heaps.pl -- heaps/priority queues

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 or A* search and Kruskal's minimum-spanning-tree algorithm.

This module implements min-heaps, meaning that key-value items are retrieved in ascending order of key. In other words, the key determines the 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 values can be arbitrary Prolog terms, the keys determine the priority, so keys must be ordered by @=</2. This means that variables can be used as keys, but binding them in between heap operations may change the ordering. It also means that rational terms (cyclic trees), for which standard order is not well-defined, cannot be used as keys.

The current version implements pairing heaps. These support insertion and merging both in constant time, deletion of the minimum in logarithmic amortized time (though delete-min, i.e., get_from_heap/3, takes linear time in the worst case).

author

- Lars Buitinck

 add_to_heap(+Heap0, +Key, ?Value, -Heap) is semidet

Adds Value with priority Key to Heap0, constructing a new heap in Heap.

 delete_from_heap(+Heap0, -Key, +Value, -Heap) is semidet

Deletes Value from Heap0, leaving its priority in Key and the resulting data structure in Heap. Fails if Value is not found in Heap0.

bug

- This predicate is extremely inefficient and exists only for SICStus compatibility.

 empty_heap(?Heap) is semidet

True if Heap is an empty heap. Complexity: constant.

 singleton_heap(?Heap, ?Key, ?Value) is semidet

True if Heap is a heap with the single element Key-Value.

Complexity: constant.

 get_from_heap(?Heap0, ?Key, ?Value, -Heap) is semidet

Retrieves the minimum-priority pair Key-Value from Heap0. Heap is Heap0 with that pair removed. Complexity: logarithmic (amortized), linear in the worst case.

 heap_size(+Heap, -Size:int) is det

Determines the number of elements in Heap. Complexity: constant.

 heap_to_list(+Heap, -List:list) is det

Constructs a list List of Key-Value terms, ordered by (ascending) priority. Complexity: O(N log N).

 is_heap(+X) is semidet

Returns true if X is a heap. Validates the consistency of the entire heap. Complexity: linear.

 list_to_heap(+List:list, -Heap) is det

If List is a list of Key-Value terms, constructs a heap out of List. Complexity: linear.

 min_of_heap(+Heap, ?Key, ?Value) is semidet

Unifies Value with the minimum-priority element of Heap and Key with its priority value. Complexity: constant.

 min_of_heap(+Heap, ?Key1, ?Value1, ?Key2, ?Value2) is semidet

Gets the two minimum-priority elements from Heap. Complexity: logarithmic (amortized).

bug

- This predicate is extremely inefficient and exists for compatibility with earlier implementations of this library and SICStus compatibility. It performs a linear amount of work in the worst case that a following get_from_heap has to re-do.

 merge_heaps(+Heap0, +Heap1, -Heap) is det

Merge the two heaps Heap0 and Heap1 in Heap. Complexity: constant.