358 lines
13 KiB
Scheme
358 lines
13 KiB
Scheme
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;;; Copyright (C) Peter McGoron 2024
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;;; This program 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, version 3 of the License.
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;;;
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;;; This program 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 this program. If not, see <https://www.gnu.org/licenses/>.
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;;; Persistent AVL sets and maps using JOIN.
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;;; ;;;;;;;;;;;;;;;;
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;;; Nodes, direction
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;;; ;;;;;;;;;;;;;;;;
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;;; Returns the slot number for
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;;; =: The node data
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;;; h: the height
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;;; <: the left child
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;;; >: the right child
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(define %set:accessor
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(lambda (sym)
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(cond
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((eq? sym '=) 0)
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((eq? sym 'h) 1)
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((eq? sym '<) 2)
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((eq? sym '>) 3)
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(else (error "invalid direction")))))
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;;; Gets data from node value given accessor symbol.
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(define %set:get
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(lambda (t sym)
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(vector-ref t (%set:accessor sym))))
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(define %set->sexpr
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(lambda (node)
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(if (null? node)
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'()
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(list (list 'data (%set:get node '=))
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(list '< (%set->sexpr (%set:get node '<)))
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(list '> (%set->sexpr (%set:get node '>)))))))
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;;; Get the height of a node, handling the empty node.
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(define %set:height
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(lambda (node)
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(if (null? node)
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0
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(%set:get node 'h))))
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;;; Get the difference between the heights of two trees.
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(define %set:height-diff
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(lambda (t1 t2)
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(- (%set:height t1) (%set:height t2))))
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;;; Get the balance factor of a tree.
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(define %set:bal
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(lambda (t) (%set:height-diff (%set:get t '<)
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(%set:get t '>))))
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;;; Set data in node given accessor symbol.
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(define %set:set!
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(lambda (node dir x)
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(vector-set! node (%set:accessor dir) x)))
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;;; Construct a new tree with data VAL.
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(define %set:node
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(lambda (val dir1 node1 dir2 node2)
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(let ((node (vector val (+ 1
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(max (%set:height node1)
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(%set:height node2)))
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'() '())))
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(%set:set! node dir1 node1)
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(%set:set! node dir2 node2)
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node)))
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(define %set:invdir
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(lambda (dir)
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(cond
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((eq? dir '<) '>)
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((eq? dir '>) '<)
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(else (error "invalid direction")))))
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;;; ;;;;;;;;;;;;;;
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;;; Tree rotations
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;;; ;;;;;;;;;;;;;;
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;;; Rotate NODE to the left (dir = '>) or right (dir = '<).
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(define %set:rotate
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(lambda (node dir)
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(if (null? node)
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#f
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(let ((invdir (%set:invdir dir)))
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(let ((child (%set:get node invdir)))
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(let ((to-swap (%set:get child dir)))
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(%set:node (%set:get child '=)
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dir (%set:node (%set:get node '=)
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dir (%set:get node dir)
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invdir to-swap)
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invdir (%set:get child invdir))))))))
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;;; ;;;;;;;;;;;;;;;;;;;
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;;; JOIN function for AVL trees.
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;;; ;;;;;;;;;;;;;;;;;;;
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;;; Handles rebalancing of the tree.
