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diff --git a/lisp/emacs-lisp/avl-tree.el b/lisp/emacs-lisp/avl-tree.el new file mode 100644 index 00000000000..ffac825acac --- /dev/null +++ b/lisp/emacs-lisp/avl-tree.el @@ -0,0 +1,534 @@ +;;; avl-tree.el --- balanced binary trees, AVL-trees + +;; Copyright (C) 1995, 2007 Free Software Foundation, Inc. + +;; Author: Per Cederqvist <ceder@lysator.liu.se> +;; Inge Wallin <inge@lysator.liu.se> +;; Thomas Bellman <bellman@lysator.liu.se> +;; Maintainer: FSF +;; Created: 10 May 1991 +;; Keywords: extensions, data structures + +;; 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, 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; see the file COPYING. If not, write to the +;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, +;; Boston, MA 02110-1301, USA. + +;;; Commentary: + +;; An AVL tree is a nearly-perfect balanced binary tree. A tree +;; consists of two cons cells, the first one holding the tag +;; 'AVL-TREE 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. +;; +;; The "public" functions (prefixed with "avl-tree") are: +;; -create, -p, -compare-function, -empty, -enter, -delete, +;; -member, -map, -first, -last, -copy, -flatten, -size, -clear. + +;;; Code: + +;;; ================================================================ +;;; Functions and macros handling an AVL tree node. + +(defmacro avl-tree-node-create (left right data balance) + ;; Create and return an avl-tree node. + `(vector ,left ,right ,data ,balance)) + +(defmacro avl-tree-node-left (node) + ;; Return the left pointer of NODE. + `(aref ,node 0)) + +(defmacro avl-tree-node-right (node) + ;; Return the right pointer of NODE. + `(aref ,node 1)) + +(defmacro avl-tree-node-data (node) + ;; Return the data of NODE. + `(aref ,node 2)) + +(defmacro avl-tree-node-set-left (node newleft) + ;; Set the left pointer of NODE to NEWLEFT. + `(aset ,node 0 ,newleft)) + +(defmacro avl-tree-node-set-right (node newright) + ;; Set the right pointer of NODE to NEWRIGHT. + `(aset ,node 1 ,newright)) + +(defmacro avl-tree-node-set-data (node newdata) + ;; Set the data of NODE to NEWDATA. + `(aset ,node 2 ,newdata)) + +(defmacro avl-tree-node-branch (node branch) + "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.\"" + `(aref ,node ,branch)) + +(defmacro avl-tree-node-set-branch (node branch newval) + "Set value of a branch of a node. + +NODE is the node, and BRANCH is the branch. +0 for left pointer, 1 for the right pointer and 2 for the data. +NEWVAL is new value of the branch.\"" + `(aset ,node ,branch ,newval)) + +(defmacro avl-tree-node-balance (node) + ;; Return the balance field of a node. + `(aref ,node 3)) + +(defmacro avl-tree-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 + +(defmacro avl-tree-root (tree) + ;; Return the root node for an avl-tree. INTERNAL USE ONLY. + `(avl-tree-node-left (car (cdr ,tree)))) + +(defmacro avl-tree-dummyroot (tree) + ;; Return the dummy node of an avl-tree. INTERNAL USE ONLY. + `(car (cdr ,tree))) + +(defmacro avl-tree-cmpfun (tree) + ;; Return the compare function of AVL tree TREE. INTERNAL USE ONLY. + `(cdr (cdr ,tree))) + +;; ---------------------------------------------------------------- +;; Deleting data + +(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) + (avl-tree-node-set-balance br 0) + t) + + ((= (avl-tree-node-balance