;; Copyright (C) 1995, 2007-2011 Free Software Foundation, Inc.
;; Author: Per Cederqvist <ceder@lysator.liu.se>
-;; Inge Wallin <inge@lysator.liu.se>
-;; Thomas Bellman <bellman@lysator.liu.se>
+;; Inge Wallin <inge@lysator.liu.se>
+;; Thomas Bellman <bellman@lysator.liu.se>
+;; Toby Cubitt <toby-predictive@dr-qubit.org>
;; Maintainer: FSF
;; Created: 10 May 1991
-;; Keywords: extensions, data structures
+;; Keywords: extensions, data structures, AVL, tree
;; This file is part of GNU Emacs.
;;; Commentary:
-;; An AVL tree is a nearly-perfect balanced binary tree. A tree consists of
-;; two elements, the root node and the compare function. The actual tree
-;; has a dummy node as its root with the real root in the left pointer.
+;; An AVL tree is a self-balancing binary tree. As such, inserting,
+;; deleting, and retrieving data from an AVL tree containing n elements
+;; is O(log n). It is somewhat more rigidly balanced than other
+;; self-balancing binary trees (such as red-black trees and AA trees),
+;; making insertion slighty slower, deletion somewhat slower, and
+;; retrieval somewhat faster (the asymptotic scaling is of course the
+;; same for all types). Thus it may be a good choice when the tree will
+;; be relatively static, i.e. data will be retrieved more often than
+;; they are modified.
+;;
+;; Internally, a tree consists of two elements, the root node and the
+;; comparison function. The actual tree has a dummy node as its root
+;; with the real root in the left pointer, which allows the root node to
+;; be treated on a par with all other nodes.
;;
;; 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.
+;; sub-tree, one right sub-tree, and a balance count. The latter is the
+;; difference in depth of the left and right sub-trees.
;;
;; The functions with names of the form "avl-tree--" are intended for
;; internal use only.
(eval-when-compile (require 'cl))
-;; ================================================================
-;;; Functions and macros handling an AVL tree node.
-(defstruct (avl-tree--node
- ;; We force a representation without tag so it matches the
- ;; pre-defstruct representation. Also we use the underlying
- ;; representation in the implementation of avl-tree--node-branch.
- (:type vector)
- (:constructor nil)
- (:constructor avl-tree--node-create (left right data balance))
- (:copier nil))
- left right data balance)
-(defalias 'avl-tree--node-branch 'aref
- ;; This implementation is efficient but breaks the defstruct abstraction.
- ;; An alternative could be
- ;; (funcall (aref [avl-tree-left avl-tree-right avl-tree-data] branch) node)
- "Get value of a branch of a node.
+;; ================================================================
+;;; Internal functions and macros for use in the AVL tree package
-NODE is the node, and BRANCH is the branch.
-0 for left pointer, 1 for right pointer and 2 for the data.\"
-\(fn node branch)")
-;; The funcall/aref trick doesn't work for the setf method, unless we try
-;; and access the underlying setter function, but this wouldn't be
-;; portable either.
-(defsetf avl-tree--node-branch aset)
-\f
-;; ================================================================
-;;; Internal functions for use in the AVL tree package
+;; ----------------------------------------------------------------
+;; Functions and macros handling an AVL tree.
(defstruct (avl-tree-
;; A tagged list is the pre-defstruct representation.
;; (:type list)
:named
(:constructor nil)
- (:constructor avl-tree-create (cmpfun))
+ (:constructor avl-tree--create (cmpfun))
(:predicate avl-tree-p)
(:copier nil))
(dummyroot (avl-tree--node-create nil nil nil 0))
(defmacro avl-tree--root (tree)
;; Return the root node for an avl-tree. INTERNAL USE ONLY.
- `(avl-tree--node-left (avl-tree--dummyroot tree)))
+ `(avl-tree--node-left (avl-tree--dummyroot ,tree)))
+
(defsetf avl-tree--root (tree) (node)
`(setf (avl-tree--node-left (avl-tree--dummyroot ,tree)) ,node))
+
+
;; ----------------------------------------------------------------
-;; Deleting data
+;; Functions and macros handling an AVL tree node.
