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I decided to implement a DisjointSet<T> data structure myself in Rust, with no dependencies except for std, for the challenge and to get better at Rust. I wanted to have as few requirements for T as possible, especially not T: Copy. I also wanted to be able to iterate over subsets easily.

use std::{
    cell::RefCell,
    collections::HashSet,
    iter::ExactSizeIterator,
    mem,
};

/// Represents a disjoint set of various subsets,
/// with fast operations to join sets together.
///
/// # Example
/// ```
/// let mut ds = DisjointSet::new();
///
/// let a = ds.make_set(1).unwrap();
/// let b = ds.make_set(2).unwrap();
///
/// assert!(ds.contains(&1) && ds.contains(&2));
/// assert_eq!(ds.same_set(a, b), Some(false));
/// assert_eq!(ds.num_sets(), 2);
///
/// assert_eq!(ds.union(a, b), Some(true));
///
/// assert_eq!(ds.same_set(a, b), Some(true));
/// assert_eq!(ds.num_sets(), 1);
/// ```
// Details about the algorithm used here can be found
// at the Wikipedia page for "Disjoint-set data structure".
#[derive(Clone)]
pub struct DisjointSet<T: Eq> {
    roots: HashSet<usize>,
    nodes: Vec<RefCell<Node<T>>>,
}

#[derive(Default, Clone)]
struct Node<T> {
    elem: T,
    parent_idx: usize,
    rank: usize,
    // We use this to be able to iterate
    // on each of our subsets.
    next: usize,
}

impl<T: Eq> DisjointSet<T> {
    /// Creates an empty `DisjointSet`.
    pub fn new() -> Self {
        Self {
            nodes: vec![],
            roots: HashSet::new(),
        }
    }

    /// Creates a new `DisjointSet` with the given capacity.
    pub fn with_capacity(capacity: usize) -> Self {
        Self {
            nodes: Vec::with_capacity(capacity),
            roots: HashSet::new(),
        }
    }

    /// Returns the number of subsets.
    pub fn num_sets(&self) -> usize {
        self.roots.len()
    }

    /// Returns the number of total elements in all subsets.
    pub fn num_elements(&self) -> usize {
        self.nodes.len()
    }

    /// Returns true if the given element is present in the `DisjointSet`.
    pub fn contains(&self, elem: &T) -> bool {
        self.position(elem).is_some()
    }

    /// Returns the index of the given element if it exists, or None otherwise.
    pub fn position(&self, elem: &T) -> Option<usize> {
        self.nodes.iter().position(|e| &e.borrow().elem == elem)
    }

    /// Adds a new set with a single, given element to
    /// the `DisjointSet`. Returns an Err with the elem
    /// if it was already present in any set, otherwise
    /// returns a Ok(usize) with the index of the element.
    pub fn make_set(&mut self, elem: T) -> Result<usize, T> {
        if !self.contains(&elem) {
            // This is the index where the node will be inserted,
            // thanks to the magic of zero-indexing.
            let insertion_idx = self.nodes.len();

            self.nodes.push(RefCell::new(Node {
                elem,
                parent_idx: insertion_idx,
                rank: 0,
                next: insertion_idx,
            }));

            self.roots.insert(insertion_idx);

            Ok(insertion_idx)
        } else {
            Err(elem)
        }
    }

    /// If present, returns an immutable reference to the element at `elem_idx`.
    pub fn get(&self, elem_idx: usize) -> Option<&T> {
        // Nothing in our code actually mutates node.elem: T using &self.
        // Even find_root_idx uses interior mutability only
        // to modify node.parent. And the caller can't
        // call get_mut or iter_mut_set while the &T here is
        // still in scope. So it all works out!
        Some(unsafe { &*self.get_raw(elem_idx)? })
    }

    /// If present, returns a mutable reference to the element at `elem_idx`.
    pub fn get_mut(&mut self, elem_idx: usize) -> Option<&mut T> {
        // RefCall::get_mut is used rarely, but here it's appropriate:
        // As long as the &mut T from this is still in scope,
        // the caller won't be able to use any other methods,
        // so interior mutability isn't a concern.
        Some(&mut self.nodes.get_mut(elem_idx)?.get_mut().elem)
    }

    /// If present, returns a raw pointer to the element at `elem_idx`.
    fn get_raw(&self, elem_idx: usize) -> Option<*mut T> {
        unsafe { Some(&mut (*self.nodes.get(elem_idx)?.as_ptr()).elem as *mut _) }
    }

