add_to_heap(+OldHeap, +Key, +Datum, -NewHeap)- inserts the new Key-Datum pair into the heap
empty_heap(?Heap)- Heap is the empty heap
get_from_heap(+OldHeap, ?Key, ?Datum, -NewHeap)- returns the Key-Datum pair in OldHeap with the smallest Key
heap_size(+Heap, ?Size)- reports the number of elements currently in the heap
heap_to_list(+Heap, -List)- returns the current set of Key-Datum pairs in the Heap as a List.
list_to_heap(+List, -Heap)- takes a list of Key-Datum pairs and forms them into a heap
min_of_heap(+Heap, ?Key, ?Datum)- returns the Key-Datum pair at the top of the heap
min_of_heap(+Heap, ?Key1, ?Datum1, ?Key2, ?Datum2)- returns the smallest and second smallest pairs in the heap
singleton_heap(?Heap, ?Key, ?Datum)- Heap is a heap with single entry Key-Datum

A heap is a labelled binary tree where the key of each node is less than or equal to the keys of its sons. The point of a heap is that we can keep on adding new elements to the heap and we can keep on taking out the minimum element. If there are N elements total, the total time is O(NlgN). If you know all the elements in advance, you are better off doing a merge-sort, but this file is for when you want to do say a best-first search, and have no idea when you start how many elements there will be, let alone what they are.

A heap is represented as a triple t(N, Free, Tree) where N is the number of elements in the tree, Free is a list of integers which specifies unused positions in the tree, and Tree is a tree made of

t terms for empty subtrees and t(Key,Datum,Lson,Rson) terms for the restThe nodes of the tree are notionally numbered like this:

1 2 3 4 6 5 7 8 12 10 14 9 13 11 15 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..The idea is that if the maximum number of elements that have been in the heap so far is M, and the tree currently has K elements, the tree is some subtreee of the tree of this form having exactly M elements, and the Free list is a list of K-M integers saying which of the positions in the M-element tree are currently unoccupied. This free list is needed to ensure that the cost of passing N elements through the heap is O(NlgM) instead of O(NlgN). For M say 100 and N say 10^4 this means a factor of two. The cost of the free list is slight. The storage cost of a heap in a copying Prolog (which Dec-10 Prolog is not) is 2K+3M words.

**Author:**R.A.O'Keefe**Copyright ©**This file is in the public domain**Date:**29 November 1983

Generated from heaps.eci on 2017-11-22 13:48