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Counts the fewest insertions, deletions, substitutions and swaps of neighbouring characters, with no character allowed to take part in more than one edit.

public static int Distance(ReadOnlySpan<char> a, ReadOnlySpan<char> b, TextElement element = TextElement.Utf16Unit)
public static int Distance<T>(ReadOnlySpan<T> a, ReadOnlySpan<T> b) where T : IEquatable<T>

Parameters — a and b are the two strings to compare. element says what counts as one character: TextElement.Utf16Unit by default, or TextElement.CodePoint for rapidfuzz's answer outside the Basic Multilingual Plane. The second overload compares any two spans of an IEquatable<T>.

Returns — int, the number of edits. Zero when the two are equal, and never negative.

Example — the pair that separates OSA from full Damerau-Levenshtein, which answers 2.

using Lodestar.Text.Distances;

int d = Osa.Distance("CA", "ABC");   // => 3

Remarks — for real text this and DamerauLevenshtein agree almost always, and this one costs less to compute — three rolling rows instead of a full matrix and a symbol table. Reach for it as the default transposition-aware distance, and only move to DamerauLevenshtein if the pairs you are matching really do need a stretch edited twice.

The trap is that "almost always" is not always, and the disagreement is silent. "CA" to "ABC" is 2 under DamerauLevenshtein and 3 here, because reaching 2 means transposing CA to AC and then inserting into that same stretch. If a test suite was built against Python's DamerauLevenshtein.distance, Osa.Distance will pass on nearly every case and fail on a handful, which is the worst way to discover the difference.

The restriction costs one property outright: unlike Levenshtein and unlike unrestricted DamerauLevenshtein, this is not a metric. The triangle inequality fails — Osa.Distance("bca", "ab") is 3, while going through "ba" costs 1 + 1 — so a BK-tree or any other structure that assumes a metric will silently return wrong neighbours. Use DamerauLevenshtein when you need to index rather than to score.

Applies to — net10.0, netstandard2.0.

See also — Osa.NormalizedSimilarity, DamerauLevenshtein.Distance, Levenshtein.Distance, the Python equivalence table.