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;;; rtree.el --- functions for manipulating range trees -*- lexical-binding:t -*-
;; Copyright (C) 2010-2020 Free Software Foundation, Inc.
;; Author: Lars Magne Ingebrigtsen <larsi@gnus.org>
;; This file is part of GNU Emacs.
;; GNU Emacs is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or
;; (at your option) any later version.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>.
;;; Commentary:
;; A "range tree" is a binary tree that stores ranges. They are
;; similar to interval trees, but do not allow overlapping intervals.
;; A range is an ordered list of number intervals, like this:
;; ((10 . 25) 56 78 (98 . 201))
;; Common operations, like lookup, deletion and insertion are O(n) in
;; a range, but an rtree is O(log n) in all these operations.
;; Transformation between a range and an rtree is O(n).
;; The rtrees are quite simple. The structure of each node is
;; (cons (cons low high) (cons left right))
;; That is, they are three cons cells, where the car of the top cell
;; is the actual range, and the cdr has the left and right child. The
;; rtrees aren't automatically balanced, but are balanced when
;; created, and can be rebalanced when deemed necessary.
;;; Code:
(defmacro rtree-make-node ()
'(list (list nil) nil))
(defmacro rtree-set-left (node left)
`(setcar (cdr ,node) ,left))
(defmacro rtree-set-right (node right)
`(setcdr (cdr ,node) ,right))
(defmacro rtree-set-range (node range)
`(setcar ,node ,range))
(defmacro rtree-low (node)
`(caar ,node))
(defmacro rtree-high (node)
`(cdar ,node))
(defmacro rtree-set-low (node number)
`(setcar (car ,node) ,number))
(defmacro rtree-set-high (node number)
`(setcdr (car ,node) ,number))
(defmacro rtree-left (node)
`(cadr ,node))
(defmacro rtree-right (node)
`(cddr ,node))
(defmacro rtree-range (node)
`(car ,node))
(defsubst rtree-normalize-range (range)
(when (numberp range)
(setq range (cons range range)))
range)
(define-obsolete-function-alias 'rtree-normalise-range
#'rtree-normalize-range "25.1")
(defun rtree-make (range)
"Make an rtree from RANGE."
;; Normalize the range.
(unless (listp (cdr-safe range))
(setq range (list range)))
(rtree-make-1 (cons nil range) (length range)))
(defun rtree-make-1 (range length)
(let ((mid (/ length 2))
(node (rtree-make-node)))
(when (> mid 0)
(rtree-set-left node (rtree-make-1 range mid)))
(rtree-set-range node (rtree-normalize-range (cadr range)))
(setcdr range (cddr range))
(when (> (- length mid 1) 0)
(rtree-set-right node (rtree-make-1 range (- length mid 1))))
node))
(defun rtree-memq (tree number)
"Return non-nil if NUMBER is present in TREE."
(while (and tree
(not (and (>= number (rtree-low tree))
(<= number (rtree-high tree)))))
(setq tree
(if (< number (rtree-low tree))
(rtree-left tree)
(rtree-right tree))))
tree)
(defun rtree-add (tree number)
"Add NUMBER to TREE."
(while tree
(cond
;; It's already present, so we don't have to do anything.
((and (>= number (rtree-low tree))
(<= number (rtree-high tree)))
(setq tree nil))
((< number (rtree-low tree))
(cond
;; Extend the low range.
((= number (1- (rtree-low tree)))
(rtree-set-low tree number)
;; Check whether we need to merge this node with the child.
(when (and (rtree-left tree)
(= (rtree-high (rtree-left tree)) (1- number)))
;; Extend the range to the low from the child.
(rtree-set-low tree (rtree-low (rtree-left tree)))
;; The child can't have a right child, so just transplant the
;; child's left tree to our left tree.
(rtree-set-left tree (rtree-left (rtree-left tree))))
(setq tree nil))
;; Descend further to the left.
((rtree-left tree)
(setq tree (rtree-left tree)))
;; Add a new node.
