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Initial revision, comprising elib-node.el and avltree.el,
with minimum modifications for standalone-compilation.
This commit is contained in:
Thien-Thi Nguyen
parent
ea404efcd1
commit
1e38b8ffcd
715
lisp/emacs-lisp/avl-tree.el
Normal file
715
lisp/emacs-lisp/avl-tree.el
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@ -0,0 +1,715 @@
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;;;; $Id: elib-node.el,v 0.8 1995/12/11 00:11:19 ceder Exp $
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;;;; Nodes used in binary trees and doubly linked lists.
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;; Copyright (C) 1991-1995 Free Software Foundation
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;; Author: Per Cederqvist <ceder@lysator.liu.se>
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;; Inge Wallin <inge@lysator.liu.se>
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;; Maintainer: elib-maintainers@lysator.liu.se
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;; Created: 20 May 1991
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;; Keywords: extensions, lisp
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;;;; This file is part of the GNU Emacs lisp library, Elib.
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;;;;
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;;;; GNU Elib is free software; you can redistribute it and/or modify
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;;;; it under the terms of the GNU General Public License as published by
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;;;; the Free Software Foundation; either version 2, or (at your option)
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;;;; any later version.
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;;;;
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;;;; GNU Elib is distributed in the hope that it will be useful,
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;;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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;;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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;;;; GNU General Public License for more details.
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;;;;
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;;;; You should have received a copy of the GNU General Public License
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;;;; along with GNU Elib; see the file COPYING. If not, write to
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;;;; the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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;;;; Boston, MA 02111-1307, USA
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;;;;
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;;;; Author: Inge Wallin
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;;;;
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;;; Commentary:
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;;; A node is implemented as an array with three elements, using
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;;; (elt node 0) as the left pointer
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;;; (elt node 1) as the right pointer
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;;; (elt node 2) as the data
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;;;
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;;; Some types of trees, e.g. AVL trees, need bigger nodes, but
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;;; as long as the first three parts are the left pointer, the
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;;; right pointer and the data field, these macros can be used.
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;;;
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;;; Code:
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;;; Begin HACKS to make avl-tree.el standalone.
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;;;
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;;; 0/ Don't do this.
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;;; (provide 'elib-node)
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;;;
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;;; End HACKS to make avl-tree.el standalone.
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(defmacro elib-node-create (left right data)
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;; Create a tree node from LEFT, RIGHT and DATA.
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(` (vector (, left) (, right) (, data))))
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(defmacro elib-node-left (node)
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;; Return the left pointer of NODE.
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(` (aref (, node) 0)))
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(defmacro elib-node-right (node)
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;; Return the right pointer of NODE.
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(` (aref (, node) 1)))
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(defmacro elib-node-data (node)
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;; Return the data of NODE.
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(` (aref (, node) 2)))
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(defmacro elib-node-set-left (node newleft)
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;; Set the left pointer of NODE to NEWLEFT.
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(` (aset (, node) 0 (, newleft))))
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(defmacro elib-node-set-right (node newright)
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;; Set the right pointer of NODE to NEWRIGHT.
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(` (aset (, node) 1 (, newright))))
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(defmacro elib-node-set-data (node newdata)
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;; Set the data of NODE to NEWDATA.
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(` (aset (, node) 2 (, newdata))))
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(defmacro elib-node-branch (node branch)
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;; Get value of a branch of a node.
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;;
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;; NODE is the node, and BRANCH is the branch.
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;; 0 for left pointer, 1 for right pointer and 2 for the data."
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(` (aref (, node) (, branch))))
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(defmacro elib-node-set-branch (node branch newval)
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;; Set value of a branch of a node.
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;;
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;; NODE is the node, and BRANCH is the branch.
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;; 0 for left pointer, 1 for the right pointer and 2 for the data.
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;; NEWVAL is new value of the branch."
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(` (aset (, node) (, branch) (, newval))))
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;;; elib-node.el ends here.
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;;;; $Id: avltree.el,v 0.8 1995/12/11 00:10:54 ceder Exp $
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;;;; This file implements balanced binary trees, AVL-trees.
