I implemented a simple find first element algorithm in a slice which is sorted in Eytzinger order.
The simple algorithm performs faster (in some cases multiple times faster), then the Rust stdlib binary_search algorithm.
I also compared a eytzinger_search method from eytzinger crate. Which performed worse then binary_search and my first_index_for_eytzinger function.
In order to find elements in a slice with binary search the slice has to be sorted in ascending order.
Rust std library provides two options for sorting - sort and sort_unstable methods on a Slice. The sort_unstable method is mostly faster then sort.
We have four options how a random slice of PartialOrd elements can conform to Eytzinger order:
- Sorting algorithm, which mutates the slice in place.
- Sorting algorithm, which produces a new array conforming to Eytzinger order from the given random slice.
- Presorting the slice and than transforming it into Eytzinger order in place.
- Presorting the slice and than creating a new array conforming to Eytzinger array order from the sorted slice.
I spent multiple attempts trying to implement the first option. As a result Eytzinger March, Eytzinger Waltz and Eytzinger Traversal sort where implemented. But all three algorithms have sub optimal performance characteristics.
I did not tried to implement option number two. I used the algorithm from eytzinger crate as option three. And implemented option four based on a functions from eytzinger crate.
I compared the result to each other and also to std sort and sort_unstable.
Following diagram shows data based on sorting and searching in a random Vec<u64>.
The values are nano seconds.