-(defun avl-tree--del-balance1 (node branch)
- ;; Rebalance a tree and return t if the height of the tree has shrunk.
- (let ((br (avl-tree--node-branch node branch))
- p1 b1 p2 b2 result)
- (cond
- ((< (avl-tree--node-balance br) 0)
- (setf (avl-tree--node-balance br) 0)
- t)
+(defstruct (avl-tree--node
+ ;; We force a representation without tag so it matches the
+ ;; pre-defstruct representation. Also we use the underlying
+ ;; representation in the implementation of
+ ;; avl-tree--node-branch.
+ (:type vector)
+ (:constructor nil)
+ (:constructor avl-tree--node-create (left right data balance))
+ (:copier nil))
+ left right data balance)
- ((= (avl-tree--node-balance br) 0)
- (setf (avl-tree--node-balance br) +1)
- nil)
- (t
- ;; Rebalance.
- (setq p1 (avl-tree--node-right br)
- b1 (avl-tree--node-balance p1))
- (if (>= b1 0)
- ;; Single RR rotation.
- (progn
- (setf (avl-tree--node-right br) (avl-tree--node-left p1))
- (setf (avl-tree--node-left p1) br)
- (if (= 0 b1)
- (progn
- (setf (avl-tree--node-balance br) +1)
- (setf (avl-tree--node-balance p1) -1)
- (setq result nil))
- (setf (avl-tree--node-balance br) 0)
- (setf (avl-tree--node-balance p1) 0)
- (setq result t))
- (setf (avl-tree--node-branch node branch) p1)
- result)
-
- ;; Double RL rotation.
- (setq p2 (avl-tree--node-left p1)
- b2 (avl-tree--node-balance p2))
- (setf (avl-tree--node-left p1) (avl-tree--node-right p2))
- (setf (avl-tree--node-right p2) p1)
- (setf (avl-tree--node-right br) (avl-tree--node-left p2))
- (setf (avl-tree--node-left p2) br)
- (setf (avl-tree--node-balance br) (if (> b2 0) -1 0))
- (setf (avl-tree--node-balance p1) (if (< b2 0) +1 0))
- (setf (avl-tree--node-branch node branch) p2)
- (setf (avl-tree--node-balance p2) 0)
- t)))))
+(defalias 'avl-tree--node-branch 'aref
+ ;; This implementation is efficient but breaks the defstruct
+ ;; abstraction. An alternative could be (funcall (aref [avl-tree-left
+ ;; avl-tree-right avl-tree-data] branch) node)
+ "Get value of a branch of a node.
+NODE is the node, and BRANCH is the branch.
+0 for left pointer, 1 for right pointer and 2 for the data.")
+
+
+;; The funcall/aref trick wouldn't work for the setf method, unless we
+;; tried to access the underlying setter function, but this wouldn't be
+;; portable either.
+(defsetf avl-tree--node-branch aset)
+
+
+
+;; ----------------------------------------------------------------
+;; Convenience macros
-(defun avl-tree--del-balance2 (node branch)
+(defmacro avl-tree--switch-dir (dir)
+ "Return opposite direction to DIR (0 = left, 1 = right)."
+ `(- 1 ,dir))
+
+(defmacro avl-tree--dir-to-sign (dir)
+ "Convert direction (0,1) to sign factor (-1,+1)."
+ `(1- (* 2 ,dir)))
+
+(defmacro avl-tree--sign-to-dir (dir)
+ "Convert sign factor (-x,+x) to direction (0,1)."
+ `(if (< ,dir 0) 0 1))
+
+
+;; ----------------------------------------------------------------
+;; Deleting data
+
+(defun avl-tree--del-balance (node branch dir)
+ "Rebalance a tree after deleting a node.
+The deletion was done from the left (DIR=0) or right (DIR=1) sub-tree of the
+left (BRANCH=0) or right (BRANCH=1) child of NODE.
