[ Reference Manual | Alphabetic Index ]# library(heaps)

Implement heaps in Prolog
## Predicates

**add_to_heap(+OldHeap, +Key, +Datum, -NewHeap)**
- inserts the new Key-Datum pair into the 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

## Description

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 rest

The 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.
## About

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

Generated from heaps.eci on 2017-07-09 15:37