br) 0) + (avl-tree-node-set-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 + (avl-tree-node-set-right br (avl-tree-node-left p1)) + (avl-tree-node-set-left p1 br) + (if (= 0 b1) + (progn + (avl-tree-node-set-balance br +1) + (avl-tree-node-set-balance p1 -1) + (setq result nil)) + (avl-tree-node-set-balance br 0) + (avl-tree-node-set-balance p1 0) + (setq result t)) + (avl-tree-node-set-branch node branch p1) + result) + + ;; Double RL rotation. + (setq p2 (avl-tree-node-left p1) + b2 (avl-tree-node-balance p2)) + (avl-tree-node-set-left p1 (avl-tree-node-right p2)) + (avl-tree-node-set-right p2 p1) + (avl-tree-node-set-right br (avl-tree-node-left p2)) + (avl-tree-node-set-left p2 br) + (if (> b2 0) + (avl-tree-node-set-balance br -1) + (avl-tree-node-set-balance br 0)) + (if (< b2 0) + (avl-tree-node-set-balance p1 +1) + (avl-tree-node-set-balance p1 0)) + (avl-tree-node-set-branch node branch p2) + (avl-tree-node-set-balance p2 0) + t))))) + +(defun avl-tree-del-balance2 (node branch) + (let ((br (avl-tree-node-branch node branch)) + p1 b1 p2 b2 result) + (cond + ((> (avl-tree-node-balance br) 0) + (avl-tree-node-set-balance br 0) + t) + + ((= (avl-tree-node-balance br) 0) + (avl-tree-node-set-balance br -1) + nil) + + (t + ;; Rebalance. + (setq p1 (avl-tree-node-left br) + b1 (avl-tree-node-balance p1)) + (if (<= b1 0) + ;; Single LL rotation. + (progn + (avl-tree-node-set-left br (avl-tree-node-right p1)) + (avl-tree-node-set-right p1 br) + (if (= 0 b1) + (progn + (avl-tree-node-set-balance br -1) + (avl-tree-node-set-balance p1 +1) + (setq result nil)) + (avl-tree-node-set-balance br 0) + (avl-tree-node-set-balance p1 0) + (setq result t)) + (avl-tree-node-set-branch node branch p1) + result) + + ;; Double LR rotation. + (setq p2 (avl-tree-node-right p1) + b2 (avl-tree-node-balance p2)) + (avl-tree-node-set-right p1 (avl-tree-node-left p2)) + (avl-tree-node-set-left p2 p1) + (avl-tree-node-set-left br (avl-tree-node-right p2)) + (avl-tree-node-set-right p2 br) + (if (< b2 0) + (avl-tree-node-set-balance br +1) + (avl-tree-node-set-balance br 0)) + (if (> b2 0) + (avl-tree-node-set-balance p1 -1) + (avl-tree-node-set-balance p1 0)) + (avl-tree-node-set-branch node branch p2) + (avl-tree-node-set-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)) + (avl-tree-node-set-data q (avl-tree-node-data br)) + (avl-tree-node-set-branch node branch + (avl-tree-node-left br)) + t))) + +(defun avl-tree-do-delete (cmpfun root branch data) + ;; Return t if the height of the tree has shrunk. + (let ((br (avl-tree-node-branch root branch))) + (cond + ((null br) + nil) + + ((funcall cmpfun data (avl-tree-node-data br)) + (if (avl-tree-do-delete cmpfun br 0 data) + (avl-tree-del-balance1 root branch))) + + ((funcall cmpfun (avl-tree-node-data br) data) + (if (avl-tree-do-delete cmpfun br 1 data) + (avl-tree-del-balance2 root branch))) + + (t + ;; Found it. Let's delete it. + (cond + ((null (avl-tree-node-right br)) + (avl-tree-node-set-branch root branch (avl-tree-node-left br)) + t) + + ((null (avl-tree-node-left br)) + (avl-tree-node-set-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)))))))) + +;; ---------------------------------------------------------------- +;; Entering data + +(defun avl-tree-enter-balance1 (node branch) + ;; Rebalance a tree and return t if the height of the tree has