+Return t if the height of the tree has shrunk."
+ ;; (or is it vice-versa for BRANCH?)
(let ((br (avl-tree--node-branch node branch))
- p1 b1 p2 b2 result)
+ ;; opposite direction: 0,1 -> 1,0
+ (opp (avl-tree--switch-dir dir))
+ ;; direction 0,1 -> sign factor -1,+1
+ (sgn (avl-tree--dir-to-sign dir))
+ p1 b1 p2 b2)
(cond
- ((> (avl-tree--node-balance br) 0)
+ ((> (* sgn (avl-tree--node-balance br)) 0)
(setf (avl-tree--node-balance br) 0)
t)
((= (avl-tree--node-balance br) 0)
- (setf (avl-tree--node-balance br) -1)
+ (setf (avl-tree--node-balance br) (- sgn))
nil)
(t
;; Rebalance.
- (setq p1 (avl-tree--node-left br)
+ (setq p1 (avl-tree--node-branch br opp)
b1 (avl-tree--node-balance p1))
- (if (<= b1 0)
- ;; Single LL rotation.
+ (if (<= (* sgn b1) 0)
+ ;; Single rotation.
(progn
- (setf (avl-tree--node-left br) (avl-tree--node-right p1))
- (setf (avl-tree--node-right p1) br)
+ (setf (avl-tree--node-branch br opp)
+ (avl-tree--node-branch p1 dir)
+ (avl-tree--node-branch p1 dir) br
+ (avl-tree--node-branch node branch) p1)
(if (= 0 b1)
(progn
- (setf (avl-tree--node-balance br) -1)
- (setf (avl-tree--node-balance p1) +1)
- (setq result nil))
+ (setf (avl-tree--node-balance br) (- sgn)
+ (avl-tree--node-balance p1) sgn)
+ nil) ; height hasn't changed
(setf (avl-tree--node-balance br) 0)
(setf (avl-tree--node-balance p1) 0)
- (setq result t))
- (setf (avl-tree--node-branch node branch) p1)
- result)
-
- ;; Double LR rotation.
- (setq p2 (avl-tree--node-right p1)
- b2 (avl-tree--node-balance p2))
- (setf (avl-tree--node-right p1) (avl-tree--node-left p2))
- (setf (avl-tree--node-left p2) p1)
- (setf (avl-tree--node-left br) (avl-tree--node-right p2))
- (setf (avl-tree--node-right p2) br)
- (setf (avl-tree--node-balance br) (if (< b2 0) +1 0))
- (setf (avl-tree--node-balance p1) (if (> b2 0) -1 0))
- (setf (avl-tree--node-branch node branch) p2)
- (setf (avl-tree--node-balance p2) 0)
+ t)) ; height has changed
+
+ ;; Double rotation.
+ (setf p2 (avl-tree--node-branch p1 dir)
+ b2 (avl-tree--node-balance p2)
+ (avl-tree--node-branch p1 dir)
+ (avl-tree--node-branch p2 opp)
+ (avl-tree--node-branch p2 opp) p1
+ (avl-tree--node-branch br opp)
+ (avl-tree--node-branch p2 dir)
+ (avl-tree--node-branch p2 dir) br
+ (avl-tree--node-balance br)
+ (if (< (* sgn b2) 0) sgn 0)
+ (avl-tree--node-balance p1)
+ (if (> (* sgn b2) 0) (- sgn) 0)
+ (avl-tree--node-branch node branch) p2
+ (avl-tree--node-balance p2) 0)
t)))))
(defun avl-tree--do-del-internal (node branch q)
(let ((br (avl-tree--node-branch node branch)))
(if (avl-tree--node-right br)
- (if (avl-tree--do-del-internal br +1 q)
- (avl-tree--del-balance2 node branch))
- (setf (avl-tree--node-data q) (avl-tree--node-data br))
- (setf (avl-tree--node-branch node branch)
- (avl-tree--node-left br))
+ (if (avl-tree--do-del-internal br 1 q)
+ (avl-tree--del-balance node branch 1))
+ (setf (avl-tree--node-data q) (avl-tree--node-data br)
+ (avl-tree--node-branch node branch)
+ (avl-tree--node-left br))
t)))
(defun avl-tree--do-delete (cmpfun root branch data)
((funcall cmpfun data (avl-tree--node-data br))
(if (avl-tree--do-delete cmpfun br 0 data)
- (avl-tree--del-balance1 root branch)))
+ (avl-tree--del-balance root branch 0)))
((funcall cmpfun (avl-tree--node-data br) data)
(if (avl-tree--do-delete cmpfun br 1 data)
- (avl-tree--del-balance2 root branch)))
+ (avl-tree--del-balance root branch 1)))
(t
;; Found it. Let's delete it.
