sortediterable

A sortediterable is a term used to describe an iterable that yields its elements in non-decreasing order according to a defined comparator. It may be a concrete sequence that has been sorted (such as a list or tuple after applying a sort operation) or a generator or stream that produces values in sorted order without storing all elements.

Key characteristics

- Order: The iteration proclaims a total order on elements; duplicates may be present and are produced in sequence.

- Form: It need not be a random-access sequence. A sortediterable can be any iterable that guarantees ordered output, including generators or streams.

- Production: The sorted order can result from pre-sorting a source collection or from a data source that inherently arranges values in order.

Practical implications

- Binary search: Performing binary search typically requires random-access sequences; a generic sortediterable may not support indexing and thus binary search may not be applicable.

- Merging and range queries: When merging multiple sortediterables, a linear-time multi-way merge is possible by repeatedly selecting the smallest current element from the inputs.

- Efficiency: If the source is not stored in sorted form, creating a sortediterable incurs sorting costs (generally O(n log n)); if the data is already sorted, downstream operations can be more efficient.

Usage and references

- In many languages and libraries, the exact term sortediterable is informal. Some ecosystems provide protocols or interfaces to denote that an object yields elements in sorted order for type checking or optimization purposes.

- Common related concepts include sorted containers, sorted sequences, and generic merge algorithms. The standard library often supports creating sorted iterables by sorting collections or by iterating over already ordered data sources.

See also: sorted containers, sequences, iterables, merge, bisect.