(t
(let ((new-node (rtree-make-node)))
(rtree-set-low new-node number)
(rtree-set-high new-node number)
(rtree-set-left tree new-node)
(setq tree nil)))))
(t
(cond
;; Extend the high range.
((= number (1+ (rtree-high tree)))
(rtree-set-high tree number)
;; Check whether we need to merge this node with the child.
(when (and (rtree-right tree)
(= (rtree-low (rtree-right tree)) (1+ number)))
;; Extend the range to the high from the child.
(rtree-set-high tree (rtree-high (rtree-right tree)))
;; The child can't have a left child, so just transplant the
;; child's left right to our right tree.
(rtree-set-right tree (rtree-right (rtree-right tree))))
(setq tree nil))
;; Descend further to the right.
((rtree-right tree)
(setq tree (rtree-right tree)))
;; Add a new node.
(t
(let ((new-node (rtree-make-node)))
(rtree-set-low new-node number)
(rtree-set-high new-node number)
(rtree-set-right tree new-node)
(setq tree nil))))))))
(defun rtree-delq (tree number)
"Remove NUMBER from TREE destructively. Returns the new tree."
(let ((result tree)
prev)
(while tree
(cond
((< number (rtree-low tree))
(setq prev tree
tree (rtree-left tree)))
((> number (rtree-high tree))
(setq prev tree
tree (rtree-right tree)))
;; The number is in this node.
(t
(cond
;; The only entry; delete the node.
((= (rtree-low tree) (rtree-high tree))
(cond
;; Two children. Replace with successor value.
((and (rtree-left tree) (rtree-right tree))
(let ((parent tree)
(successor (rtree-right tree)))
(while (rtree-left successor)
(setq parent successor
successor (rtree-left successor)))
;; We now have the leftmost child of our right child.
(rtree-set-range tree (rtree-range successor))
;; Transplant the child (if any) to the parent.
(rtree-set-left parent (rtree-right successor))))
(t
(let ((rest (or (rtree-left tree)
(rtree-right tree))))
;; One or zero children. Remove the node.
(cond
((null prev)
(setq result rest))
((eq (rtree-left prev) tree)
(rtree-set-left prev rest))
(t
(rtree-set-right prev rest)))))))
;; The lowest in the range; just adjust.
((= number (rtree-low tree))
(rtree-set-low tree (1+ number)))
;; The highest in the range; just adjust.
((= number (rtree-high tree))
(rtree-set-high tree (1- number)))
;; We have to split this range.
(t
(let ((new-node (rtree-make-node)))
(rtree-set-low new-node (rtree-low tree))
(rtree-set-high new-node (1- number))
(rtree-set-low tree (1+ number))
(cond
;; Two children; insert the new node as the predecessor
;; node.
((and (rtree-left tree) (rtree-right tree))
(let ((predecessor (rtree-left tree)))
(while (rtree-right predecessor)
(setq predecessor (rtree-right predecessor)))
(rtree-set-right predecessor new-node)))
((rtree-left tree)
(rtree-set-right new-node tree)
(rtree-set-left new-node (rtree-left tree))
(rtree-set-left tree nil)
(cond
((null prev)
(setq result new-node))
((eq (rtree-left prev) tree)
(rtree-set-left prev new-node))
(t
(rtree-set-right prev new-node))))
(t
(rtree-set-left tree new-node))))))
(setq tree nil))))
result))
(defun rtree-extract (tree)
"Convert TREE to range form."
(let (stack result)
(while (or stack
tree)
(if tree
(progn
(push tree stack)
(setq tree (rtree-right tree)))
(setq tree (pop stack))
(push (if (= (rtree-low tree)
(rtree-high tree))
(rtree-low tree)
(rtree-range tree))
result)
(setq tree (rtree-left tree))))
result))
(defun rtree-length (tree)
"Return the number of numbers stored in TREE."
(if (null tree)
0
(+ (rtree-length (rtree-left tree))
(1+ (- (rtree-high tree)
(rtree-low tree)))
(rtree-length (rtree-right tree)))))
(provide 'rtree)
;;; rtree.el ends here
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