(cond
((null (avl-tree--node-right br))
- (setf (avl-tree--node-branch root branch) (avl-tree--node-left br))
- t)
+ (setf (avl-tree--node-branch root branch) (avl-tree--node-left br))
+ t)
((null (avl-tree--node-left br))
- (setf (avl-tree--node-branch root branch) (avl-tree--node-right br))
- t)
+ (setf (avl-tree--node-branch root branch)
+ (avl-tree--node-right br))
+ t)
(t
- (if (avl-tree--do-del-internal br 0 br)
- (avl-tree--del-balance1 root branch))))))))
+ (if (avl-tree--do-del-internal br 0 br)
+ (avl-tree--del-balance root branch 0))))))))
;; ----------------------------------------------------------------
;; Entering data
-(defun avl-tree--enter-balance1 (node branch)
- ;; Rebalance a tree and return t if the height of the tree has grown.
+(defun avl-tree--enter-balance (node branch dir)
+ "Rebalance tree after an insertion
+into the left (DIR=0) or right (DIR=1) sub-tree of the
+left (BRANCH=0) or right (BRANCH=1) child of NODE.
+Return t if the height of the tree has grown."
(let ((br (avl-tree--node-branch node branch))
+ ;; opposite direction: 0,1 -> 1,0
+ (opp (avl-tree--switch-dir dir))
+ ;; direction 0,1 -> sign factor -1,+1
+ (sgn (avl-tree--dir-to-sign dir))
p1 p2 b2 result)
(cond
- ((< (avl-tree--node-balance br) 0)
+ ((< (* sgn (avl-tree--node-balance br)) 0)
(setf (avl-tree--node-balance br) 0)
nil)
((= (avl-tree--node-balance br) 0)
- (setf (avl-tree--node-balance br) +1)
+ (setf (avl-tree--node-balance br) sgn)
t)
(t
;; Tree has grown => Rebalance.
- (setq p1 (avl-tree--node-right br))
- (if (> (avl-tree--node-balance p1) 0)
- ;; Single RR rotation.
+ (setq p1 (avl-tree--node-branch br dir))
+ (if (> (* sgn (avl-tree--node-balance p1)) 0)
+ ;; Single rotation.
(progn
- (setf (avl-tree--node-right br) (avl-tree--node-left p1))
- (setf (avl-tree--node-left p1) br)
+ (setf (avl-tree--node-branch br dir)
+ (avl-tree--node-branch p1 opp))
+ (setf (avl-tree--node-branch p1 opp) br)
(setf (avl-tree--node-balance br) 0)
(setf (avl-tree--node-branch node branch) p1))
- ;; Double RL rotation.
- (setq p2 (avl-tree--node-left p1)
- b2 (avl-tree--node-balance p2))
- (setf (avl-tree--node-left p1) (avl-tree--node-right p2))
- (setf (avl-tree--node-right p2) p1)
- (setf (avl-tree--node-right br) (avl-tree--node-left p2))
- (setf (avl-tree--node-left p2) br)
- (setf (avl-tree--node-balance br) (if (> b2 0) -1 0))
- (setf (avl-tree--node-balance p1) (if (< b2 0) +1 0))
- (setf (avl-tree--node-branch node branch) p2))
- (setf (avl-tree--node-balance (avl-tree--node-branch node branch)) 0)
- nil))))
-
-(defun avl-tree--enter-balance2 (node branch)
- ;; Return t if the tree has grown.
