The Double Singly-Linked List

We struggled with doubly-linked lists because they have tangled ownership semantics: no node strictly owns any other node. However we struggled with this because we brought in our preconceived notions of what a linked list is. Namely, we assumed that all the links go in the same direction.

Instead, we can smash our list into two halves: one going to the left, and one going to the right:

// lib.rs
// ...
pub mod silly1;     // NEW!

// silly1.rs
use crate::second::List as Stack;

struct List<T> {
    left: Stack<T>,
    right: Stack<T>,
}

Now, rather than having a mere safe stack, we have a general purpose list. We can grow the list leftwards or rightwards by pushing onto either stack. We can also "walk" along the list by popping values off one end and onto the other. To avoid needless allocations, we're going to copy the source of our safe Stack to get access to its private details:

pub struct Stack<T> {
    head: Link<T>,
}

type Link<T> = Option<Box<Node<T>>>;

struct Node<T> {
    elem: T,
    next: Link<T>,
}

impl<T> Stack<T> {
    pub fn new() -> Self {
        Stack { head: None }
    }

    pub fn push(&mut self, elem: T) {
        let new_node = Box::new(Node {
            elem: elem,
            next: self.head.take(),
        });

        self.head = Some(new_node);
    }

    pub fn pop(&mut self) -> Option<T> {
        self.head.take().map(|node| {
            let node = *node;
            self.head = node.next;
            node.elem
        })
    }

    pub fn peek(&self) -> Option<&T> {
        self.head.as_ref().map(|node| {
            &node.elem
        })
    }

    pub fn peek_mut(&mut self) -> Option<&mut T> {
        self.head.as_mut().map(|node| {
            &mut node.elem
        })
    }
}

impl<T> Drop for Stack<T> {
    fn drop(&mut self) {
        let mut cur_link = self.head.take();
        while let Some(mut boxed_node) = cur_link {
            cur_link = boxed_node.next.take();
        }
    }
}

And just rework push and pop a bit:

pub fn push(&mut self, elem: T) {
    let new_node = Box::new(Node {
        elem: elem,
        next: None,
    });

    self.push_node(new_node);
}

fn push_node(&mut self, mut node: Box<Node<T>>) {
    node.next = self.head.take();
    self.head = Some(node);
}

pub fn pop(&mut self) -> Option<T> {
    self.pop_node().map(|node| {
        node.elem
    })
}

fn pop_node(&mut self) -> Option<Box<Node<T>>> {
    self.head.take().map(|mut node| {
        self.head = node.next.take();
        node
    })
}

Now we can make our List:

pub struct List<T> {
    left: Stack<T>,
    right: Stack<T>,
}

impl<T> List<T> {
    fn new() -> Self {
        List { left: Stack::new(), right: Stack::new() }
    }
}

And we can do the usual stuff:

pub fn push_left(&mut self, elem: T) { self.left.push(elem) }
pub fn push_right(&mut self, elem: T) { self.right.push(elem) }
pub fn pop_left(&mut self) -> Option<T> { self.left.pop() }
pub fn pop_right(&mut self) -> Option<T> { self.right.pop() }
pub fn peek_left(&self) -> Option<&T> { self.left.peek() }
pub fn peek_right(&self) -> Option<&T> { self.right.peek() }
pub fn peek_left_mut(&mut self) -> Option<&mut T> { self.left.peek_mut() }
pub fn peek_right_mut(&mut self) -> Option<&mut T> { self.right.peek_mut() }

But most interestingly, we can walk around!

pub fn go_left(&mut self) -> bool {
    self.left.pop_node().map(|node| {
        self.right.push_node(node);
    }).is_some()
}

pub fn go_right(&mut self) -> bool {
    self.right.pop_node().map(|node| {
        self.left.push_node(node);
    }).is_some()
}

We return booleans here as just a convenience to indicate whether we actually managed to move. Now let's test this baby out:

#[cfg(test)]
mod test {
    use super::List;

    #[test]
    fn walk_aboot() {
        let mut list = List::new();             // [_]

        list.push_left(0);                      // [0,_]
        list.push_right(1);                     // [0, _, 1]
        assert_eq!(list.peek_left(), Some(&0));
        assert_eq!(list.peek_right(), Some(&1));

        list.push_left(2);                      // [0, 2, _, 1]
        list.push_left(3);                      // [0, 2, 3, _, 1]
        list.push_right(4);                     // [0, 2, 3, _, 4, 1]

        while list.go_left() {}                 // [_, 0, 2, 3, 4, 1]

        assert_eq!(list.pop_left(), None);
        assert_eq!(list.pop_right(), Some(0));  // [_, 2, 3, 4, 1]
        assert_eq!(list.pop_right(), Some(2));  // [_, 3, 4, 1]

        list.push_left(5);                      // [5, _, 3, 4, 1]
        assert_eq!(list.pop_right(), Some(3));  // [5, _, 4, 1]
        assert_eq!(list.pop_left(), Some(5));   // [_, 4, 1]
        assert_eq!(list.pop_right(), Some(4));  // [_, 1]
        assert_eq!(list.pop_right(), Some(1));  // [_]

        assert_eq!(list.pop_right(), None);
        assert_eq!(list.pop_left(), None);

    }
}

> cargo test

     Running target/debug/lists-5c71138492ad4b4a

running 16 tests
test fifth::test::into_iter ... ok
test fifth::test::basics ... ok
test fifth::test::iter ... ok
test fifth::test::iter_mut ... ok
test fourth::test::into_iter ... ok
test fourth::test::basics ... ok
test fourth::test::peek ... ok
test first::test::basics ... ok
test second::test::into_iter ... ok
test second::test::basics ... ok
test second::test::iter ... ok
test second::test::iter_mut ... ok
test third::test::basics ... ok
test third::test::iter ... ok
test second::test::peek ... ok
test silly1::test::walk_aboot ... ok

test result: ok. 16 passed; 0 failed; 0 ignored; 0 measured

This is an extreme example of a finger data structure, where we maintain some kind of finger into the structure, and as a consequence can support operations on locations in time proportional to the distance from the finger.

We can make very fast changes to the list around our finger, but if we want to make changes far away from our finger we have to walk all the way over there. We can permanently walk over there by shifting the elements from one stack to the other, or we could just walk along the links with an &mut temporarily to do the changes. However the &mut can never go back up the list, while our finger can!