;;;; $Id: avltree.el,v 0.8 1995/12/11 00:10:54 ceder Exp $
;;;; This file implements balanced binary trees, AVL-trees.
;; Copyright (C) 1991-1995 Free Software Foundation
;; Author: Inge Wallin <inge@lysator.liu.se>
;; Thomas Bellman <bellman@lysator.liu.se>
;; Maintainer: elib-maintainers@lysator.liu.se
;; Created: 10 May 1991
;; Keywords: extensions, lisp
;;;; This file is part of the GNU Emacs lisp library, Elib.
;;;;
;;;; GNU Elib 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 2, or (at your option)
;;;; any later version.
;;;;
;;;; GNU Elib 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 Elib; see the file COPYING. If not, write to
;;;; the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
;;;; Boston, MA 02111-1307, USA
;;;;
;;;; Initial author: Thomas Bellman
;;;; Lysator Computer Club
;;;; Linkoping University
;;;; Sweden
;;;;
;;;; Bugfixes and completion: Inge Wallin
;;;;
;;; Commentary:
;;;
;;; An AVL tree is a nearly-perfect balanced binary tree. A tree
;;; consists of two cons cells, the first one holding the tag
;;; 'AVLTREE in the car cell, and the second one having the tree
;;; in the car and the compare function in the cdr cell. The tree has
;;; a dummy node as its root with the real tree in the left pointer.
;;;
;;; Each node of the tree consists of one data element, one left
;;; sub-tree and one right sub-tree. Each node also has a balance
;;; count, which is the difference in depth of the left and right
;;; sub-trees.
;;;
;;; Code:
(require 'elib-node)
(require 'stack-m)
(provide 'avltree)
;;; ================================================================
;;; Functions and macros handling an AVL tree node.
;;
;; The rest of the functions needed here can be found in
;; elib-node.el.
;;
(defmacro elib-avl-node-create (left right data balance)
;; Create and return an avl-tree node.
(` (vector (, left) (, right) (, data) (, balance))))
(defmacro elib-avl-node-balance (node)
;; Return the balance field of a node.
(` (aref (, node) 3)))
(defmacro elib-avl-node-set-balance (node newbal)
;; Set the balance field of a node.
(` (aset (, node) 3 (, newbal))))
;;; ================================================================
;;; Internal functions for use in the AVL tree package
;;;
;;; The functions and macros in this section all start with `elib-avl-'.
;;;
(defmacro elib-avl-root (tree)
;; Return the root node for an avl-tree. INTERNAL USE ONLY.
(` (elib-node-left (car (cdr (, tree))))))
(defmacro elib-avl-dummyroot (tree)
;; Return the dummy node of an avl-tree. INTERNAL USE ONLY.
(` (car (cdr (, tree)))))
(defmacro elib-avl-cmpfun (tree)
;; Return the compare function of AVL tree TREE. INTERNAL USE ONLY.
(` (cdr (cdr (, tree)))))
;; ----------------------------------------------------------------
;; Deleting data
(defun elib-avl-del-balance1 (node branch)
;; Rebalance a tree and return t if the height of the tree has shrunk.
