ring-seq

Circular (ring) sequence operations for Rust slices.

Treat any [T], Vec<T>, array, or Box<[T]> as a circular sequence — the element after the last wraps back to the first.

Zero dependencies. Zero unsafe. #![no_std] with a default alloc feature.
All transforms return lazy views or iterators; allocation is opt-in.
Single entry point: slice.circular() gives you a Circular<T> wrapper that hosts every operation.

Quick start

[dependencies]
ring-seq = "0.3"

use ring_seq::AsCircular;

let r = [10, 20, 30].circular();

// Indexing wraps in both directions
assert_eq!(*r.apply(4), 20);
assert_eq!(*r.apply(-1), 30);

// Reindexed views — no allocation
let rotated: Vec<_> = r.rotate_right(1).iter().copied().collect();
assert_eq!(rotated, [30, 10, 20]);

// Comparison up to rotation / reflection
assert!(r.is_rotation_of(&[20, 30, 10]));
assert!(r.is_reflection_of(&[10, 30, 20]));

// Canonical (necklace) form — Booth's O(n)
assert_eq!(r.canonical(), [10, 20, 30]);

// Lazy iterators of views compose naturally
let firsts: Vec<i32> = r.rotations().map(|v| *v.apply(0)).collect();
assert_eq!(firsts, [10, 20, 30]);

// Symmetry detection
assert_eq!([0, 1, 0, 1].circular().rotational_symmetry(), 2);

Operations on `Circular<T>`

Indexing & iteration

Method	Returns	Description
`apply(i)`	`&T`	Element at circular index (panics if empty)
`index_from(i)`	`usize`	Normalize a circular index to `[0, len)`
`iter()`	`CircularIter`	Walk the view's elements (lazy)

Reindexed views (lazy)

Method	Returns	Description
`start_at(i)`	`Circular`	View starts at circular index `i`
`rotate_left(step)`	`Circular`	Shift left by `step` (negative = right)
`rotate_right(step)`	`Circular`	Shift right by `step` (negative = left)
`reflect_at(i)`	`Circular`	Reflect around index `i`

Bounded iteration (lazy)

Method	Returns	Description
`slice(from, to)`	`CircularIter`	`max(to - from, 0)` elements, wrapping
`take_while(pred, from)`	`impl Iterator`	Prefix satisfying `pred` (≤ one lap)
`drop_while(pred, from)`	`impl Iterator`	Remainder after the prefix
`enumerate(from)`	`Enumerate`	`(&T, ring_index)` pairs

Iterators of views (lazy)

Method	Yields	Description
`rotations()`	`Circular` × `n`	Every rotation
`reflections()`	`Circular` × 2	Original + `reflect_at(0)`
`reversions()`	`Circular` × 2	Original + reverse
`rotations_and_reflections()`	`Circular` × `2n`	All dihedral variants
`windows(size)`	`CircularIter` × `n`	Sliding windows, step 1
`chunks(size)`	`CircularIter` × `ceil(n/size)`	Non-overlapping chunks

Comparison

Method	Description
`is_rotation_of(other)`	Same elements, possibly rotated?
`is_reflection_of(other)`	Equals `self` or `self.reflect_at(0)`
`is_reversion_of(other)`	Equals `self` or its reverse
`is_rotation_or_reflection_of(other)`	Any dihedral variant
`rotation_offset(other)`	`Some(k)` where `self.start_at(k) == other`
`hamming_distance(other)`	Positional mismatches
`min_rotational_hamming_distance(other)`	Minimum over all rotations
`contains_slice(needle)`	Does `needle` appear circularly?
`index_of_slice(needle, from)`	First circular index where `needle` matches

Necklace & symmetry

Method	Returns	Notes
`canonical_index()`	`usize`	Index of lex-smallest rotation (Booth's O(n); `alloc`)
`canonical()`	`Vec<T>`	Lex-smallest rotation (`alloc`)
`bracelet()`	`Vec<T>`	Lex-smallest under rotation + reflection (`alloc`)
`rotational_symmetry()`	`usize`	Order of rotational symmetry
`symmetry()`	`usize`	Number of reflectional axes
`symmetry_indices()`	`Vec<usize>`	Shifts where the view equals its reverse (`alloc`)
`reflectional_symmetry_axes()`	`Vec<(AxisLocation, AxisLocation)>`	Full axis geometry (`alloc`)

Materialization

Method	Returns	Notes
`to_vec()`	`Vec<T>`	Materialize the view (`alloc`, `T: Clone`)

`no_std`

[dependencies]
ring-seq = { version = "0.3", default-features = false }

Disabling the default alloc feature drops the methods that return owned collections (canonical, bracelet, symmetry_indices, reflectional_symmetry_axes, to_vec) and canonical_index (Booth's algorithm needs an internal Vec). Everything else — the Circular wrapper, every reindexed-view method, every iterator — depends only on core.

Use cases

Bioinformatics — circular DNA/RNA sequence alignment and comparison
Graphics — polygon vertex manipulation, closed curve operations
Procedural generation — tile rings, symmetry-aware pattern generation
Music theory — pitch-class sets, chord inversions
Combinatorics — necklace/bracelet enumeration, Burnside's lemma
Embedded / robotics — circular sensor arrays, rotary encoder positions

Minimum Rust version

1.63

Other languages

The same library, adapted for the specific idiom, is available also for:

Python — ring-seq-py
Scala — ring-seq

License

Licensed under either of

at your option.

ring-seq 0.3.0