- (let ((br (avl-tree--node-branch node branch))
- p1 p2 b2)
- (cond
- ((> (avl-tree--node-balance br) 0)
- (setf (avl-tree--node-balance br) 0)
- nil)
-
- ((= (avl-tree--node-balance br) 0)
- (setf (avl-tree--node-balance br) -1)
- t)
-
- (t
- ;; Balance was -1 => Rebalance.
- (setq p1 (avl-tree--node-left br))
- (if (< (avl-tree--node-balance p1) 0)
- ;; Single LL rotation.
- (progn
- (setf (avl-tree--node-left br) (avl-tree--node-right p1))
- (setf (avl-tree--node-right p1) br)
- (setf (avl-tree--node-balance br) 0)
- (setf (avl-tree--node-branch node branch) p1))
-
- ;; Double LR rotation.
- (setq p2 (avl-tree--node-right p1)
- b2 (avl-tree--node-balance p2))
- (setf (avl-tree--node-right p1) (avl-tree--node-left p2))
- (setf (avl-tree--node-left p2) p1)
- (setf (avl-tree--node-left br) (avl-tree--node-right p2))
- (setf (avl-tree--node-right p2) br)
- (setf (avl-tree--node-balance br) (if (< b2 0) +1 0))
- (setf (avl-tree--node-balance p1) (if (> b2 0) -1 0))
- (setf (avl-tree--node-branch node branch) p2))
- (setf (avl-tree--node-balance (avl-tree--node-branch node branch)) 0)
+ ;; Double rotation.
+ (setf p2 (avl-tree--node-branch p1 opp)
+ b2 (avl-tree--node-balance p2)
+ (avl-tree--node-branch p1 opp)
+ (avl-tree--node-branch p2 dir)
+ (avl-tree--node-branch p2 dir) p1
+ (avl-tree--node-branch br dir)
+ (avl-tree--node-branch p2 opp)
+ (avl-tree--node-branch p2 opp) br
+ (avl-tree--node-balance br)
+ (if (> (* sgn b2) 0) (- sgn) 0)
+ (avl-tree--node-balance p1)
+ (if (< (* sgn b2) 0) sgn 0)
+ (avl-tree--node-branch node branch) p2
+ (avl-tree--node-balance
+ (avl-tree--node-branch node branch)) 0))
nil))))
(defun avl-tree--do-enter (cmpfun root branch data)
((funcall cmpfun data (avl-tree--node-data br))
(and (avl-tree--do-enter cmpfun br 0 data)
- (avl-tree--enter-balance2 root branch)))
+ (avl-tree--enter-balance root branch 0)))
((funcall cmpfun (avl-tree--node-data br) data)
(and (avl-tree--do-enter cmpfun br 1 data)
- (avl-tree--enter-balance1 root branch)))
+ (avl-tree--enter-balance root branch 1)))
(t
(setf (avl-tree--node-data br) data)
;; ----------------------------------------------------------------
-(defun avl-tree--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.
+
+;;; INTERNAL USE ONLY
+(defun avl-tree--mapc (map-function root dir)
+ "Apply MAP-FUNCTION to all nodes in the tree starting with ROOT.
+The function is applied in-order, either ascending (DIR=0) or
+descending (DIR=1).
+
+Note: MAP-FUNCTION is applied to the node and not to the data
+itself."
(let ((node root)
(stack nil)
- (go-left t))
+ (go-dir t))
(push nil stack)
(while node
- (if (and go-left
- (avl-tree--node-left node))
- ;; Do the left subtree first.
+ (if (and go-dir
+ (avl-tree--node-branch node dir))
+ ;; Do the DIR subtree first.