(let* ((br (elib-node-branch node branch))
p1
b1
p2
b2
result)
(cond
((< (elib-avl-node-balance br) 0)
(elib-avl-node-set-balance br 0)
t)
((= (elib-avl-node-balance br) 0)
(elib-avl-node-set-balance br +1)
nil)
(t ; Rebalance
(setq p1 (elib-node-right br)
b1 (elib-avl-node-balance p1))
(if (>= b1 0)
;; Single RR rotation
(progn
(elib-node-set-right br (elib-node-left p1))
(elib-node-set-left p1 br)
(if (= 0 b1)
(progn
(elib-avl-node-set-balance br +1)
(elib-avl-node-set-balance p1 -1)
(setq result nil))
(elib-avl-node-set-balance br 0)
(elib-avl-node-set-balance p1 0)
(setq result t))
(elib-node-set-branch node branch p1)
result)
;; Double RL rotation
(setq p2 (elib-node-left p1)
b2 (elib-avl-node-balance p2))
(elib-node-set-left p1 (elib-node-right p2))
(elib-node-set-right p2 p1)
(elib-node-set-right br (elib-node-left p2))
(elib-node-set-left p2 br)
(if (> b2 0)
(elib-avl-node-set-balance br -1)
(elib-avl-node-set-balance br 0))
(if (< b2 0)
(elib-avl-node-set-balance p1 +1)
(elib-avl-node-set-balance p1 0))
(elib-node-set-branch node branch p2)
(elib-avl-node-set-balance p2 0)
t)
))
))
(defun elib-avl-del-balance2 (node branch)
(let* ((br (elib-node-branch node branch))
p1
b1
p2
b2
result)
(cond
((> (elib-avl-node-balance br) 0)
(elib-avl-node-set-balance br 0)
t)
((= (elib-avl-node-balance br) 0)
(elib-avl-node-set-balance br -1)
nil)
(t ; Rebalance
(setq p1 (elib-node-left br)
b1 (elib-avl-node-balance p1))
(if (<= b1 0)
;; Single LL rotation
(progn
(elib-node-set-left br (elib-node-right p1))
(elib-node-set-right p1 br)
(if (= 0 b1)
(progn
(elib-avl-node-set-balance br -1)
(elib-avl-node-set-balance p1 +1)
(setq result nil))
(elib-avl-node-set-balance br 0)
(elib-avl-node-set-balance p1 0)
(setq result t))
(elib-node-set-branch node branch p1)
result)
;; Double LR rotation
(setq p2 (elib-node-right p1)
b2 (elib-avl-node-balance p2))
(elib-node-set-right p1 (elib-node-left p2))
(elib-node-set-left p2 p1)
(elib-node-set-left br (elib-node-right p2))
(elib-node-set-right p2 br)
(if (< b2 0)
(elib-avl-node-set-balance br +1)
(elib-avl-node-set-balance br 0))
(if (> b2 0)
(elib-avl-node-set-balance p1 -1)
(elib-avl-node-set-balance p1 0))
(elib-node-set-branch node branch p2)
(elib-avl-node-set-balance p2 0)
t)
))
))
(defun elib-avl-do-del-internal (node branch q)
(let* ((br (elib-node-branch node branch)))
(if (elib-node-right br)
(if (elib-avl-do-del-internal br +1 q)
(elib-avl-del-balance2 node branch))
(elib-node-set-data q (elib-node-data br))
(elib-node-set-branch node branch
(elib-node-left br))
t)))
(defun elib-avl-do-delete (cmpfun root branch data)
;; Return t if the height of the tree has shrunk.
(let* ((br (elib-node-branch root branch)))
(cond
((null br)
nil)
((funcall cmpfun data (elib-node-data br))
(if (elib-avl-do-delete cmpfun br 0 data)
(elib-avl-del-balance1 root branch)))
((funcall cmpfun (elib-node-data br) data)
(if (elib-avl-do-delete cmpfun br 1 data)
(elib-avl-del-balance2 root branch)))
(t
;; Found it. Let's delete it.
(cond
((null (elib-node-right br))
(elib-node-set-branch root branch (elib-node-left br))
t)
((null (elib-node-left br))
(elib-node-set-branch root branch (elib-node-right br))
t)
(t
(if (elib-avl-do-del-internal br 0 br)
(elib-avl-del-balance1 root branch)))))
)))
;; ----------------------------------------------------------------
;; Entering data
(defun elib-avl-enter-balance1 (node branch)
;; Rebalance a tree and return t if the height of the tree has grown.
