(l2.search(&i));
}
assert!(!l.search(&5));
assert!(l2.search(&5));
}
#[test]
fn test_avl_map() {
let l = AVL::empty().put(1, 999);
let l2 = l.clone().put(1, 123).put(2, 3);
assert_eq!(l.find(&1), Some(&999));
assert_eq!(l2.find(&1), Some(&123));
assert!(l.find(&2).is_none());
assert!(l2.find(&2).is_some());
}
#[test]
fn test_avl_delete() {
let l = AVL::empty()
.insert(1)
.insert(2)
.insert(3)
.insert(4)
.insert(5);
let l = l.delete(&3);
assert!(!l.search(&3));
assert!(l.search(&1));
assert!(l.search(&2));
assert!(l.search(&4));
assert!(l.search(&5));
}
}