1 ;;; rtree.el --- functions for manipulating range trees
3 ;; Copyright (C) 2010-2014 Free Software Foundation, Inc.
5 ;; Author: Lars Magne Ingebrigtsen <larsi@gnus.org>
7 ;; This file is part of GNU Emacs.
9 ;; GNU Emacs is free software: you can redistribute it and/or modify
10 ;; it under the terms of the GNU General Public License as published by
11 ;; the Free Software Foundation, either version 3 of the License, or
12 ;; (at your option) any later version.
14 ;; GNU Emacs is distributed in the hope that it will be useful,
15 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
16 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 ;; GNU General Public License for more details.
19 ;; You should have received a copy of the GNU General Public License
20 ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
24 ;; A "range tree" is a binary tree that stores ranges. They are
25 ;; similar to interval trees, but do not allow overlapping intervals.
27 ;; A range is an ordered list of number intervals, like this:
29 ;; ((10 . 25) 56 78 (98 . 201))
31 ;; Common operations, like lookup, deletion and insertion are O(n) in
32 ;; a range, but an rtree is O(log n) in all these operations.
33 ;; Transformation between a range and an rtree is O(n).
35 ;; The rtrees are quite simple. The structure of each node is
37 ;; (cons (cons low high) (cons left right))
39 ;; That is, they are three cons cells, where the car of the top cell
40 ;; is the actual range, and the cdr has the left and right child. The
41 ;; rtrees aren't automatically balanced, but are balanced when
42 ;; created, and can be rebalanced when deemed necessary.
49 (defmacro rtree-make-node ()
50 `(list (list nil) nil))
52 (defmacro rtree-set-left (node left)
53 `(setcar (cdr ,node) ,left))
55 (defmacro rtree-set-right (node right)
56 `(setcdr (cdr ,node) ,right))
58 (defmacro rtree-set-range (node range)
59 `(setcar ,node ,range))
61 (defmacro rtree-low (node)
64 (defmacro rtree-high (node)
67 (defmacro rtree-set-low (node number)
68 `(setcar (car ,node) ,number))
70 (defmacro rtree-set-high (node number)
71 `(setcdr (car ,node) ,number))
73 (defmacro rtree-left (node)
76 (defmacro rtree-right (node)
79 (defmacro rtree-range (node)
82 (defsubst rtree-normalise-range (range)
84 (setq range (cons range range)))
87 (defun rtree-make (range)
88 "Make an rtree from RANGE."
89 ;; Normalize the range.
90 (unless (listp (cdr-safe range))
91 (setq range (list range)))
92 (rtree-make-1 (cons nil range) (length range)))
94 (defun rtree-make-1 (range length)
95 (let ((mid (/ length 2))
96 (node (rtree-make-node)))
98 (rtree-set-left node (rtree-make-1 range mid)))
99 (rtree-set-range node (rtree-normalise-range (cadr range)))
100 (setcdr range (cddr range))
101 (when (> (- length mid 1) 0)
102 (rtree-set-right node (rtree-make-1 range (- length mid 1))))
105 (defun rtree-memq (tree number)
106 "Return non-nil if NUMBER is present in TREE."
108 (not (and (>= number (rtree-low tree))
109 (<= number (rtree-high tree)))))
111 (if (< number (rtree-low tree))
113 (rtree-right tree))))
116 (defun rtree-add (tree number)
117 "Add NUMBER to TREE."
120 ;; It's already present, so we don't have to do anything.
121 ((and (>= number (rtree-low tree))
122 (<= number (rtree-high tree)))
124 ((< number (rtree-low tree))
126 ;; Extend the low range.
127 ((= number (1- (rtree-low tree)))
128 (rtree-set-low tree number)
129 ;; Check whether we need to merge this node with the child.
130 (when (and (rtree-left tree)
131 (= (rtree-high (rtree-left tree)) (1- number)))
132 ;; Extend the range to the low from the child.
133 (rtree-set-low tree (rtree-low (rtree-left tree)))
134 ;; The child can't have a right child, so just transplant the
135 ;; child's left tree to our left tree.