grown. + (let ((br (avl-tree-node-branch node branch)) + p1 p2 b2 result) + (cond + ((< (avl-tree-node-balance br) 0) + (avl-tree-node-set-balance br 0) + nil) + + ((= (avl-tree-node-balance br) 0) + (avl-tree-node-set-balance br +1) + t) + + (t + ;; Tree has grown => Rebalance. + (setq p1 (avl-tree-node-right br)) + (if (> (avl-tree-node-balance p1) 0) + ;; Single RR rotation. + (progn + (avl-tree-node-set-right br (avl-tree-node-left p1)) + (avl-tree-node-set-left p1 br) + (avl-tree-node-set-balance br 0) + (avl-tree-node-set-branch node branch p1)) + + ;; Double RL rotation. + (setq p2 (avl-tree-node-left p1) + b2 (avl-tree-node-balance p2)) + (avl-tree-node-set-left p1 (avl-tree-node-right p2)) + (avl-tree-node-set-right p2 p1) + (avl-tree-node-set-right br (avl-tree-node-left p2)) + (avl-tree-node-set-left p2 br) + (if (> b2 0) + (avl-tree-node-set-balance br -1) + (avl-tree-node-set-balance br 0)) + (if (< b2 0) + (avl-tree-node-set-balance p1 +1) + (avl-tree-node-set-balance p1 0)) + (avl-tree-node-set-branch node branch p2)) + (avl-tree-node-set-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) + (avl-tree-node-set-balance br 0) + nil) + + ((= (avl-tree-node-balance br) 0) + (avl-tree-node-set-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 + (avl-tree-node-set-left br (avl-tree-node-right p1)) + (avl-tree-node-set-right p1 br) + (avl-tree-node-set-balance br 0) + (avl-tree-node-set-branch node branch p1)) + + ;; Double LR rotation. + (setq p2 (avl-tree-node-right p1) + b2 (avl-tree-node-balance p2)) + (avl-tree-node-set-right p1 (avl-tree-node-left p2)) + (avl-tree-node-set-left p2 p1) + (avl-tree-node-set-left br (avl-tree-node-right p2)) + (avl-tree-node-set-right p2 br) + (if (< b2 0) + (avl-tree-node-set-balance br +1) + (avl-tree-node-set-balance br 0)) + (if (> b2 0) + (avl-tree-node-set-balance p1 -1) + (avl-tree-node-set-balance p1 0)) + (avl-tree-node-set-branch node branch p2)) + (avl-tree-node-set-balance (avl-tree-node-branch node branch) 0) + nil)))) + +(defun avl-tree-do-enter (cmpfun root branch data) + ;; Return t if height of tree ROOT has grown. INTERNAL USE ONLY. + (let ((br (avl-tree-node-branch root branch))) + (cond + ((null br) + ;; Data not in tree, insert it. + (avl-tree-node-set-branch + root branch (avl-tree-node-create nil nil data 0)) + t) + + ((funcall cmpfun data (avl-tree-node-data br)) + (and (avl-tree-do-enter cmpfun br 0 data) + (avl-tree-enter-balance2 root branch))) + + ((funcall cmpfun (avl-tree-node-data br) data) + (and (avl-tree-do-enter cmpfun br 1 data) + (avl-tree-enter-balance1 root branch))) + + (t + (avl-tree-node-set-data br data) + nil)))) + +;; ---------------------------------------------------------------- + +(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. + (let ((node root) + (stack nil) + (go-left t)) + (push nil stack) + (while node + (if (and go-left + (avl-tree-node-left node)) + ;; Do the left subtree first. + (progn + (push node stack) + (setq node (avl-tree-node-left node))) + ;; Apply the function... + (funcall map-function node) + ;; and do the right subtree. + (if (avl-tree-node-right node) + (setq node (avl-tree-node-right node) + go-left t) + (setq node (pop stack) + go-left nil)))))) + +(defun avl-tree-do-copy (root) + ;; Copy the avl tree with ROOT as root. + ;; Highly recursive. INTERNAL USE ONLY. + (if (null