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;; Copyright (C) 1991-1995 Free Software Foundation
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;; Author: Inge Wallin <inge@lysator.liu.se>
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;; Thomas Bellman <bellman@lysator.liu.se>
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;; Maintainer: elib-maintainers@lysator.liu.se
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;; Created: 10 May 1991
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;; Keywords: extensions, lisp
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;;;; This file is part of the GNU Emacs lisp library, Elib.
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;;;;
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;;;; GNU Elib is free software; you can redistribute it and/or modify
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;;;; it under the terms of the GNU General Public License as published by
|
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;;;; the Free Software Foundation; either version 2, or (at your option)
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;;;; any later version.
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;;;;
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;;;; GNU Elib is distributed in the hope that it will be useful,
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;;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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;;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
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;;;; GNU General Public License for more details.
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;;;;
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;;;; You should have received a copy of the GNU General Public License
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;;;; along with GNU Elib; see the file COPYING. If not, write to
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;;;; the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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;;;; Boston, MA 02111-1307, USA
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;;;;
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;;;; Initial author: Thomas Bellman
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;;;; Lysator Computer Club
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;;;; Linkoping University
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;;;; Sweden
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;;;;
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;;;; Bugfixes and completion: Inge Wallin
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;;;;
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;;; Commentary:
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;;;
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;;; An AVL tree is a nearly-perfect balanced binary tree. A tree
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;;; consists of two cons cells, the first one holding the tag
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;;; 'AVLTREE in the car cell, and the second one having the tree
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;;; in the car and the compare function in the cdr cell. The tree has
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;;; a dummy node as its root with the real tree in the left pointer.
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;;;
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;;; Each node of the tree consists of one data element, one left
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;;; sub-tree and one right sub-tree. Each node also has a balance
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;;; count, which is the difference in depth of the left and right
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;;; sub-trees.
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;;;
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;;; Code:
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;;; Begin HACKS to make avl-tree.el standalone.
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;;;
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;;; 1/ See above for inlined elib-node.el.
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;;; (require 'elib-node)
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;;;
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;;; 2/ This requirement has been replaced w/ new code.
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;;; (require 'stack-m)
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;;;
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;;; 3/ New code:
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(eval-when-compile (require 'cl))
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(defun elib-stack-create () (list))
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(defmacro elib-stack-push (stack object) `(push ,object ,stack))
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(defmacro elib-stack-pop (stack) `(pop ,stack))
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;;;
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;;; 4/ Provide `avl-tree' instead of `avltree'.
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(provide 'avl-tree)
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;;;
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;;; End HACKS to make avl-tree.el standalone.
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;;; ================================================================
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;;; Functions and macros handling an AVL tree node.
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;;
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;; The rest of the functions needed here can be found in
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;; elib-node.el.
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;;
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(defmacro elib-avl-node-create (left right data balance)
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;; Create and return an avl-tree node.
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(` (vector (, left) (, right) (, data) (, balance))))
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(defmacro elib-avl-node-balance (node)
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;; Return the balance field of a node.
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(` (aref (, node) 3)))
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(defmacro elib-avl-node-set-balance (node newbal)
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;; Set the balance field of a node.
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(` (aset (, node) 3 (, newbal))))
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;;; ================================================================
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;;; Internal functions for use in the AVL tree package
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;;;
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;;; The functions and macros in this section all start with `elib-avl-'.
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;;;
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(defmacro elib-avl-root (tree)
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;; Return the root node for an avl-tree. INTERNAL USE ONLY.
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(` (elib-node-left (car (cdr (, tree))))))
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(defmacro elib-avl-dummyroot (tree)
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;; Return the dummy node of an avl-tree. INTERNAL USE ONLY.
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(` (car (cdr (, tree)))))
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(defmacro elib-avl-cmpfun (tree)
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;; Return the compare function of AVL tree TREE. INTERNAL USE ONLY.
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(` (cdr (cdr (, tree)))))
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;; ----------------------------------------------------------------
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;; Deleting data
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(defun elib-avl-del-balance1 (node branch)
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;; Rebalance a tree and return t if the height of the tree has shrunk.