(let* ((br (elib-node-branch node branch))
p1
p2
b2
result)
(cond
((< (elib-avl-node-balance br) 0)
(elib-avl-node-set-balance br 0)
nil)
((= (elib-avl-node-balance br) 0)
(elib-avl-node-set-balance br +1)
t)
(t
;; Tree has grown => Rebalance
(setq p1 (elib-node-right br))
(if (> (elib-avl-node-balance p1) 0)
;; Single RR rotation
(progn
(elib-node-set-right br (elib-node-left p1))
(elib-node-set-left p1 br)
(elib-avl-node-set-balance br 0)
(elib-node-set-branch node branch p1))
;; Double RL rotation
(setq p2 (elib-node-left p1)
b2 (elib-avl-node-balance p2))
(elib-node-set-left p1 (elib-node-right p2))
(elib-node-set-right p2 p1)
(elib-node-set-right br (elib-node-left p2))
(elib-node-set-left p2 br)
(if (> b2 0)
(elib-avl-node-set-balance br -1)
(elib-avl-node-set-balance br 0))
(if (< b2 0)
(elib-avl-node-set-balance p1 +1)
(elib-avl-node-set-balance p1 0))
(elib-node-set-branch node branch p2))
(elib-avl-node-set-balance (elib-node-branch node branch) 0)
nil))
))
(defun elib-avl-enter-balance2 (node branch)
;; Return t if the tree has grown.
(let* ((br (elib-node-branch node branch))
p1
p2
b2)
(cond
((> (elib-avl-node-balance br) 0)
(elib-avl-node-set-balance br 0)
nil)
((= (elib-avl-node-balance br) 0)
(elib-avl-node-set-balance br -1)
t)
(t
;; Balance was -1 => Rebalance
(setq p1 (elib-node-left br))
(if (< (elib-avl-node-balance p1) 0)
;; Single LL rotation
(progn
(elib-node-set-left br (elib-node-right p1))
(elib-node-set-right p1 br)
(elib-avl-node-set-balance br 0)
(elib-node-set-branch node branch p1))
;; Double LR rotation
(setq p2 (elib-node-right p1)
b2 (elib-avl-node-balance p2))
(elib-node-set-right p1 (elib-node-left p2))
(elib-node-set-left p2 p1)
(elib-node-set-left br (elib-node-right p2))
(elib-node-set-right p2 br)
(if (< b2 0)
(elib-avl-node-set-balance br +1)
(elib-avl-node-set-balance br 0))
(if (> b2 0)
(elib-avl-node-set-balance p1 -1)
(elib-avl-node-set-balance p1 0))
(elib-node-set-branch node branch p2))
(elib-avl-node-set-balance (elib-node-branch node branch) 0)
nil))
))
(defun elib-avl-do-enter (cmpfun root branch data)
;; Return t if height of tree ROOT has grown. INTERNAL USE ONLY.
(let ((br (elib-node-branch root branch)))
(cond
((null br)
;; Data not in tree, insert it
(elib-node-set-branch root branch
(elib-avl-node-create nil nil data 0))
t)
((funcall cmpfun data (elib-node-data br))
(and (elib-avl-do-enter cmpfun
br
0 data)
(elib-avl-enter-balance2 root branch)))
((funcall cmpfun (elib-node-data br) data)
(and (elib-avl-do-enter cmpfun
br
1 data)
(elib-avl-enter-balance1 root branch)))
(t
(elib-node-set-data br data)
nil))))
;; ----------------------------------------------------------------
(defun elib-avl-mapc (map-function root)
;; Apply MAP-FUNCTION to all nodes in the tree starting with ROOT.
;; The function is applied in-order.
;;
;; Note: MAP-FUNCTION is applied to the node and not to the data itself.
;; INTERNAL USE ONLY.
(let ((node root)
(stack (elib-stack-create))
(go-left t))
(elib-stack-push stack nil)
(while node
(if (and go-left
(elib-node-left node))
(progn ; Do the left subtree first.
(elib-stack-push stack node)
(setq node (elib-node-left node)))
(funcall map-function node) ; Apply the function...
(if (elib-node-right node) ; and do the right subtree.
(setq node (elib-node-right node)
go-left t)
(setq node (elib-stack-pop stack)
go-left nil))))))
(defun elib-avl-do-copy (root)
;; Copy the tree with ROOT as root.