(progn
(push node stack)
- (setq node (avl-tree--node-left node)))
+ (setq node (avl-tree--node-branch node dir)))
;; Apply the function...
(funcall map-function node)
- ;; and do the right subtree.
- (setq node (if (setq go-left (avl-tree--node-right node))
- (avl-tree--node-right node)
+ ;; and do the opposite subtree.
+ (setq node (if (setq go-dir (avl-tree--node-branch
+ node (avl-tree--switch-dir dir)))
+ (avl-tree--node-branch
+ node (avl-tree--switch-dir dir))
(pop stack)))))))
+;;; INTERNAL USE ONLY
(defun avl-tree--do-copy (root)
- ;; Copy the avl tree with ROOT as root.
- ;; Highly recursive. INTERNAL USE ONLY.
+ "Copy the avl tree with ROOT as root. Highly recursive."
(if (null root)
nil
(avl-tree--node-create
(avl-tree--node-data root)
(avl-tree--node-balance root))))
-\f
+
;; ================================================================
;;; The public functions which operate on AVL trees.
+;; define public alias for constructors so that we can set docstring
+(defalias 'avl-tree-create 'avl-tree--create
+ "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.")
+
(defalias 'avl-tree-compare-function 'avl-tree--cmpfun
"Return the comparison function for the avl tree TREE.
"In the avl tree TREE insert DATA.
Return DATA."
(avl-tree--do-enter (avl-tree--cmpfun tree)
- (avl-tree--dummyroot tree)
- 0
- data)
+ (avl-tree--dummyroot tree)
+ 0
+ data)
data)
(defun avl-tree-delete (tree data)
If there is no such element in the tree, the value is nil."
(let ((node (avl-tree--root tree))
- (compare-function (avl-tree--cmpfun tree))
- found)
- (while (and node
- (not found))
- (cond
- ((funcall compare-function data (avl-tree--node-data node))
- (setq node (avl-tree--node-left node)))
- ((funcall compare-function (avl-tree--node-data node) data)
- (setq node (avl-tree--node-right node)))
- (t
- (setq found t))))
- (if node
- (avl-tree--node-data node)
+ (compare-function (avl-tree--cmpfun tree)))
+ (catch 'found
+ (while node
+ (cond
+ ((funcall compare-function data (avl-tree--node-data node))
+ (setq node (avl-tree--node-left node)))
+ ((funcall compare-function (avl-tree--node-data node) data)
+ (setq node (avl-tree--node-right node)))
+ (t (throw 'found (avl-tree--node-data node)))))
nil)))
-(defun avl-tree-map (__map-function__ tree)
- "Apply __MAP-FUNCTION__ to all elements in the avl tree TREE."
+(defun avl-tree-map (__map-function__ tree &optional reverse)
+ "Modify all elements in the avl tree TREE by applying FUNCTION.
+
+Each element is replaced by the return value of FUNCTION applied
+to that element.
+
+FUNCTION is applied to the elements in ascending order, or
+descending order if REVERSE is non-nil."
(avl-tree--mapc
(lambda (node)
(setf (avl-tree--node-data node)
(funcall __map-function__ (avl-tree--node-data node))))
- (avl-tree--root tree)))
+ (avl-tree--root tree)
+ (if reverse 1 0)))
(defun avl-tree-first (tree)
"Return the first element in TREE, or nil if TREE is empty."
(defun avl-tree-flatten (tree)
"Return a sorted list containing all elements of TREE."
- (nreverse
(let ((treelist nil))
(avl-tree--mapc
(lambda (node) (push (avl-tree--node-data node) treelist))
- (avl-tree--root tree))
- treelist)))
+ (avl-tree--root tree) 1)
+ treelist))
(defun avl-tree-size (tree)
"Return the number of elements in TREE."
(let ((treesize 0))
(avl-tree--mapc
(lambda (data) (setq treesize (1+ treesize)))
- (avl-tree--root tree))
+ (avl-tree--root tree) 0)
treesize))
(defun avl-tree-clear (tree)
projects / emacs.git / commitdiff