#merge-sort #hash-sort #set-operations #ranking-searching #printing-vectors


Vecs sorting, merging, indexing, ranking, searching, reversing, intersecting, printing, etc

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Uses new Rust 2021

new 1.4.13 Jan 25, 2023
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#69 in Data structures

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Indxvec GitHub last commit Actions Status crates.io crates.io docs.rs

Vectors searching, indexing, ranking, sorting, merging, reversing, intersecting, printing, etc.

The following will import everything

use indxvec::{ here, compare, MinMax, Binarysearch, Indices, Vecops, Mutops, Printing, printing::* };


Indxvec is lightweight and has no dependencies. The methods of all traits can be functionally chained to achieve numerous manipulations of Ranges, Vecs, and their indices, in compact form.

The facilities provided are:

  • general binary search
  • ranking, sorting (merge sort and hash sort), merging, indexing, selecting, partitioning
  • many useful operations on generic vectors and their indices
  • set operations
  • serialising generic slices and slices of vectors to Strings: to_plainstr()
  • printing generic slices and slices of vectors: pvec()
  • writing generic slices and slices of vectors to files: wvec(&mut f)
  • coloured pretty printing (ANSI terminal output, mainly for testing)
  • macro here!() for more informative errors reporting

It is highly recommended to read and run tests/tests.rs to learn from examples of usage. Use a single thread to run them. It may be a bit slower but it will write the results in the right order. It is also necessary to run the timing benchmark sorts() on its own for meaningful results.

cargo test --release -- --test-threads=1 --nocapture --color always

or you can just click the above test badge and then click your way to the latest automated test log.


  • Sort Index - is obtained by stable merge sort sort_indexed or by hashsort_indexed. The original data is immutable (unchanged). The sort index produced is a list of subscripts to the data, such that the first subscript identifies the smallest item in the data, and so on (in ascending order). Suitable for bulky data that are not easily moved. It answers the question: 'what data item occupies a given sort position?'.

  • K-Sort Index - allows more efficient sort implementation when only the first k items of the Sort Index are needed.

  • Reversing an index - sort index can be reversed by generic reversal operation revs(), or mutrevs(). This has the effect of changing between ascending/descending sort orders without re-sorting or even reversing the (possibly bulky) actual data.

  • Rank Index - corresponds to the given data order, listing the sort positions (ranks) for the data items, e.g.the third entry in the rank index gives the rank of the third data item. Some statistical measures require ranks of data. It answers the question: 'what is the sort position of a given data item?'.

  • Inverting an index - sort index and rank index are mutually inverse. Thus they can be easily switched by invindex(). This is usually the easiest way to obtain a rank index. They will both be equal to 0..n for data that is already in ascending order.

  • Complement of an index - beware that the standard reversal will not convert directly between ascending and descending ranks. This purpose is served by complindex(). Alternatively, descending ranks can be reconstructed by applying invindex() to a descending sort index.

  • Unindexing - given a sort index and some data, unindex() will pick the data in the new order defined by the sort index. It can be used to efficiently transform lots of data vectors into the same (fixed) order. For example: Suppose we have vectors: keys and data_1,..data_n, not explicitly joined together in some bulky Struct elements. The sort index obtained by: let indx = keys.sort_indexed() can then be efficiently applied to sort the data vectors individually, e.g. indx.unindex(data_n,true) (false to obtain a descending order at no extra cost).

There are two traits dedicated to search: Binarysearch and Search. Binarysearch is safer and easier to use:

Trait Binarysearch

/// Binary search algoritms implemented on RangeInclusive<T>
pub trait Binarysearch<T, U> {
    /// Binary search for target: returns the first match and its enclosing range
    fn find_any(self, sample: &mut impl FnMut(&T) -> U, target: U) -> (T, Range<T>);
    /// Binary search for target, returns full range of all matches
    fn find_all(self, sample: &mut impl FnMut(&T) -> U, target: U) -> Range<T>;

find_all is the main general purpose method. This algorithm is new and unique in its generality. It is very fast, especially over long ranges and is capable of many varied uses.

The method is applied to a RangeInclusive of indices of any numeric type (self). Thus it can be used in functionally chained 'builder style APIs', to select only the subrange closer bracketing the target.

It takes a closure that samples some sorted data source in the given range. Descending order of data is also allowed and is detected automatically. The target is specified by the last argument.

When the target is not found, an empty Range (idx..idx) is returned, where idx is the target's sorted order insert position. This can be at the beginning or just after the given range, if the target lies outside it.

The first hit encountered will be anywhere within some number of matching partially equal items. The algorithm then conducts two more binary searches in both directions away from the first hit. These secondary searches are applied only within the last (narrowest) range found during the first search. First non-matching positions in both directions are found, giving the full enclosed matching range.

find_any is similar but it finds and returns only the first hit. It can be used for example to solve non-linear equations, using range values of f64 type. The following example finds pi/4 by solving the equation tan(x) = 1 (it also gives error range for the found root). Of course, some care has to be taken to choose the right initial bracketing interval.

let (quarterpi,rng) = (0.5..=1_f64).find_any(&mut |&x| x.tan(),1_f64);
println!("pi:\t{} error: {:e}", 4.0*quarterpi, rng.end-rng.start);

is used by the above. It can also be used directly in special situations, where custom comparisons are needed. The closure fetches the sample internally only and now additionally defines an ordering test on it. An example use of custom ordering is when binary_all calls binary_any to look for the first non-matching item.

