#search #string #str #uneven


Binary Search Single Sorted String: Perform binary search on a single, delimited string slice of sorted but unevenly sized substrings

7 releases

0.3.4 Aug 21, 2023
0.3.3 Aug 5, 2023
0.3.1 Jul 31, 2023
0.3.0 Jun 11, 2023
0.1.0 Jun 11, 2023

#346 in Algorithms

36 downloads per month

MIT license

136 lines


Binary Search Single Sorted String: Perform binary search on a single, delimited string slice of sorted but unevenly sized substrings.

The docs are best viewed via docs.rs.



There are generally two ways to setup this crate: at compile-time, or at runtime. The main (only...) method of interest is [SortedString::binary_search()]. View its documentation for detailed context.


use b4s::{AsciiChar, SortedString};

fn main() {
    match SortedString::new_checked("abc,def,ghi,jkl,mno,pqr,stu,vwx,yz", AsciiChar::Comma) {
        Ok(ss) => {
            match ss.binary_search("ghi") {
                Ok(r) => println!("Found at range: {:?}", r),
                Err(r) => println!("Not found, last looked at range: {:?}", r),
        Err(e) => println!("Error: {:?}", e),


For convenience, there's also a const fn, usable statically. As a tradeoff, instance creation will not perform correctness checks. An unsorted string will result in binary search misbehaving. Though no panics occur, you will be handed back an Error. See the documentation of [SortedString::new_unchecked()] for details.

use b4s::{AsciiChar, SortedString};

static SS: SortedString =
    SortedString::new_unchecked("abc,def,ghi,jkl,mno,pqr,stu,vwx,yz", AsciiChar::Comma);

fn main() {
    match SS.binary_search("ghi") {
        Ok(r) => println!("Found at range: {:?}", r),
        Err(r) => println!("Not found, last looked at range: {:?}", r),

The source for the input string can be anything, for example a file prepared at compile time:

static SS: SortedString =
    SortedString::new_unchecked(include_str!("path/to/file"), AsciiChar::LineFeed);

This is convenient if a delimited (\n, ...) file is already at hand. It only needs to be sorted once previously, and is then available for string containment checks at good, albeit not perfect, runtime performance, at essentially no startup cost.


The itch to be scratched is the following:

  • there's an array of strings to do lookup in, for example a word list
  • the lookup is a simple containment check, with no modification
  • the word list is available and prepared (sorted) at compile-time (e.g. in build.rs)
  • the word list is large (potentially much larger than the code itself); think 5MB or more
  • the list is to be distributed as part of the binary

A couple possible approaches come to mind. The summary table, where n is the number of words in the dictionary and k the number of characters in a word to look up, is (for more context, see the individual sections below):

Approach Pre-compile preprocessing[^1] Compile time prepr. Runtime lookup Binary size
b4s O(n log n) Single ref: O(1) O(log n) O(n)
fst O(n log n)[^2] Single ref: O(1) O(k) < O(n)[^3]
slice O(n log n) Many refs: O(n) O(log n) ~ O(3n)
phf None Many refs: O(n) Hash: O(1) ~ O(3n)
HashSet None Many refs: O(n) Hash: O(1) ~ O(3n)
padded &str ~ O(n log n) Single ref: O(1) Bin. search: O(log n) ~ O(n)

This crate is an attempt to provide a solution with:

  1. good, not perfect runtime performance,
  2. very little, one-time compile-time preprocessing needed (just sorting),
  3. essentially no additional startup cost (unlike, say, constructing a HashSet at runtime)[^4],
  4. binary sizes as small as possible,
  5. compile times as fast as possible.

It was found that approaches using slices and hash sets (via phf) absolutely tanked developer experience, with compile times north of 20 minutes (!) for 30 MB word lists (even on fast hardware), large binaries, and clippy imploding, taking the IDE with it. This crate was born as a solution. Its main downside is suboptimal runtime performance. If that is your primary goal, opt for phf or similar crates. This crate is not suitable for long-running applications, where initial e.g. HashSet creation is a fraction of overall runtime costs.

Alternative approaches

The following alternatives might be considered, but were found unsuitable for one reason or another. See this thread for more discussion.


A simple slice is an obvious choice, and can be generated in a build script.

static WORDS: &[&str] = &["abc", "def", "ghi", "jkl"];

assert_eq!(WORDS.binary_search(&"ghi").unwrap(), 2);

There are two large pains in this approach:

  1. compile times become very slow (in the rough ballpark of 1 minute per 100.000 words, YMMV considerably)

  2. binary size becomes large.

    The words are much shorter than the &str they are contained in. On 64-bit hardware, a &str is 16 bytes, with a usize address pointer and a usize length. For large word lists, this leads to incredible bloat for the resulting binary.

