236 lines
5.8 KiB
Prolog
236 lines
5.8 KiB
Prolog
% This file has been included as an YAP library by Vitor Santos Costa, 1999
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% File : TREES.PL
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% Author : R.A.O'Keefe
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% Updated: 8 November 1983
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% Purpose: Updatable binary trees.
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/* These are the routines I meant to describe in DAI-WP-150, but the
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wrong version went in. We have
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list_to_tree : O(N)
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tree_to_list : O(N)
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tree_size : O(N)
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map_tree : O(N)
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get_label : O(lg N)
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put_label : O(lg N)
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where N is the number of elements in the tree. The way get_label
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and put_label work is worth noting: they build up a pattern which
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is matched against the whole tree when the position number finally
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reaches 1. In effect they start out from the desired node and
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build up a path to the root. They still cost O(lg N) time rather
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than O(N) because the patterns contain O(lg N) distinct variables,
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with no duplications. put_label simultaneously builds up a pattern
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to match the old tree and a pattern to match the new tree.
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*/
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/** @defgroup Trees Updatable Binary Trees
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@ingroup library
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@{
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The following queue manipulation routines are available once
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included with the `use_module(library(trees))` command.
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@pred get_label(+ _Index_, + _Tree_, ? _Label_)
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Treats the tree as an array of _N_ elements and returns the
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_Index_-th.
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*/
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/** @pred list_to_tree(+ _List_, - _Tree_)
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Takes a given _List_ of _N_ elements and constructs a binary
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_Tree_.
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*/
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/** @pred map_tree(+ _Pred_, + _OldTree_, - _NewTree_)
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Holds when _OldTree_ and _NewTree_ are binary trees of the same shape
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and `Pred(Old,New)` is true for corresponding elements of the two trees.
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*/
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/** @pred put_label(+ _Index_, + _OldTree_, + _Label_, - _NewTree_)
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constructs a new tree the same shape as the old which moreover has the
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same elements except that the _Index_-th one is _Label_.
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*/
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/** @pred tree_size(+ _Tree_, - _Size_)
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Calculates the number of elements in the _Tree_.
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*/
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/** @pred tree_to_list(+ _Tree_, - _List_)
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Is the converse operation to list_to_tree.
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*/
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:- module(trees, [
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get_label/3,
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list_to_tree/2,
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map_tree/3,
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put_label/4,
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tree_size/2,
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tree_to_list/2
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]).
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:- meta_predicate
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map_tree(2, ?, ?).
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/*
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:- mode
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get_label(+, +, ?),
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find_node(+, +, +),
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list_to_tree(+, -),
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list_to_tree(+, +, -),
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list_to_tree(+),
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map_tree(+, +, -),
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put_label(+, +, +, -),
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find_node(+, +, +, -, +),
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tree_size(+, ?),
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tree_size(+, +, -),
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tree_to_list(+, -),
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tree_to_list(+, -, -).
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*/
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% get_label(Index, Tree, Label)
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% treats the tree as an array of N elements and returns the Index-th.
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% If Index < 1 or > N it simply fails, there is no such element.
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get_label(N, Tree, Label) :-
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find_node(N, Tree, t(Label,_,_)).
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find_node(1, Tree, Tree) :- !.
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find_node(N, Tree, Node) :-
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N > 1,
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0 is N mod 2,
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M is N / 2, !,
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find_node(M, Tree, t(_,Node,_)).
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find_node(N, Tree, Node) :-
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N > 2,
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1 is N mod 2,
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M is N / 2, !,
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find_node(M, Tree, t(_,_,Node)).
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% list_to_tree(List, Tree)
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% takes a given List of N elements and constructs a binary Tree
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% where get_label(K, Tree, Lab) <=> Lab is the Kth element of List.
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list_to_tree(List, Tree) :-
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list_to_tree(List, [Tree|Tail], Tail).
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list_to_tree([Head|Tail], [t(Head,Left,Right)|Qhead], [Left,Right|Qtail]) :-
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list_to_tree(Tail, Qhead, Qtail).
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list_to_tree([], Qhead, []) :-
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list_to_tree(Qhead).
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list_to_tree([t|Qhead]) :-
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list_to_tree(Qhead).
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list_to_tree([]).
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% map_tree(Pred, OldTree, NewTree)
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% is true when OldTree and NewTree are binary trees of the same shape
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% and Pred(Old,New) is true for corresponding elements of the two trees.
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% In fact this routine is perfectly happy constructing either tree given
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% the other, I have given it the mode I have for that bogus reason
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% "efficiency" and because it is normally used this way round. This is
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% really meant more as an illustration of how to map over trees than as
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% a tool for everyday use.
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map_tree(Pred, t(Old,OLeft,ORight), t(New,NLeft,NRight)) :-
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once(call(Pred, Old, New)),
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map_tree(Pred, OLeft, NLeft),
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map_tree(Pred, ORight, NRight).
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map_tree(_, t, t).
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% put_label(Index, OldTree, Label, NewTree)
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% constructs a new tree the same shape as the old which moreover has the
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% same elements except that the Index-th one is Label. Unlike the
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% "arrays" of Arrays.Pl, OldTree is not modified and you can hang on to
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% it as long as you please. Note that O(lg N) new space is needed.
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put_label(N, Old, Label, New) :-
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find_node(N, Old, t(_,Left,Right), New, t(Label,Left,Right)).
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find_node(1, Old, Old, New, New) :- !.
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find_node(N, Old, OldSub, New, NewSub) :-
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N > 1,
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0 is N mod 2,
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M is N / 2, !,
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find_node(M, Old, t(Label,OldSub,Right), New, t(Label,NewSub,Right)).
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find_node(N, Old, OldSub, New, NewSub) :-
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N > 2,
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1 is N mod 2,
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M is N / 2, !,
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find_node(M, Old, t(Label,Left,OldSub), New, t(Label,Left,NewSub)).
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% tree_size(Tree, Size)
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% calculates the number of elements in the Tree. All trees made by
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% list_to_tree that are the same size have the same shape.
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tree_size(Tree, Size) :-
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tree_size(Tree, 0, Total), !,
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Size = Total.
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tree_size(t(_,Left,Right), SoFar, Total) :-
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tree_size(Right, SoFar, M),
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N is M+1, !,
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tree_size(Left, N, Total).
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tree_size(t, Accum, Accum).
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% tree_to_list(Tree, List)
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% is the converse operation to list_to_tree. Any mapping or checking
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% operation can be done by converting the tree to a list, mapping or
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% checking the list, and converting the result, if any, back to a tree.
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% It is also easier for a human to read a list than a tree, as the
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% order in the tree goes all over the place.
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tree_to_list(Tree, List) :-
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tree_to_list([Tree|Tail], Tail, List).
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tree_to_list([], [], []) :- !.
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tree_to_list([t|_], _, []) :- !.
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tree_to_list([t(Head,Left,Right)|Qhead], [Left,Right|Qtail], [Head|Tail]) :-
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tree_to_list(Qhead, Qtail, Tail).
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list(0, []).
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list(N, [N|L]) :- M is N-1, list(M, L).
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