radn-rs/src/flow/binary/balancing.rs

use std::fmt::Display;

use super::{avl::*, bound::*, *};

pub trait BinaryTreesUnbalanced<'a>: BinaryTreesHeight<'a> {
    fn tree_of_with_height(&self, node: Self::Node, height: u64) -> BTWrap<'a, Self, Self::Tree>;

    fn balancing_error<T: 'a>(&self, error: BalancingError) -> BTWrap<'a, Self, T>;

    fn balancing_bind<A: 'a, B: 'a>(
        &self,
        ra: Result<A, BalancingError>,
        f: impl FnOnce(A) -> BTWrap<'a, Self, B>,
    ) -> BTWrap<'a, Self, B> {
        match ra {
            Ok(a) => f(a),
            Err(e) => self.balancing_error(e),
        }
    }

    fn node_heights(&self, node: &Self::Node) -> (u64, u64) {
        let (tl, tr, _) = self.split(node);
        (self.height(&tl), self.height(&tr))
    }
}

#[derive(Clone)]
pub struct BalancedTrees<BT>(BT);

impl<BT> BalancedTrees<BT> {
    pub fn new(bt: BT) -> Self {
        Self(bt)
    }
}

impl<'a, BT: FunctorContext<'a>> FunctorContext<'a> for BalancedTrees<BT> {
    type T = BT::T;
}

#[derive(Debug)]
pub enum BalancingError {
    LeafHeight(u64),
    NodeHeight,
    Balance(u64, u64),
    HeightOverflow,
    HeightMismatch { children: (u64, u64), parent: u64 },
}

impl Display for BalancingError {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        match self {
            Self::NodeHeight => write!(f, "invalid AVL non-leaf height: 0."),
            Self::LeafHeight(height) => {
                write!(f, "invalid AVL leaf height: {height}!=0.")
            }
            Self::Balance(hl, hr) => write!(f, "unbalanced AVL node: {hl} {hr}."),
            Self::HeightOverflow => write!(f, "AVL tree height overflow"),
            Self::HeightMismatch { children, parent } => {
                write!(
                    f,
                    "AVL child-parent height mismatch: {children:?}, {parent}"
                )
            }
        }
    }
}

fn balanced(hl: u64, hr: u64) -> Result<(), BalancingError> {
    if hl.abs_diff(hr) > 1 {
        Err(BalancingError::Balance(hl, hr))
    } else {
        Ok(())
    }
}

fn parent_height(hl: u64, hr: u64) -> Result<u64, BalancingError> {
    balanced(hl, hr)?;
    std::cmp::max(hl, hr)
        .checked_add(1)
        .ok_or(BalancingError::HeightOverflow)
}

fn matches_height(hl: u64, hr: u64, hp: u64) -> Result<(), BalancingError> {
    if parent_height(hl, hr)? == hp {
        Ok(())
    } else {
        Err(BalancingError::HeightMismatch {
            children: (hl, hr),
            parent: hp,
        })
    }
}

impl<'a, BT: BinaryTreesUnbalanced<'a>> BinaryTrees<'a> for BalancedTrees<BT> {
    type Node = BT::Node;

    type Reference = (BT::Reference, u64);

    type Tree = BT::Tree;

    type Key = BT::Key;

    type Comparator = BT::Comparator;

    type _Tm = Self::T;

    fn comparator(&self) -> &Self::Comparator {
        self.0.comparator()
    }

    fn split(&self, node: &Self::Node) -> Split<'a, Self> {
        self.0.split(node)
    }

    fn resolve(&self, (reference, hp): &Self::Reference) -> BTWrap<'a, Self, Self::Node> {
        let hp = *hp;
        let ctx = self.0.clone();
        Self::bind(self.0.resolve(reference), move |node| {
            let (hl, hr) = ctx.node_heights(&node);
            ctx.balancing_bind(matches_height(hl, hr, hp), |_| Self::pure(node))
        })
    }

    fn equal(&self, (rl, hl): &Self::Reference, (rr, hr): &Self::Reference) -> bool {
        hl == hr && self.0.equal(rl, rr)
    }

    fn refer(&self, tree: &Self::Tree) -> Option<Self::Reference> {
        Some((self.0.refer(tree)?, self.0.height(tree)))
    }
}

impl<'a, BT: BinaryTreesUnbalanced<'a>> BinaryTreesTreeOf<'a> for BalancedTrees<BT> {
    fn tree_of(&self, node: Self::Node) -> BTWrap<'a, Self, Self::Tree> {
        let (hl, hr) = self.0.node_heights(&node);
        self.0.balancing_bind(parent_height(hl, hr), |height| {
            self.0.tree_of_with_height(node, height)
        })
    }
}

impl<'a, BT: BinaryTreesUnbalanced<'a> + BinaryTreesEmpty<'a>> BinaryTreesEmpty<'a>
    for BalancedTrees<BT>
{
    fn empty(&self) -> Self::Tree {
        self.0.empty()
    }

    fn split_key_empty(
        &self,
        tree: Self::Tree,
        key: Self::Key,
    ) -> BTWrap<'a, Self, KeySplit<'a, Self>> {
        self.0.split_key_empty(tree, key)
    }
}

impl<'a, BT: BinaryTreesUnbalanced<'a>> BinaryTreesHeight<'a> for BalancedTrees<BT> {
    fn height(&self, tree: &Self::Tree) -> u64 {
        self.0.height(tree)
    }

    fn leaf_height_error<T: 'a>(&self, height: u64) -> BTWrap<'a, Self, T> {
        self.0.leaf_height_error(height)
    }
}

impl<'a, BT: BinaryTreesUnbalanced<'a> + BinaryTreesTryJoin<'a>> BinaryTreesTryJoin<'a>
    for BalancedTrees<BT>
{
    fn try_join(
        &self,
        tl: Self::Tree,
        key: Self::Key,
        tr: Self::Tree,
    ) -> BTWrap<'a, Self, Self::Node> {
        let (hl, hr) = (self.0.height(&tl), self.0.height(&tr));
        self.0
            .balancing_bind(balanced(hl, hr), |_| self.0.try_join(tl, key, tr))
    }
}

impl<'a, BT: BinaryTreesUnbalanced<'a> + BinaryTreesBindable<'a>> BinaryTreesBindable<'a>
    for BalancedTrees<BT>
{
    fn bounds_error<T: 'a>(&self, error: bounds::BoundsError<Self::Key>) -> BTWrap<'a, Self, T> {
        self.0.bounds_error(error)
    }
}

impl<'a, BT: BinaryTreesUnbalanced<'a> + BinaryTreesEmpty<'a> + BinaryTreesTryJoin<'a>>
    BinaryTreesMutable<'a> for BalancedTrees<BT>
{
    fn join_key(
        self,
        tl: Self::Tree,
        key: Self::Key,
        tr: Self::Tree,
    ) -> BTWrap<'a, Self, Self::Node> {
        self.join_key_balanced(tl, key, tr)
    }
}