136 (rtree-set-left tree (rtree-left (rtree-left tree))))
138 ;; Descend further to the left.
140 (setq tree (rtree-left tree)))
143 (let ((new-node (rtree-make-node)))
144 (rtree-set-low new-node number)
145 (rtree-set-high new-node number)
146 (rtree-set-left tree new-node)
150 ;; Extend the high range.
151 ((= number (1+ (rtree-high tree)))
152 (rtree-set-high tree number)
153 ;; Check whether we need to merge this node with the child.
154 (when (and (rtree-right tree)
155 (= (rtree-low (rtree-right tree)) (1+ number)))
156 ;; Extend the range to the high from the child.
157 (rtree-set-high tree (rtree-high (rtree-right tree)))
158 ;; The child can't have a left child, so just transplant the
159 ;; child's left right to our right tree.
160 (rtree-set-right tree (rtree-right (rtree-right tree))))
162 ;; Descend further to the right.
164 (setq tree (rtree-right tree)))
167 (let ((new-node (rtree-make-node)))
168 (rtree-set-low new-node number)
169 (rtree-set-high new-node number)
170 (rtree-set-right tree new-node)
171 (setq tree nil))))))))
173 (defun rtree-delq (tree number)
174 "Remove NUMBER from TREE destructively. Returns the new tree."
179 ((< number (rtree-low tree))
181 tree (rtree-left tree)))
182 ((> number (rtree-high tree))
184 tree (rtree-right tree)))
185 ;; The number is in this node.
188 ;; The only entry; delete the node.
189 ((= (rtree-low tree) (rtree-high tree))
191 ;; Two children. Replace with successor value.
192 ((and (rtree-left tree) (rtree-right tree))
194 (successor (rtree-right tree)))
195 (while (rtree-left successor)
196 (setq parent successor
197 successor (rtree-left successor)))
198 ;; We now have the leftmost child of our right child.
199 (rtree-set-range tree (rtree-range successor))
200 ;; Transplant the child (if any) to the parent.
201 (rtree-set-left parent (rtree-right successor))))
203 (let ((rest (or (rtree-left tree)
204 (rtree-right tree))))
205 ;; One or zero children. Remove the node.
209 ((eq (rtree-left prev) tree)
210 (rtree-set-left prev rest))
212 (rtree-set-right prev rest)))))))
213 ;; The lowest in the range; just adjust.
214 ((= number (rtree-low tree))
215 (rtree-set-low tree (1+ number)))
216 ;; The highest in the range; just adjust.
217 ((= number (rtree-high tree))
218 (rtree-set-high tree (1- number)))
219 ;; We have to split this range.
221 (let ((new-node (rtree-make-node)))
222 (rtree-set-low new-node (rtree-low tree))
223 (rtree-set-high new-node (1- number))
224 (rtree-set-low tree (1+ number))
226 ;; Two children; insert the new node as the predecessor
228 ((and (rtree-left tree) (rtree-right tree))
229 (let ((predecessor (rtree-left tree)))
230 (while (rtree-right predecessor)
231 (setq predecessor (rtree-right predecessor)))
232 (rtree-set-right predecessor new-node)))
234 (rtree-set-right new-node tree)
235 (rtree-set-left new-node (rtree-left tree))
236 (rtree-set-left tree nil)
239 (setq result new-node))
240 ((eq (rtree-left prev) tree)
241 (rtree-set-left prev new-node))
243 (rtree-set-right prev new-node))))
245 (rtree-set-left tree new-node))))))
249 (defun rtree-extract (tree)
250 "Convert TREE to range form."
257 (setq tree (rtree-right tree)))
258 (setq tree (pop stack))
259 (push (if (= (rtree-low tree)
264 (setq tree (rtree-left tree))))
267 (defun rtree-length (tree)
268 "Return the number of numbers stored in TREE."
271 (+ (rtree-length (rtree-left tree))
272 (1+ (- (rtree-high tree)
274 (rtree-length (rtree-right tree)))))
278 ;;; rtree.el ends here