    /// Returns an `&T` iterator over all elements in the set
    /// elem_idx belongs to, if it exists.
    // We use both applicable Iterator types here to give the caller
    // the maximum possible flexbility when using the returned value.
    pub fn iter_set(
        &self,
        elem_idx: usize,
    ) -> Option<impl ExactSizeIterator<Item = &T> + DoubleEndedIterator> {
        Some(
            self.get_set_idxs(elem_idx)?
                .into_iter()
                .map(move |i| self.get(i).unwrap()),
        )
    }

    /// Returns an `&mut T` iterator over all elements in the set
    /// elem_idx belongs to, if it exists.
    pub fn iter_mut_set(
        &mut self,
        elem_idx: usize,
    ) -> Option<impl ExactSizeIterator<Item = &mut T> + DoubleEndedIterator> {
        let set_idxs = self.get_set_idxs(elem_idx)?;

        Some(set_idxs.into_iter().map(move |i| {
            // In reality this is safe because there'll
            // be no duplicate indexes. But Rust doesn't
            // have any way of knowing that.
            unsafe { &mut *(self.get_mut(i).unwrap() as *mut _) }
        }))
    }

    pub fn iter_all_sets(
        &self,
    ) -> impl ExactSizeIterator<Item = impl ExactSizeIterator<Item = &T> + DoubleEndedIterator>
           + DoubleEndedIterator {
        // Put roots into a Vec to satisfy DoubleEndedIterator
        let roots = self.roots.iter().collect::<Vec<_>>();

        roots.into_iter().map(move |&r| self.iter_set(r).unwrap())
    }

    pub fn iter_mut_all_sets(
        &mut self,
    ) -> impl ExactSizeIterator<Item = impl ExactSizeIterator<Item = &mut T> + DoubleEndedIterator>
           + DoubleEndedIterator {
        // This function can't be as simple as iter_all_sets,
        // because Rust won't like it if we just straight up take
        // &mut self several times over.
        self.roots
            .iter()
            .map(|&root| {
                self.get_set_idxs(root)
                    .unwrap()
                    .into_iter()
                    .map(|i| {
                        // No duplicate indexes means that using this
                        // pointer as a &mut T is safe. We can't
                        // use get_mut here because that takes &mut self.
                        unsafe { &mut *self.get_raw(i).unwrap() }
                    })
                    .collect::<Vec<_>>()
            })
            // In order to avoid the closures that borrow
            // self outliving the function itself, we collect
            // their results and then turn them back into iterators.
            .collect::<Vec<_>>()
            .into_iter()
            .map(|v| v.into_iter())
    }

    /// Returns Some(true) if the elements at both the given indexes
    /// are in the same set, or None of either of them aren't present altogether.
    pub fn same_set(&self, elem1_idx: usize, elem2_idx: usize) -> Option<bool> {
        // The ? ensures this'll short-circuit and return None if either of the indexes are None,
        // meaning we don't end up returning Some(true) if both elements don't exist.
        Some(self.find_root_idx(elem1_idx)? == self.find_root_idx(elem2_idx)?)
    }

    /// Performs a union for the two sets containing the given elements.
    /// Returns Some(true) if the operation was performed, Some(false) if not,
    /// and None if either element doesn't exist.
    ///
    /// # Example
    /// ```
    /// let mut ds = DisjointSet::new();
    ///
    /// // Ommitted: adding 5 seperate elements to the set a..e
    /// # let a = ds.make_set(1).unwrap();
    /// # let b = ds.make_set(2).unwrap();
    /// # let c = ds.make_set(3).unwrap();
    /// # let d = ds.make_set(4).unwrap();
    /// # let e = ds.make_set(5).unwrap();
    ///
    /// assert_eq!(ds.union(a, b), Some(true));
    ///
    /// assert_eq!(ds.same_set(a, b), Some(true));
    /// assert_eq!(ds.num_sets(), 4);
    ///
    /// assert_eq!(ds.union(a, b), Some(false));
    /// assert_eq!(ds.union(c, d), Some(true));
    /// assert_eq!(ds.union(e, c), Some(true));
    ///
    /// // Now we have {a, b} and {c, d, e}
    ///
    /// assert_eq!(ds.num_sets(), 2);
    /// assert_eq!(ds.same_set(a, c), Some(false));
    /// assert_eq!(ds.same_set(d, e), Some(true));
    ///
    /// assert_eq!(ds.union(a, e), Some(true));
    ///
    /// assert_eq!(ds.num_sets(), 1);
    /// ```
    pub fn union(&mut self, elem_x_idx: usize, elem_y_idx: usize) -> Option<bool> {
        let (mut x_root_idx, mut y_root_idx) = (
            self.find_root_idx(elem_x_idx)?,
            self.find_root_idx(elem_y_idx)?,
        );

