lisp/rtree.el

   1 ;;; rtree.el --- functions for manipulating range trees
   2
   3 ;; Copyright (C) 2010-2017 Free Software Foundation, Inc.
   4
   5 ;; Author: Lars Magne Ingebrigtsen <larsi@gnus.org>
   6
   7 ;; This file is part of GNU Emacs.
   8
   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.
  13
  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.
  18
  19 ;; You should have received a copy of the GNU General Public License
  20 ;; along with GNU Emacs.  If not, see <https://www.gnu.org/licenses/>.
  21
  22 ;;; Commentary:
  23
  24 ;; A "range tree" is a binary tree that stores ranges.  They are
  25 ;; similar to interval trees, but do not allow overlapping intervals.
  26
  27 ;; A range is an ordered list of number intervals, like this:
  28
  29 ;; ((10 . 25) 56 78 (98 . 201))
  30
  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).
  34
  35 ;; The rtrees are quite simple.  The structure of each node is
  36
  37 ;; (cons (cons low high) (cons left right))
  38
  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.
  43
  44 ;;; Code:
  45
  46 (eval-when-compile
  47   (require 'cl))
  48
  49 (defmacro rtree-make-node ()
  50   `(list (list nil) nil))
  51
  52 (defmacro rtree-set-left (node left)
  53   `(setcar (cdr ,node) ,left))
  54
  55 (defmacro rtree-set-right (node right)
  56   `(setcdr (cdr ,node) ,right))
  57
  58 (defmacro rtree-set-range (node range)
  59   `(setcar ,node ,range))
  60
  61 (defmacro rtree-low (node)
  62   `(caar ,node))
  63
  64 (defmacro rtree-high (node)
  65   `(cdar ,node))
  66
  67 (defmacro rtree-set-low (node number)
  68   `(setcar (car ,node) ,number))
  69
  70 (defmacro rtree-set-high (node number)
  71   `(setcdr (car ,node) ,number))
  72
  73 (defmacro rtree-left (node)
  74   `(cadr ,node))
  75
  76 (defmacro rtree-right (node)
  77   `(cddr ,node))
  78
  79 (defmacro rtree-range (node)
  80   `(car ,node))
  81
  82 (defsubst rtree-normalize-range (range)
  83   (when (numberp range)
  84     (setq range (cons range range)))
  85   range)
  86
  87 (define-obsolete-function-alias 'rtree-normalise-range
  88   'rtree-normalize-range "25.1")
  89
  90 (defun rtree-make (range)
  91   "Make an rtree from RANGE."
  92   ;; Normalize the range.
  93   (unless (listp (cdr-safe range))
  94     (setq range (list range)))
  95   (rtree-make-1 (cons nil range) (length range)))
  96
  97 (defun rtree-make-1 (range length)
  98   (let ((mid (/ length 2))
  99         (node (rtree-make-node)))
 100     (when (> mid 0)
 101       (rtree-set-left node (rtree-make-1 range mid)))
 102     (rtree-set-range node (rtree-normalize-range (cadr range)))
 103     (setcdr range (cddr range))
 104     (when (> (- length mid 1) 0)
 105       (rtree-set-right node (rtree-make-1 range (- length mid 1))))
 106     node))
 107
 108 (defun rtree-memq (tree number)
 109   "Return non-nil if NUMBER is present in TREE."
 110   (while (and tree
 111               (not (and (>= number (rtree-low tree))
 112                         (<= number (rtree-high tree)))))
 113     (setq tree
 114           (if (< number (rtree-low tree))
 115               (rtree-left tree)
 116             (rtree-right tree))))
 117   tree)
 118
 119 (defun rtree-add (tree number)
 120   "Add NUMBER to TREE."
 121   (while tree
 122     (cond
 123      ;; It's already present, so we don't have to do anything.
 124      ((and (>= number (rtree-low tree))
 125            (<= number (rtree-high tree)))
 126       (setq tree nil))
 127      ((< number (rtree-low tree))
 128       (cond
 129        ;; Extend the low range.
 130        ((= number (1- (rtree-low tree)))
 131         (rtree-set-low tree number)
 132         ;; Check whether we need to merge this node with the child.
 133         (when (and (rtree-left tree)
 134                    (= (rtree-high (rtree-left tree)) (1- number)))
 135           ;; Extend the range to the low from the child.
 136           (rtree-set-low tree (rtree-low (rtree-left tree)))
 137           ;; The child can't have a right child, so just transplant the
 138           ;; child's left tree to our left tree.
 139           (rtree-set-left tree (rtree-left (rtree-left tree))))
 140         (setq tree nil))
 141        ;; Descend further to the left.
 142        ((rtree-left tree)
 143         (setq tree (rtree-left tree)))
 144        ;; Add a new node.
 145        (t
 146         (let ((new-node (rtree-make-node)))
 147           (rtree-set-low new-node number)
 148           (rtree-set-high new-node number)
 149           (rtree-set-left tree new-node)
 150           (setq tree nil)))))
 151      (t
 152       (cond
 153        ;; Extend the high range.