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(define %set:join
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(lambda (heavier val lighter heavier-dir)
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(let ((heavy-val (%set:get heavier '=))
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(lighter-dir (%set:invdir heavier-dir)))
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(let ((heavy-heavy (%set:get heavier heavier-dir))
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(heavy-light (%set:get heavier lighter-dir)))
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(if (<= (abs (%avl:diff heavy-light lighter) 1))
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(let ((node (%set:node val
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heavier-dir heavy-light
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lighter-dir lighter)))
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(if (<= (abs (%set:bal node)) 1)
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(%set:node heavy-val
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heavier-dir heavy-heavy
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lighter-dir node)
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(%set:rotate (%set:node heavy-val
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heavier-dir heavy-heavy
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lighter-dir
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(%set:rotate node lighter-dir))
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heavier-dir)))
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(let ((new-light (%set:join heavy-light val lighter heavier-dir)))
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(let ((node (%set:node heavy-val
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heavier-dir heavy-heavy
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lighter-dir new-light)))
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(if (<= (abs (%set:bal node)) 1)
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node
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(%set:rotate node heavier-dir)))))))))
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;;; JOIN takes two trees and the data for a node, such that all nodes
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;;; in LEFT are less than or equal to VAL, and all nodes in RIGHT are
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;;; greater than or equal to VAL, and outputs a balanced binary search
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;;; tree.
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(define set:join
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(lambda (left val right)
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(let ((diff (%set:diff left right)))
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(cond
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((> diff 1) (%set:join left val right '<))
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((< diff -1) (%set:join right val left '>))
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(else (set:node val '< left '> right))))))
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(define set:join2
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(letrec
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((join2
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(lambda (left right)
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(if (null? left)
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right
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(let ((split-last-tree (split-last left)))
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(set:join (bst:get split-last-tree '<)
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(bst:get split-last-tree '=)
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right)))))
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(split-last
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(lambda (tree)
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(let ((right (set:get tree '>)))
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(if (null? right)
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tree
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(let ((last (split-last right)))
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(bst:node (set:get last '=)
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(join (set:get tree '<)
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(set:get tree '=)
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(set:get last '<))
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'())))))))
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join2))
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;;; ;;;;;;;;;;;;;;;;;
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;;; Element functions
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;;; ;;;;;;;;;;;;;;;;;
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;;; (SET:IN <=>) generates a search function for comparison function <=>.
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;;; (SEARCH TREE DATA) searches TREE for a node that matches DATA.
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;;; It will return the node that contains the matched DATA, or #F.
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(define set:in
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(lambda (<=>)
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(lambda (tree data)
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(letrec
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((loop
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(lambda (tree)
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(if (null? tree)
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#f
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(let ((dir (<=> (%set:get tree '=) data)))
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(if (eq? dir '=)
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tree
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(loop (set:get tree dir))))))))
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(loop tree)))))
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;;; (SET:INSERT <=>) generates an insert function for comparison function
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;;; <=>.
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;;; (INSERT TREE NODE) inserts NODE into TREE. It returns
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;;; (CONS NEWTREE FOUND), where FOUND is the node that was replaced by
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;;; NODE, and #F otherwise, and NEWTREE is the new root of the tree.
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(define set:insert
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(lambda (<=>)
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(lambda (tree node)
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(let ((found #f))
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(letrec
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((loop
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(lambda (tree)
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(if (null? tree)
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node
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(let ((dir (<=> (%set:get tree '=)
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(%set:get node '=)))
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(left (%set:get tree '<))
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(right (%set:get tree '>)))
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(if (eq? dir '=)
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(begin
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(set! found tree)
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(set:node (set:get node '=)
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'< left '> right))
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(join (set:node (%set:get tree '=)
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dir (loop left)
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(set:invdir dir) right))))))))
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(let ((newtree (loop tree)))
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(cons newtree found)))))))
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;;; (SET:DELETE <=>) generates a delete function for comparison function
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;;; <=>.
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;;; (DELETE TREE DATA) deletes a node from TREE that compares equal to
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;;; DATA. The function returns (CONS NEWTREE FOUND), where FOUND is the
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;;; deleted node, or #F if not found, and NEWTREE is the root of the new
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;;; tree.
