//! Traversible binary trees.

pub mod unbalanced;

use std::rc::Rc;

use crate::func::*;

/// Result returned by [`Comparator::pick_smaller`].
#[derive(Debug, PartialEq)]
pub enum Comparison {
    L,
    /// Compared values were equal.
    E,
    R,
}

fn and(_l: (), _r: ()) {}

/// Returns [`Comparison`] saying which value is smaller.
///
/// ```rust
/// # use radn_rs::flow::traversible::*;
/// assert_eq!(DefaultComparator.pick_smaller(&1, &3), Comparison::L);
/// assert_eq!(DefaultComparator.pick_smaller(&2, &2), Comparison::E);
/// assert_eq!(DefaultComparator.pick_smaller(&3, &1), Comparison::R);
/// ```
pub trait Comparator<A> {
    fn pick_smaller(&self, kl: &A, kr: &A) -> Comparison;
}

/// Implementation of a [Comparator] relying on [`PartialOrd`].
pub struct DefaultComparator;

impl<A: PartialOrd> Comparator<A> for DefaultComparator {
    fn pick_smaller(&self, kl: &A, kr: &A) -> Comparison {
        if kl < kr {
            Comparison::L
        } else if kr < kl {
            Comparison::R
        } else {
            Comparison::E
        }
    }
}

pub type Split<'a, T, A, D> = (
    Rc<dyn TraversibleBinaryTree<'a, T, A, D>>,
    Rc<dyn TraversibleBinaryTree<'a, T, A, D>>,
    Rc<A>,
);

pub trait TraversibleBinaryNode<'a, T: 'a + Monad, A: 'a, D: 'a + PartialEq>: 'a {
    fn split(&self) -> Split<'a, T, A, D>;

    fn to_tree(self: Rc<Self>) -> Rc<dyn TraversibleBinaryTree<'a, T, A, D>>;
}

pub trait TraversibleBinaryReference<'a, T: 'a + Monad, A: 'a, D: 'a + PartialEq>: 'a {
    fn resolve(&self) -> <T as WeakFunctor>::F<'a, Rc<dyn TraversibleBinaryNode<'a, T, A, D>>>;

    /// This should be enough to compare reference for equality.
    fn data(&self) -> D;
}

pub trait TraversibleBinaryTree<'a, T: 'a + Monad, A: 'a, D: 'a + PartialEq>: 'a {
    fn refer(&self) -> Option<Rc<dyn TraversibleBinaryReference<'a, T, A, D>>>;
}

pub fn n_contains<'a, T: 'a + MonadFail<()>, A: 'a, D: 'a + PartialEq>(
    comparator: &'a dyn Comparator<A>,
    n_set: Rc<dyn TraversibleBinaryNode<'a, T, A, D>>,
    key: Rc<A>,
) -> T::F<'a, ()> {
    let (t_setl, t_setr, k_set) = n_set.split();
    match comparator.pick_smaller(key.as_ref(), k_set.as_ref()) {
        Comparison::L => t_contains(comparator, t_setl, key),
        Comparison::E => T::pure(()),
        Comparison::R => t_contains(comparator, t_setr, key),
    }
}

pub fn r_contains<'a, T: 'a + MonadFail<()>, A: 'a, D: 'a + PartialEq>(
    comparator: &'a dyn Comparator<A>,
    r_set: Rc<dyn TraversibleBinaryReference<'a, T, A, D>>,
    key: Rc<A>,
) -> T::F<'a, ()> {
    T::bind(r_set.resolve(), |n_set| n_contains(comparator, n_set, key))
}

pub fn t_contains<'a, T: 'a + MonadFail<()>, A: 'a, D: 'a + PartialEq>(
    comparator: &'a dyn Comparator<A>,
    t_set: Rc<dyn TraversibleBinaryTree<'a, T, A, D>>,
    key: Rc<A>,
) -> T::F<'a, ()> {
    match t_set.refer() {
        Some(r_set) => r_contains(comparator, r_set, key),
        None => T::fail(()),
    }
}