 154        ((= number (1+ (rtree-high tree)))
 155         (rtree-set-high tree number)
 156         ;; Check whether we need to merge this node with the child.
 157         (when (and (rtree-right tree)
 158                    (= (rtree-low (rtree-right tree)) (1+ number)))
 159           ;; Extend the range to the high from the child.
 160           (rtree-set-high tree (rtree-high (rtree-right tree)))
 161           ;; The child can't have a left child, so just transplant the
 162           ;; child's left right to our right tree.
 163           (rtree-set-right tree (rtree-right (rtree-right tree))))
 164         (setq tree nil))
 165        ;; Descend further to the right.
 166        ((rtree-right tree)
 167         (setq tree (rtree-right tree)))
 168        ;; Add a new node.
 169        (t
 170         (let ((new-node (rtree-make-node)))
 171           (rtree-set-low new-node number)
 172           (rtree-set-high new-node number)
 173           (rtree-set-right tree new-node)
 174           (setq tree nil))))))))
 175
 176 (defun rtree-delq (tree number)
 177   "Remove NUMBER from TREE destructively.  Returns the new tree."
 178   (let ((result tree)
 179         prev)
 180     (while tree
 181       (cond
 182        ((< number (rtree-low tree))
 183         (setq prev tree
 184               tree (rtree-left tree)))
 185        ((> number (rtree-high tree))
 186         (setq prev tree
 187               tree (rtree-right tree)))
 188        ;; The number is in this node.
 189        (t
 190         (cond
 191          ;; The only entry; delete the node.
 192          ((= (rtree-low tree) (rtree-high tree))
 193           (cond
 194            ;; Two children.  Replace with successor value.
 195            ((and (rtree-left tree) (rtree-right tree))
 196             (let ((parent tree)
 197                   (successor (rtree-right tree)))
 198               (while (rtree-left successor)
 199                 (setq parent successor
 200                       successor (rtree-left successor)))
 201               ;; We now have the leftmost child of our right child.
 202               (rtree-set-range tree (rtree-range successor))
 203               ;; Transplant the child (if any) to the parent.
 204               (rtree-set-left parent (rtree-right successor))))
 205            (t
 206             (let ((rest (or (rtree-left tree)
 207                             (rtree-right tree))))
 208               ;; One or zero children.  Remove the node.
 209               (cond
 210                ((null prev)
 211                 (setq result rest))
 212                ((eq (rtree-left prev) tree)
 213                 (rtree-set-left prev rest))
 214                (t
 215                 (rtree-set-right prev rest)))))))
 216          ;; The lowest in the range; just adjust.
 217          ((= number (rtree-low tree))
 218           (rtree-set-low tree (1+ number)))
 219          ;; The highest in the range; just adjust.
 220          ((= number (rtree-high tree))
 221           (rtree-set-high tree (1- number)))
 222          ;; We have to split this range.
 223          (t
 224           (let ((new-node (rtree-make-node)))
 225             (rtree-set-low new-node (rtree-low tree))
 226             (rtree-set-high new-node (1- number))
 227             (rtree-set-low tree (1+ number))
 228             (cond
 229              ;; Two children; insert the new node as the predecessor
 230              ;; node.
 231              ((and (rtree-left tree) (rtree-right tree))
 232               (let ((predecessor (rtree-left tree)))
 233                 (while (rtree-right predecessor)
 234                   (setq predecessor (rtree-right predecessor)))
 235                 (rtree-set-right predecessor new-node)))
 236              ((rtree-left tree)
 237               (rtree-set-right new-node tree)
 238               (rtree-set-left new-node (rtree-left tree))
 239               (rtree-set-left tree nil)
 240               (cond
 241                ((null prev)
 242                 (setq result new-node))
 243                ((eq (rtree-left prev) tree)
 244                 (rtree-set-left prev new-node))
 245                (t
 246                 (rtree-set-right prev new-node))))
 247              (t
 248               (rtree-set-left tree new-node))))))
 249         (setq tree nil))))
 250     result))
 251
 252 (defun rtree-extract (tree)
 253   "Convert TREE to range form."
 254   (let (stack result)
 255     (while (or stack
 256                tree)
 257       (if tree
 258           (progn
 259             (push tree stack)
 260             (setq tree (rtree-right tree)))
 261         (setq tree (pop stack))
 262         (push (if (= (rtree-low tree)
 263                      (rtree-high tree))
 264                   (rtree-low tree)
 265                 (rtree-range tree))
 266               result)
 267         (setq tree (rtree-left tree))))
 268     result))
 269
 270 (defun rtree-length (tree)
 271   "Return the number of numbers stored in TREE."
 272   (if (null tree)
 273       0
 274     (+ (rtree-length (rtree-left tree))
 275        (1+ (- (rtree-high tree)
 276               (rtree-low tree)))
 277        (rtree-length (rtree-right tree)))))
 278
 279 (provide 'rtree)
 280
 281 ;;; rtree.el ends here