shortlist

A data structure to track the largest items pushed to it with no heap allocations and O(1) amortized time per push.

Features

• Time complexity for pushing is O(1) amortized and O(log n) worst case (if the inputs are already sorted)
• No heap allocations except when creating a new Shortlist
• 0 dependencies, and only ~150 lines of source code
• No unsafe

The Problem

Suppose that you are running a brute force search over a very large search space, but want to keep more than just the single best item - for example, you want to find the best 100 items out of a search of a billion options.

I.e. you want to implement the following function:

fn get_best<T: Ord>(
    big_computation: impl Iterator<Item = T>,
    n: usize
) -> Vec<T> {
    // Somehow get the `n` largest items produced by `big_computation` ...
}

A bad solution

The naive approach to this would be to store every item that we searched. Then once the search is complete, sort this list and then take however many items we need from the end of the list. This corresponds to roughly the following code:

fn get_best<T: Ord>(
    big_computation: impl Iterator<Item = T>,
    n: usize
) -> Vec<T> {
    // Collect all the results into a big sorted vec
    let mut giant_vec: Vec<T> = big_computation.collect();
    giant_vec.sort();
    // Return the last and therefore biggest n items with some iterator magic
    giant_vec.drain(..).rev().take(n).rev().collect()
}

But this is massively inefficient in (at least) two ways:

• Sorting very large lists is very slow, and we are sorting potentially billions of items that we will never need.
• For any decently large search space, storing these items will likely crash the computer by making it run out of memory.

The solution used by this crate

This is where using a Shortlist is useful.

A Shortlist is a data structure that will dynamically keep a 'shortlist' of the best items given to it so far, with O(1) amortized time for pushing new items. It will also only perform one heap allocation when the Shortlist is created and every subsequent operation will be allocation free. Therefore, to the user of this library the code becomes:

use shortlist::Shortlist;

fn get_best<T: Ord>(
    big_computation: impl Iterator<Item = T>,
    n: usize
) -> Vec<T> {
    // Create a new Shortlist that will take at most `n` items
    let mut shortlist = Shortlist::new(n);
    // Feed it all the results from `big_computation`
    for v in big_computation {
        shortlist.push(v);
    }
    // Return the shortlisted values as a sorted vec
    shortlist.into_sorted_vec()
}

Or as a one-liner:

use shortlist::Shortlist;

fn get_best<T: Ord>(big_computation: impl Iterator<Item = T>, n: usize) -> Vec<T> {
    Shortlist::from_iter(n, big_computation).into_sorted_vec()
}

In both cases, the code will make exactly one heap allocation (to reserve space for the Shortlist).

License: MIT