;; Highly recursive. INTERNAL USE ONLY.
(if (null root)
nil
(elib-avl-node-create (elib-avl-do-copy (elib-node-left root))
(elib-avl-do-copy (elib-node-right root))
(elib-node-data root)
(elib-avl-node-balance root))))
;;; ================================================================
;;; The public functions which operate on AVL trees.
(defun avltree-create (compare-function)
"Create an empty avl tree.
COMPARE-FUNCTION is a function which takes two arguments, A and B,
and returns non-nil if A is less than B, and nil otherwise."
(cons 'AVLTREE
(cons (elib-avl-node-create nil nil nil 0)
compare-function)))
(defun avltree-p (obj)
"Return t if OBJ is an avl tree, nil otherwise."
(eq (car-safe obj) 'AVLTREE))
(defun avltree-compare-function (tree)
"Return the comparision function for the avl tree TREE."
(elib-avl-cmpfun tree))
(defun avltree-empty (tree)
"Return t if TREE is emtpy, otherwise return nil."
(null (elib-avl-root tree)))
(defun avltree-enter (tree data)
"In the avl tree TREE insert DATA.
Return DATA."
(elib-avl-do-enter (elib-avl-cmpfun tree)
(elib-avl-dummyroot tree)
0
data)
data)
(defun avltree-delete (tree data)
"From the avl tree TREE, delete DATA.
Return the element in TREE which matched DATA, nil if no element matched."
(elib-avl-do-delete (elib-avl-cmpfun tree)
(elib-avl-dummyroot tree)
0
data))
(defun avltree-member (tree data)
"Return the element in the avl tree TREE which matches DATA.
Matching uses the compare function previously specified in `avltree-create'
when TREE was created.
If there is no such element in the tree, the value is nil."
(let ((node (elib-avl-root tree))
(compare-function (elib-avl-cmpfun tree))
found)
(while (and node
(not found))
(cond
((funcall compare-function data (elib-node-data node))
(setq node (elib-node-left node)))
((funcall compare-function (elib-node-data node) data)
(setq node (elib-node-right node)))
(t
(setq found t))))
(if node
(elib-node-data node)
nil)))
(defun avltree-map (__map-function__ tree)
"Apply MAP-FUNCTION to all elements in the avl tree TREE."
(elib-avl-mapc
(function (lambda (node)
(elib-node-set-data node
(funcall __map-function__
(elib-node-data node)))))
(elib-avl-root tree)))
(defun avltree-first (tree)
"Return the first element in TREE, or nil if TREE is empty."
(let ((node (elib-avl-root tree)))
(if node
(progn
(while (elib-node-left node)
(setq node (elib-node-left node)))
(elib-node-data node))
nil)))
(defun avltree-last (tree)
"Return the last element in TREE, or nil if TREE is empty."
(let ((node (elib-avl-root tree)))
(if node
(progn
(while (elib-node-right node)
(setq node (elib-node-right node)))
(elib-node-data node))
nil)))
(defun avltree-copy (tree)
"Return a copy of the avl tree TREE."
(let ((new-tree (avltree-create
(elib-avl-cmpfun tree))))
(elib-node-set-left (elib-avl-dummyroot new-tree)
(elib-avl-do-copy (elib-avl-root tree)))
new-tree))
(defun avltree-flatten (tree)
"Return a sorted list containing all elements of TREE."
(nreverse
(let ((treelist nil))
(elib-avl-mapc (function (lambda (node)
(setq treelist (cons (elib-node-data node)
treelist))))
(elib-avl-root tree))
treelist)))
(defun avltree-size (tree)
"Return the number of elements in TREE."
(let ((treesize 0))
(elib-avl-mapc (function (lambda (data)
(setq treesize (1+ treesize))
data))
(elib-avl-root tree))
treesize))
(defun avltree-clear (tree)
"Clear the avl tree TREE."
(elib-node-set-left (elib-avl-dummyroot tree) nil))
;;; avltree.el ends here