/// Lower level binary search algoritms implemented on RangeInclusive<T>
pub trait Search<T> {
    /// Unchecked first hit or insert order, and the final search range.
    /// The comparator must take into account the data order.
    /// Used internally by `binary_all`
    fn binary_any(&self, cmpr: &mut impl FnMut(&T) -> Ordering) -> (T, Range<T>);
    /// General Binary Search using a closure to sample and compare data,
    /// data order must be explicitly specified
    fn binary_all(&self, cmpr: &mut impl FnMut(&T) -> Ordering, ascending: bool) -> Range<T>;

Trait Indices

use indxvec::{Indices};

The methods of this trait are implemented for slices of subscripts, i.e. they take the type &[usize] as input (self) and produce new index Vec<usize>, new data vector Vec<T> or Vec<f64>, or other results, as appropriate. Please see the Glossary below for descriptions of the indices and operations on them.

/// Methods to manipulate indices of `Vec<usize>` type.
pub trait Indices {
    /// Reverse an index slice by simple reverse iteration.
    fn revindex(self) -> Vec<usize>;
    /// Invert an index - turns a sort index into rank index and vice-versa
    fn invindex(self) -> Vec<usize>;
    /// Complement of an index - reverses the ranking order
    fn complindex(self) -> Vec<usize>;
    /// Collect values from `v` in the order of index in self. Or opposite order.
    fn unindex<T: Clone>(self, v:&[T], ascending:bool) -> Vec<T>;
    /// Pearson's correlation coefficient of two slices, typically ranks.  
    fn ucorrelation(self, v: &[usize]) -> f64;
    /// Potentially useful clone-recast of &[usize] to Vec<f64>
    fn indx_to_f64 (self) -> Vec<f64>;

Trait Vecops

use indxvec::{Vecops};

The methods of this trait are applicable to all generic slices &[T] (the data). Thus they will work on all Rust primitive numeric end types, such as f64. They can also work on slices holding any arbitrarily complex end type T, as long as the required traits, PartialOrd and/or Clone, are implemented for T. The methods are too numerous to list here, please see the documentation.

Trait Mutops

use indxvec::{Mutops};

This trait contains muthashsort, which overwrites self with sorted data. When we do not need to keep the original order, this is the most efficient way to sort. A non-destructive version sorth in in trait Vecops.

Nota bene: muthashsort really wins on longer Vecs. For about one thousand items upwards, it is on average about 25%-30% faster than the default Rust (Quicksort) sort_unstable.

/// Mutable Operators on `&mut[T]`
pub trait Mutops<T> {
    /// Sorts a mutable slice in place.
    fn mutquicksort(self)
        T: PartialOrd;
    /// mutable reversal, general utility
    fn mutrevs(self);
    /// utility that mutably swaps two indexed items into ascending order
    fn mutsorttwo(self, i0: usize, i1: usize) -> bool
        T: PartialOrd;
    /// utility that mutably bubble sorts three indexed items into ascending order
    fn mutsortthree(self, i0: usize, i1: usize, i2: usize)
        T: PartialOrd;
    /// Possibly the fastest sort for long lists. Wrapper for `muthashsortslice`.
    fn muthashsort(self, quantify: &mut impl FnMut(&T) -> f64)
        T: PartialOrd + Clone;

    /// Sorts n items from i in self. Used by muthashsort.
    fn muthashsortslice(
        i: usize,
        n: usize,
        min: f64,
        max: f64,
        quantify: &mut impl FnMut(&T) -> f64,
    ) where
        T: PartialOrd + Clone;

Trait Printing

use indxvec::Printing;    // the trait methods
use indxvec::printing::*; // the ANSI colour constants

See tests/tests.rs for examples of usage.

/// Trait to serialize tuples `&(T,T)` and `&(T,T,T)` and 
/// slices `&[T]`, `&[&[T]]`, `&[Vec<T>]`.
/// Suitable for printing or writing to files pairs, triplets,
/// all kinds of Vecs and slices and irregularly shaped 2D matrices.  
/// All are converted into Strings and optionally decorated and coloured.
/// Included are methods and constants to render the resulting String
/// in six primary bold ANSI terminal colours.
pub trait Printing<T>
    Self: Sized,
    /// Printable in red
    fn rd(self) -> String {
        format!("{RD}{}{UN}", self.to_str())
    /// Printable in green
    fn gr(self) -> String {
        format!("{GR}{}{UN}", self.to_str())
    /// Printable in blue    
    fn bl(self) -> String {
        format!("{BL}{}{UN}", self.to_str())
    /// Printable in yellow
    fn yl(self) -> String {
        format!("{YL}{}{UN}", self.to_str())
    /// Printable in magenta
    fn mg(self) -> String {
        format!("{MG}{}{UN}", self.to_str())
    /// Printable in cyan
    fn cy(self) -> String {
        format!("{CY}{}{UN}", self.to_str())

    /// Method to write vector(s) to file f (space separated, without brackets).
    /// Passes up io errors
    fn wvec(self, f: &mut File) -> Result<(), io::Error> {
        Ok(write!(*f, "{} ", self.to_plainstr())?)