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(define set:delete
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(lambda (<=>)
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(lambda (tree node)
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(let ((found #f))
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(letrec
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((loop
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(lambda (tree)
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(if (null? tree)
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node
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(let ((dir (<=> (%set:get tree '=)
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(%set:get node '=)))
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(left (%set:get tree '<))
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(right (%set:get tree '>)))
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(if (eq? dir '=)
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(begin
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(set! found tree)
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(set:join2 left right))
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(join (set:node (%set:get tree '=)
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dir (loop left)
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(set:invdir dir) right))))))))
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(let ((newtree (loop tree)))
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(cons newtree found)))))))
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;;; ;;;;;;;;;;;
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;;; For strings
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;;; ;;;;;;;;;;;
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(cond-expand
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((not miniscm-unslisp)
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(define (string<=> x y)
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(cond
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((string<? x y) '<)
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((string>? x y) '>)
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(else '=)))))
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(define map:string<=>
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(lambda (x y)
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(string<=> (car x) (car y))))
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(define %smap:insert (set:insert map:string<=>))
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(define smap:insert
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(lambda (tree key val)
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(%smap:insert tree (%set:node (cons key val)
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'< '()
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'> '()))))
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(define %smap:search (set:in map:string<=>))
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(define smap:search
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(lambda (tree key)
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(%smap:search tree (cons key '()))))
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(define %smap:delete (set:delete map:string<=>))
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(define smap:delete
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(lambda (tree key)
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(%smap:delete tree (%set:node (cons key '())
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'< '() '> '()))))
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(define smap:key
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(lambda (node) (car (%set:get node '=))))
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(define smap:val
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(lambda (node) (cdr (%set:get node '=))))
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(define %set:tests
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(list
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(cons "rotate right"
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(lambda ()
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(let ((right (%set:rotate (%set:node 1
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'< (%set:node 2
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'< (%set:node 3
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'< '()
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'> '())
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'> (%set:node 4
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'< '()
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'> '()))
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'> (%set:node 5 '< '() '> '()))
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'>)))
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(cond
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((not (eqv? (%set:get right '=) 2)) "bad parent")
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((not (eqv? (%set:get (%set:get right '>) '=) 1)) "bad right child")
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((not (eqv? (%set:get (%set:get right '<) '=) 3)) "bad left child")
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((not (eqv? (%set:get (%set:get (%set:get right '>) '>) '=) 5))
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"bad right child of right child")
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((not (eqv? (%set:get (%set:get (%set:get right '>) '<) '=) 4))
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"bad left child of right child")
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(else #t)))))
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(cons "rotate left"
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(lambda ()
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(let ((right (%set:rotate (%set:node 1
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'> (%set:node 2
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'< (%set:node 3
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'< '()
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'> '())
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'> (%set:node 4
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'< '()
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'> '()))
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'< (%set:node 5 '< '() '> '()))
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'<)))
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(cond
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((not (eqv? (%set:get right '=) 2)) "bad parent")
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((not (eqv? (%set:get (%set:get right '>) '=) 4)) "bad right child")
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((not (eqv? (%set:get (%set:get right '<) '=) 1)) "bad left child")
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((not (eqv? (%set:get (%set:get (%set:get right '<) '>) '=) 3))
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"bad right child of left child")
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((not (eqv? (%set:get (%set:get (%set:get right '<) '<) '=) 5))
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"bad left child of left child")
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(else #t)))))
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(cons "insert then delete"
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(lambda ()
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(let ((insert-return (smap:insert '() (string #\a) 5)))
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(cond
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((not (pair? insert-return)) "invalid insert return")
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((cdr insert-return) "string found in empty tree")
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(else
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(let ((tree (car insert-return)))
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(let ((found (smap:search tree (string #\a))))
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(cond
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((not found) "string not in tree")
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((not (equal? (smap:key tree) (string #\a)))
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"returned key not equal to a")
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((not (equal? (smap:val tree) 5))
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"returned value not equal to 5")
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(else
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(let ((delete-return (smap:delete tree (string #\a))))
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(cond
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((not (pair? delete-return))
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"invalid delete return")
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((not (cdr delete-return)) "string not found")
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((not (eqv? (car delete-return) '()))
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"returned tree not null")
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(else #t))))))))))))))
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