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(let* ((br (elib-node-branch node branch))
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p1
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b1
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p2
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b2
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result)
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(cond
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((< (elib-avl-node-balance br) 0)
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(elib-avl-node-set-balance br 0)
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t)
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((= (elib-avl-node-balance br) 0)
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(elib-avl-node-set-balance br +1)
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nil)
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(t ; Rebalance
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(setq p1 (elib-node-right br)
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b1 (elib-avl-node-balance p1))
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(if (>= b1 0)
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;; Single RR rotation
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(progn
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(elib-node-set-right br (elib-node-left p1))
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(elib-node-set-left p1 br)
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(if (= 0 b1)
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(progn
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(elib-avl-node-set-balance br +1)
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(elib-avl-node-set-balance p1 -1)
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(setq result nil))
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(elib-avl-node-set-balance br 0)
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(elib-avl-node-set-balance p1 0)
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(setq result t))
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(elib-node-set-branch node branch p1)
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result)
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;; Double RL rotation
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(setq p2 (elib-node-left p1)
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b2 (elib-avl-node-balance p2))
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(elib-node-set-left p1 (elib-node-right p2))
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(elib-node-set-right p2 p1)
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(elib-node-set-right br (elib-node-left p2))
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(elib-node-set-left p2 br)
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(if (> b2 0)
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(elib-avl-node-set-balance br -1)
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(elib-avl-node-set-balance br 0))
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(if (< b2 0)
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(elib-avl-node-set-balance p1 +1)
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(elib-avl-node-set-balance p1 0))
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(elib-node-set-branch node branch p2)
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(elib-avl-node-set-balance p2 0)
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t)
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))
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))
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(defun elib-avl-del-balance2 (node branch)
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(let* ((br (elib-node-branch node branch))
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p1
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b1
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p2
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b2
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result)
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(cond
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((> (elib-avl-node-balance br) 0)
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(elib-avl-node-set-balance br 0)
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t)
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((= (elib-avl-node-balance br) 0)
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(elib-avl-node-set-balance br -1)
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nil)
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(t ; Rebalance
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(setq p1 (elib-node-left br)
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b1 (elib-avl-node-balance p1))
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(if (<= b1 0)
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;; Single LL rotation
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(progn
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(elib-node-set-left br (elib-node-right p1))
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(elib-node-set-right p1 br)
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(if (= 0 b1)
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(progn
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(elib-avl-node-set-balance br -1)
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(elib-avl-node-set-balance p1 +1)
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(setq result nil))
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(elib-avl-node-set-balance br 0)
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(elib-avl-node-set-balance p1 0)
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(setq result t))
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(elib-node-set-branch node branch p1)
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result)
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;; Double LR rotation
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(setq p2 (elib-node-right p1)
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b2 (elib-avl-node-balance p2))
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(elib-node-set-right p1 (elib-node-left p2))
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(elib-node-set-left p2 p1)
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(elib-node-set-left br (elib-node-right p2))
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(elib-node-set-right p2 br)
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(if (< b2 0)
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(elib-avl-node-set-balance br +1)
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(elib-avl-node-set-balance br 0))
|
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(if (> b2 0)
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(elib-avl-node-set-balance p1 -1)
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(elib-avl-node-set-balance p1 0))
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(elib-node-set-branch node branch p2)
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(elib-avl-node-set-balance p2 0)
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t)
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))
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))
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(defun elib-avl-do-del-internal (node branch q)
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(let* ((br (elib-node-branch node branch)))
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(if (elib-node-right br)
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(if (elib-avl-do-del-internal br +1 q)
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(elib-avl-del-balance2 node branch))
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(elib-node-set-data q (elib-node-data br))
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(elib-node-set-branch node branch
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(elib-node-left br))
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t)))
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(defun elib-avl-do-delete (cmpfun root branch data)
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;; Return t if the height of the tree has shrunk.
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(let* ((br (elib-node-branch root branch)))
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(cond
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||||
((null br)
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||||
nil)
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||||
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||||
((funcall cmpfun data (elib-node-data br))
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(if (elib-avl-do-delete cmpfun br 0 data)
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(elib-avl-del-balance1 root branch)))
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||||
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||||
((funcall cmpfun (elib-node-data br) data)
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||||
(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
|
||||
Loading…
Reference in New Issue
Block a user