在球拍中创建二进制搜索树？

Question

try to create immutable binary search tree. i started by create constructor to create empty list, and method to add element to tree one by one using the following code.

#lang racket
(define (constructTree) '())

(define (addToTree Tree k v)

 (cond [(null? Tree)
           (cons Tree cons((cons k  '()) v))]
       [else
        (cond [(>(car Tree) k)
               (cons Tree cons((cons k  '()) v))
               ]
              [else
               (cons Tree '() cons((cons k  '()) v) )
               ]
              )]
      )
)


(define bst (addToTree (addToTree (addToTree (addToTree (constructTree)3 "3") 1 "1") 2 "2") 5 "5"))
bst 

what i mean by immutable is if i call (define b0 (constructTree))
b0 should return '()
(define b1 (addToTree b0 4 "4"))
b1 should return '(4 "4" () ())
(define b2 (addToTree b1 6 "6"))
b2 should return '(4 "4" () (6 "6" () ()))
...etc.
but i am getting this error: application: not a procedure; expected a procedure that can be applied to arguments given: '(3) arguments...:
any clue why i am getting this error or what i am doing wrong? thank you in advance.

Answer 1

I think you may be looking for something like this:

(define emptyTree '())

(define (addToTree Tree k v)
  (match Tree
    ['()
     (list k v '() '())]
    [(list key val left right)
     (if (> k key)
       (list key val left (addToTree right k v))
       (list key val (addToTree left k v) right))]))

Note that because of immutability, there's no need to construct a new empty tree each time. You can just make emptyTree an alias for the empty list.