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Kings day in the Netherlandsheaps.pl -- heaps/priority queues
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Heaps are data structures that return the entries inserted into them in an ordered fashion, based on a priority. This makes them the data structure of choice for implementing priority queues, a central element of algorithms such as best-first/A* search and Kruskal's minimum-spanning-tree algorithm.

This module implements min-heaps, meaning that items are retrieved in ascending order of key/priority. It was designed to be compatible with the SICStus Prolog library module of the same name. merge_heaps/3 and singleton_heap/3 are SWI-specific extension. The portray_heap/1 predicate is not implemented.

Although the data items can be arbitrary Prolog data, keys/priorities must be ordered by @=</2. Be careful when using variables as keys, since binding them in between heap operations may change the ordering.

The current version implements pairing heaps. All operations can be performed in at most O(lg n) amortized time, except for delete_from_heap/4, heap_to_list/2, is_heap/1 and list_to_heap/2.

(The actual time complexity of pairing heaps is complicated and not yet determined conclusively; see, e.g. S. Pettie (2005), Towards a final analysis of pairing heaps, Proc. FOCS'05.)

- Lars Buitinck
- The "decrease key" operation is not implemented.
add_to_heap(+Heap0, +Priority, ?Key, -Heap) is semidet
Adds Key with priority Priority to Heap0, constructing a new heap in Heap.
delete_from_heap(+Heap0, -Priority, +Key, -Heap) is semidet
Deletes Key from Heap0, leaving its priority in Priority and the resulting data structure in Heap. Fails if Key is not found in Heap0.
- This predicate is extremely inefficient and exists only for SICStus compatibility.
empty_heap(?Heap) is semidet
True if Heap is an empty heap.
singleton_heap(?Heap, ?Priority, ?Key) is semidet
True if Heap is a heap with the single element Priority-Key.
get_from_heap(?Heap0, ?Priority, ?Key, -Heap) is semidet
Retrieves the minimum-priority pair Priority-Key from Heap0. Heap is Heap0 with that pair removed.
heap_size(+Heap, -Size:int) is det
Determines the number of elements in Heap.
heap_to_list(+Heap, -List:list) is det
Constructs a list List of Priority-Element terms, ordered by (ascending) priority.
is_heap(+X) is semidet
Returns true if X is a heap. Validates the consistency of the entire heap.
list_to_heap(+List:list, -Heap) is det
If List is a list of Priority-Element terms, constructs a heap out of List.
min_of_heap(+Heap, ?Priority, ?Key) is semidet
Unifies Key with the minimum-priority element of Heap and Priority with its priority value.
min_of_heap(+Heap, ?Priority1, ?Key1, ?Priority2, ?Key2) is semidet
Gets the two minimum-priority elements from Heap.
merge_heaps(+Heap0, +Heap1, -Heap) is det
Merge the two heaps Heap0 and Heap1 in Heap.