root) + nil + (avl-tree-node-create + (avl-tree-do-copy (avl-tree-node-left root)) + (avl-tree-do-copy (avl-tree-node-right root)) + (avl-tree-node-data root) + (avl-tree-node-balance root)))) + + +;;; ================================================================ +;;; The public functions which operate on AVL trees. + +(defun avl-tree-create (compare-function) + "Create a new empty avl tree and return it. +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 'AVL-TREE + (cons (avl-tree-node-create nil nil nil 0) + compare-function))) + +(defun avl-tree-p (obj) + "Return t if OBJ is an avl tree, nil otherwise." + (eq (car-safe obj) 'AVL-TREE)) + +(defun avl-tree-compare-function (tree) + "Return the comparison function for the avl tree TREE." + (avl-tree-cmpfun tree)) + +(defun avl-tree-empty (tree) + "Return t if avl tree TREE is emtpy, otherwise return nil." + (null (avl-tree-root tree))) + +(defun avl-tree-enter (tree data) + "In the avl tree TREE insert DATA. +Return DATA." + (avl-tree-do-enter (avl-tree-cmpfun tree) + (avl-tree-dummyroot tree) + 0 + data) + data) + +(defun avl-tree-delete (tree data) + "From the avl tree TREE, delete DATA. +Return the element in TREE which matched DATA, +nil if no element matched." + (avl-tree-do-delete (avl-tree-cmpfun tree) + (avl-tree-dummyroot tree) + 0 + data)) + +(defun avl-tree-member (tree data) + "Return the element in the avl tree TREE which matches DATA. +Matching uses the compare function previously specified in +`avl-tree-create' when TREE was created. + +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) + nil))) + +(defun avl-tree-map (__map-function__ tree) + "Apply __MAP-FUNCTION__ to all elements in the avl tree TREE." + (avl-tree-mapc + (function (lambda (node) + (avl-tree-node-set-data + node (funcall __map-function__ + (avl-tree-node-data node))))) + (avl-tree-root tree))) + +(defun avl-tree-first (tree) + "Return the first element in TREE, or nil if TREE is empty." + (let ((node (avl-tree-root tree))) + (if node + (progn + (while (avl-tree-node-left node) + (setq node (avl-tree-node-left node))) + (avl-tree-node-data node)) + nil))) + +(defun avl-tree-last (tree) + "Return the last element in TREE, or nil if TREE is empty." + (let ((node (avl-tree-root tree))) + (if node + (progn + (while (avl-tree-node-right node) + (setq node (avl-tree-node-right node))) + (avl-tree-node-data node)) + nil))) + +(defun avl-tree-copy (tree) + "Return a copy of the avl tree TREE." + (let ((new-tree (avl-tree-create (avl-tree-cmpfun tree)))) + (avl-tree-node-set-left (avl-tree-dummyroot new-tree) + (avl-tree-do-copy (avl-tree-root tree))) + new-tree)) + +(defun avl-tree-flatten (tree) + "Return a sorted list containing all elements of TREE." + (nreverse + (let ((treelist nil)) + (avl-tree-mapc + (function (lambda (node) + (setq treelist (cons (avl-tree-node-data node) + treelist)))) + (avl-tree-root tree)) + treelist))) + +(defun avl-tree-size (tree) + "Return the number of elements in TREE." + (let ((treesize 0)) + (avl-tree-mapc + (function (lambda (data) + (setq treesize (1+ treesize)) + data)) + (avl-tree-root tree)) + treesize)) + +(defun avl-tree-clear (tree) + "Clear the avl tree TREE." + (avl-tree-node-set-left (avl-tree-dummyroot tree) nil)) + +(provide 'avl-tree) + +;; arch-tag: 47e26701-43c9-4222-bd79-739eac6357a9 +;;; avl-tree.el ends here |