        // We don't have to do anything if this is the case.
        // Also, if we didn't check this, we'd panic below because
        // we'd attempt two mutable borrowings of the same RefCell.
        if x_root_idx == y_root_idx {
            return Some(false);
        }

        let (mut x_root, mut y_root) = (
            self.nodes[x_root_idx].borrow_mut(),
            self.nodes[y_root_idx].borrow_mut(),
        );

        if x_root.rank < y_root.rank {
            // Must use mem::swap here. If we shadowed,
            // it'd go out of scope when the if block ended.
            mem::swap(&mut x_root_idx, &mut y_root_idx);
            mem::swap(&mut x_root, &mut y_root);
        }

        // Now x_root.rank >= y_root.rank no matter what.
        // Therefore, make X the parent of Y.
        y_root.parent_idx = x_root_idx;
        self.roots.remove(&y_root_idx);
        if x_root.rank == y_root.rank {
            x_root.rank += 1;
        }

        // Drop the RefMuts so we can check self.last,
        // which needs to immutably borrow, without conflicts.
        drop(x_root);
        drop(y_root);

        let x_last_idx = self.last(x_root_idx).unwrap();
        let mut x_last = self.nodes[x_last_idx].borrow_mut();
        x_last.next = y_root_idx;

        Some(true)
    }

    /// Returns the index of the root of the subset
    /// `elem_idx` belongs to, if it exists.
    pub fn find_root_idx(&self, elem_idx: usize) -> Option<usize> {
        if self.roots.contains(&elem_idx) {
            return Some(elem_idx);
        }

        let mut curr_idx = elem_idx;
        let mut curr = self.nodes.get(curr_idx)?.borrow_mut();

        while curr.parent_idx != curr_idx {
            let parent_idx = curr.parent_idx;
            let parent = self.nodes[parent_idx].borrow_mut();

            // Set the current node's parent to its grandparent.
            // This is called *path splitting*: (see the Wikipedia
            // page for details) a simpler to implement, one-pass
            // version of path compression that also, apparently,
            // turns out to be more efficient in practice.
            curr.parent_idx = parent.parent_idx;

            // Move up a level for the next iteration
            curr_idx = parent_idx;
            curr = parent;
        }

        Some(curr_idx)
    }

    /// Returns the last element of the subset with
    /// `elem_idx` in it, if it exists.
    fn last(&self, elem_idx: usize) -> Option<usize> {
        self.get_set_idxs(elem_idx)?.pop()
    }

    /// Returns the indexes of all the items in the subset
    /// `elem_idx` belongs to in arbitrary order, if it exists.
    fn get_set_idxs(&self, elem_idx: usize) -> Option<Vec<usize>> {
        let mut curr_idx = self.find_root_idx(elem_idx)?;
        let mut curr = self.nodes[curr_idx].borrow();

        let mut set_idxs = Vec::with_capacity(self.num_elements());

        // We can't check the condition up here
        // using while because that would make
        // it so the last node is never pushed.
        loop {
            set_idxs.push(curr_idx);

            // This is the last node
            if curr_idx == curr.next {
                break;
            }

            curr_idx = curr.next;
            curr = self.nodes[curr.next].borrow();
        }

        set_idxs.shrink_to_fit();

        Some(set_idxs)
    }
}

I think I succeeded for the most part, having only needed T: Eq and using interior mutability with RefCell to make a mostly sensible public API - mainly for the sake of find_root_idx, which pretends to be an immutable operation by taking &self but actually needs to mutate in order to maintain the performance of union-find. I did have to add a next field to the normal union-find node in order to be able to iterate on subsets.

I'm mainly looking for feedback on the "Rustiness" (idiomacity) of this code and how I could make some of the more hacky bits better, such as the get and iter_set family of functions with its unsafe code to get around lifetime issues (especially iter_mut_all_sets - the two collects needed feel reall dirty) and union with its need to manually use mem::drop for two RefMut<Node<T>>s.

Additionally, in general the soundness of this code is hard to guarantee - I'm reasonably sure that there shouldn't be any RefCell panics or memory unsafety no matter what the caller does (given that they only use safe code), but the code has spiraled out such that I don't know 100%.

Extensibility is also somewhat of a concern - if I wanted to add a "delete" operation to the set as its currently set up, it would be quite the refactor job. If I wanted to make it thread-safe with RwLock or something similar, that'd be an even bigger problem thanks to the aforementioned unsafe code.

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2
  • \$\begingroup\$ Are you sure you want to tag this as [beginner]? I'd say those unsafe blocks are beyond what neophytes can navigate. \$\endgroup\$ – L. F. Feb 26 at 11:54
  • \$\begingroup\$ @L.F. Well, I tagged it that because I was a beginner to the language. But fair enough, removed. \$\endgroup\$ – naiveai 2 days ago

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