    /// Method to print vector(s) to stdout (space separated,without brackets).
    fn pvec(self) {
        print!("{} ", self.to_plainstr())

    /// Method to serialize.
    /// Decorates Vecs with square brackets and tuples with round ones.
    /// Implementation code is in `printing.rs`.
    fn to_str(self) -> String;

    /// Method to serialize in plain form: space separated, no brackets 
    /// Implementation code is in `printing.rs`.
    fn to_plainstr(self) -> String;

Note that all these types are unprintable in Rust (they do not have Display implemented). Which is a big stumbling block for beginners. These methods convert all these types to printable (writeable) strings. The colouring methods add the relevant colouring to the stringified output. This makes testing output much prettier and avoids reliance on Debug mode in production code.

fn wvec(self,f:&mut File) -> Result<(), io::Error> where Self: Sized;
writes plain space separated values (.ssv) to files, possibly raising io::Error(s).

fn pvec(self) where Self: Sized;
prints to stdout.

For finer control of the colouring, import the colour constants from printing::* and use them in formatting strings manually. For example, switching colours:

use indxvec::printing::*; // ANSI colours constants
println!("{GR}green text, {RD}red warning, {BL}feeling blue{UN}");

Note that all of these methods and interpolations set their own new colour regardless of the previous settings. Interpolating {UN} resets the terminal to its default foreground rendering. UN is automatically appended at the end of strings produced by the colouring methods rd()..cy(). Be careful to always close with one of these, or explicit {UN}, otherwise all the following output will continue with the last selected colour foreground rendering.

Example from tests/tests.rs:

println!("Memsearch for {BL}{midval}{UN}, found at: {}", vm
    .map_or_else(||"None".rd(),|x| x.gr())

memsearch returns Option(None), when midval is not found in vm. Here, None will be printed in red, while any found item will be printed in green. This is also an example of how to process Options without the long-winded match statements.

Struct and Utility Functions

use indxvec::{MinMax,here};
  • pub struct Minmax holds minimum and maximum values of a Vec and their indices.
  • here!() is a macro giving the filename, line number and function name of the place from where it was invoked. It can be interpolated into any error/tracing messages and reports.

Release Notes (Latest First)

Version 1.4.13 Added to trait Printing the capability to print pairs &(T,T) and triples &(T,T,T), to avoid reliance on Debug mode in common situations (passing simple uniform tuple results).

Version 1.4.11 - Added to Vecops smallest_k method, similar to smallest_k_heap, except it avoids unnecessary copying (is suitable for complex types T). It returns just the final Vec of k smallest items. Also added max_1_min_k and max_2_min_k, to be used in crate medians. The point of these methods is that they find these values in the most efficient manner, using BinaryHeap. Added here because there may be also other uses for them. Typically picking a group to qualify to 'the final' and some overall winners.

Version 1.4.10 - Added method
smallest_k_heap(self, k: usize) -> BinaryHeap<T>
to Vecops. It efficiently returns max heap of k smallest items.

Version 1.4.9 - Breaking change of hash sort methods. They now require a closure quantify for converting any user type T to f64 (it defines how to build an f64 sort key from any type). This makes prerequisite for sorth explicit and gives more power to the user. It is no longer necessary to implement From trait for every such user type and its methods of quantification, of which there could be many. It is not reasonable to expect the users to have to do that. This new capability is demonstrated at the beginning of test text() (fast sorting of words by their length with a simple closure).

Version 1.4.8 - Added trait Binarysearch with two convenient and safer wrapper methods for the previously introduced methods in Search. Now using RangeInclusive<T> for safe input range.

Version 1.4.7 - General tidying up, mostly just of the documentation.

Version 1.4.6 - Added function search_all which is a kind of easier wrapper for binary_all, without the need to specify the sort order.

Version 1.4.5 - Improved binary_all usage. Added solve to trait Search for solving equations (with guaranteed convergence, unlike secant methods). Added demonstration to tests.rs.

Version 1.4.4 - No change to functionality. Added fully automated github action testing, outputs can be found by clicking the test badge at the top of this document.

Version 1.4.3 - Updated dev dependency ran. Added github action.

Version 1.4.2 - Introduced automatic sort order detection in binary_all, thus allowing more code simplification in methods binsearch and binsearch_indexed that depend on it.

Version 1.4.1 - Rewritten binsearch and binsearch_indexed from trait Vecops as encapsulations of the general purpose binary_all from trait Sort. Reduced the code size.

Version 1.4.0 - Introduced new trait Search: impl<T> Search<T> for Range<T>. The search algorithms can now be applied in 'builder style chained API's', filtering the ranges.

Version 1.3.11 - Added module search.rs. Improved general binary_any and binary_all search algorithms now within.

No runtime deps