pub fn n_subset_of_n<'a, T: 'a + MonadFail<()>, A: 'a, D: 'a + PartialEq>(
    comparator: &'a dyn Comparator<A>,
    n_subset: Rc<dyn TraversibleBinaryNode<'a, T, A, D>>,
    n_superset: Rc<dyn TraversibleBinaryNode<'a, T, A, D>>,
    k_l: Option<Rc<A>>,
    k_r: Option<Rc<A>>,
) -> T::F<'a, ()> {
    let (t_superl, t_superr, k_super) = n_superset.split();
    if let Some(ref a_l) = k_l {
        if let Comparison::R = comparator.pick_smaller(a_l.as_ref(), k_super.as_ref()) {
            return t_subset_of_t(comparator, n_subset.to_tree(), t_superr, k_l, k_r);
        }
    }
    if let Some(ref a_r) = k_r {
        if let Comparison::L = comparator.pick_smaller(a_r.as_ref(), k_super.as_ref()) {
            return t_subset_of_t(comparator, n_subset.to_tree(), t_superl, k_l, k_r);
        }
    }
    let (t_subl, t_subr, k_sub) = n_subset.split();
    match comparator.pick_smaller(k_sub.as_ref(), k_super.as_ref()) {
        Comparison::L => T::la2(
            and,
            t_contains(comparator, t_superl.clone(), k_sub.clone()),
            T::la2(
                and,
                t_subset_of_t(comparator, t_subl, t_superl, k_l, Some(k_sub.clone())),
                t_subset_of_t(
                    comparator,
                    t_subr,
                    n_superset.to_tree(),
                    Some(k_sub.clone()),
                    k_r,
                ),
            ),
        ),
        Comparison::E => T::la2(
            and,
            t_subset_of_t(comparator, t_subl, t_superl, k_l, Some(k_sub.clone())),
            t_subset_of_t(comparator, t_subr, t_superr, Some(k_sub.clone()), k_r),
        ),
        Comparison::R => T::la2(
            and,
            t_contains(comparator, t_superr.clone(), k_sub.clone()),
            T::la2(
                and,
                t_subset_of_t(
                    comparator,
                    t_subl,
                    n_superset.to_tree(),
                    k_l,
                    Some(k_sub.clone()),
                ),
                t_subset_of_t(comparator, t_subr, t_superr, Some(k_sub.clone()), k_r),
            ),
        ),
    }
}

pub fn r_subset_of_r<'a, T: 'a + MonadFail<()>, A: 'a, D: 'a + PartialEq>(
    comparator: &'a dyn Comparator<A>,
    r_subset: Rc<dyn TraversibleBinaryReference<'a, T, A, D>>,
    r_superset: Rc<dyn TraversibleBinaryReference<'a, T, A, D>>,
    k_l: Option<Rc<A>>,
    k_r: Option<Rc<A>>,
) -> T::F<'a, ()> {
    T::join(T::la2(
        move |n_subset, n_superset| n_subset_of_n(comparator, n_subset, n_superset, k_l, k_r),
        r_subset.resolve(),
        r_superset.resolve(),
    ))
}

pub fn t_subset_of_t<'a, T: MonadFail<()>, A, D: 'a + PartialEq>(
    comparator: &'a dyn Comparator<A>,
    t_subset: Rc<dyn TraversibleBinaryTree<'a, T, A, D>>,
    t_superset: Rc<dyn TraversibleBinaryTree<'a, T, A, D>>,
    k_l: Option<Rc<A>>,
    k_r: Option<Rc<A>>,
) -> T::F<'a, ()> {
    match (t_subset.refer(), t_superset.refer()) {
        (None, _) => T::pure(()),
        (Some(_), None) => T::fail(()),
        (Some(r_subset), Some(r_superset)) => {
            if r_subset.data() == r_superset.data() {
                T::pure(())
            } else {
                r_subset_of_r(comparator, r_subset, r_superset, k_l, k_r)
            }
        }
    }
}