# `derangements`

This library provides predicates for generating and querying derangements over lists. Derangements are full-length permutations where no result element is identical to the input element at the same position. The following categories of predicates are provided:

- Generation operations - Predicates for generating derangements.

- Ordering variants - Predicates that support an additional order argument (`default`, `lexicographic`, or `shortlex`) for controlling output order.

- Distinct-value generation - Predicates for generating derangements while deduplicating equal-valued results.

- Indexed access - Predicates for direct access to derangements at specific positions, including distinct derangements.

- Lexicographic stepping - Predicates for navigating derangements in lexicographic order.

- Counting operations - Predicates for counting derangements and distinct derangements.

- Random selection - Predicates for randomly selecting and sampling derangements and distinct derangements.

Dedicated `permutations`, `arrangements`, `cartesian_products`, `combinations`, `multisets`, `partitions`, and `subsequences` libraries are also available for focused APIs on related operations.

## API documentation

Open the ../../apis/library_index.html#derangements link in a web browser.

## Loading

To load all entities in this library, load the `loader.lgt` file:

    | ?- logtalk_load(derangements(loader)).

## Testing

To test this library predicates, load the `tester.lgt` file:

    | ?- logtalk_load(derangements(tester)).