Hash Set

Regular HashSets are not available at compile time. Crates like phf change that:

use phf::{phf_set, Set};

static WORDS: Set<&'static str> = phf_set! {


Similar downsides as for the slices case apply: very long compile times, and considerable binary bloat from smart pointers. A hash set ultimately is a slice with computed indices, so this is expected.

Finite State Transducer/Acceptor (Automaton)

The fst crate is a fantastic candidate, brought up by its author (same author as ripgrep and regex fame):

use fst::Set; // Don't need FST, just FSA here

static WORDS: &[&str] = &["abc", "def", "ghi", "jkl"];

let set = Set::from_iter(WORDS.into_iter()).unwrap();

It offers:

In some sense, for all intents and purposes, fst is likely the best solution for the niche use case mentioned above.

For faster lookups than fst (closing the gap towards hash sets), but giving up compression (TANSTAAFL!), try an automaton from regex-automata. Note that should your use case involve an initial decompression step, the slower runtime lookups but built-in compression of fst might still come out ahead in combination.

Single, sorted and padded string

Another approach could be to use a single string (saving pointer bloat), but pad all words to the longest occurring length, facilitating easy binary search (and increasing bloat to some extent):

static WORDS: &str = "abc␣␣def␣␣ghi␣␣jklmn";

// Perform binary search...

The binary search implementation is then straightforward, as the elements are of known, fixed lengths (in this case, 5). This approach was found to not perform well. Find its (bare-bones) implementation in the benchmarks.

Higher-order data structures

In certain scenarios, one might reach for more sophisticated approaches, such as tries. This is not a case this crate is designed for. Such a structure would have to be either:

  • built at runtime, for example as

    use trie_rs::TrieBuilder;
    let mut builder = TrieBuilder::new();
    let trie = builder.build(); // Takes time

    or alternatively

  • deserialized from a pre-built structure.

While tools like bincode are fantastic, the latter approach is still numbingly slow at application startup, compared to the (much more ham-fisted) approach the crate at hand takes.

This is only included here and in the benchmarks as a sanity check and baseline. Linear search like

static WORDS: &[&str] = &["abc", "def", "ghi", "jkl"];

is $O(n)$, and slower by a couple orders of magnitude for large lists. If your current implementation relies on linear search, this create might offer an almost drop-in replacement with a significant performance improvement.


The below benchmarks show a performance comparison. The benchmarks run a search for representative words (start, middle, end, shortest and longest words found in the pre-sorted input list), on various different input word list lengths.

Sets are unsurprisingly fastest, but naive binary search (the built-in one) seems incredibly optimized and just as fast. b4s is slower by a factor of 5 to 10. The "padded string" variant is slowest. One can observe how, as the input lists get longer ("within X entries"), b4s becomes slower.

In the context of this crate's purpose, the slowness might not be an issue: if application startup is measured in milliseconds, and lookups in nanoseconds (!), one can perform in the rough ballpark of, say, 100,000 lookups before the tradeoff of this crate (fast startup) becomes a problem (this crate would be terrible for a web server).

benchmark results violin plot

Linear search performance

The benchmark plot including linear search is largely illegible, as the linear horizontal axis scaling dwarfs all other search methods. It is therefore linked separately, but paints a clear picture.


The benchmarks were run on a machine with the following specs:

  • AMD Ryzen 7 5800X3D; DDR4 @ 3600MHz; NVMe SSD
  • Debian 12 inside WSL 2 on Windows 10 21H2
  • libraries with versions as of commit 9e2f11c39342f1ea3460dda810a92b225ee9d4b8 (refer to its Cargo.toml)

The benchmarks are not terribly scientific (low sample sizes etc.), but serve as a rough guideline and sanity check. Run them yourself from the repository root with cargo install just && just bench.

Note on name

The 3-letter name is neat. Should you have a more meaningful, larger project that could make better use of it, let me know. I might move this crate to a different name.

[^1]: Note that pre-compile preprocessing is ordinarily performed only a single time, unless the word list itself changes. This column might be moot, and considered essentially zero-cost. This viewpoint benefits this crate. [^2]: Building itself is O(n), but the raw input might be unsorted (as is assumed for all other approaches as well). Sorting is O(n log n), so building the automaton collapses to O(n + n log n) = O(n log n). [^3]: As an automaton, the finite state transducer (in this case, finite state acceptor) compresses all common prefixes, like a trie, but also all suffixes, unlike a prefix tree. That's a massive advantage should compression be of concern. Languages like German benefit greatly. Take the example of übersehen: the countless conjugations are shared among all words, so are only encoded once in the entire automaton. The prefix über is also shared among many words, and is also only encoded once. Compression is built-in. [^4]: The program this crate was initially designed for is sensitive to startup-time, as the program's main processing is rapid. Even just 50ms of startup time would be very noticeable, slowing down a program run by a factor of about 10.


~11K SLoC