(fixing a code for) racket-- deleting a node from a tree - racket

Question

So I'm currently stuck in the intermediate level of racket, and have looked at various codes, but most of them I can't figure out
I'm trying to delete a node from a binary search tree
So, I've so far come up with this, which includes an empty node and the first and final node in the wrong order
(define-struct node (key value left right))
(define (delete bst k)
(local [(define empty-l (empty? (node-left bst)))
(define empty-r (empty? (node-right bst)))
(define full-l (not empty-l))
(define full-r (not empty-r))]
(local [(define (replace bst)
;;takes node and takes it away, finding the next part that should take over its spot
(cond
[(empty? bst) empty]
[(and empty-l empty-r) empty]
[(and empty-l full-r) (node-right bst)]
[(and full-l empty-r) (node-left bst)]
[(and full-l full-r) (make-node
(if (**empty? (node-right bst)) "MAKE_THIS_KEY_GO_AWAY"** (node-key (node-right bst)))
(if (**empty? (node-right bst)) "MAKE_THIS_VALUE_GO_AWAY"** (node-value (node-right bst)))
;(node-value (node-right bst))
(node-left bst)
(replace (node-right bst)))]))]
;(local ((define (find k bst)
;;if finds k, puts it through replace to replace it
(cond
[(empty? bst) empty]
[(= k (node-key bst)) (replace bst)]
[(< k (node-key bst)) (make-node (node-key bst)
(node-value bst)
(delete k (node-left bst))
(node-right bst))]
[else (make-node (node-key bst)
(node-value bst)
(node-left bst)
(delete k (node-right bst)))]))))
;; Example binary search tree for check-expect
(define t (make-node 5 "" (make-node 3 "" (make-node 2 "" (make-node 1 "" empty empty)
empty)
(make-node 4 "" empty empty))
(make-node 7 "" (make-node 6 "" empty empty) empty)))
(check-expect (delete t 5)
(**make-node 6 ""** (make-node 3 "" (make-node 2 "" (make-node 1 "" empty empty)
empty)
(make-node 4 "" empty empty))
(**make-node 7 ""** empty empty)))
;;What I actually get
(**make-node
7
""**
(make-node
3
""
(make-node
2
""
(make-node 1 "" empty empty)
empty)
(make-node 4 "" empty empty))
(**make-node
"MAKE_THIS_KEY_GO_AWAY"
"MAKE_THIS_VALUE_GO_AWAY"**
(**make-node 6 ""** empty empty)
empty))

Answer 1

The (full-l full-r) case is all messed up. To handle that case, you need to pick either what Wikipedia calls the "in-order predecessor" or the "in-order successor" of the instance of bst being handled by replace, then delete that key from replace's bst and make it be the replacement. These functions can be used to find the in-order predecessor/successor:
(define (in-order-predecessor tree)
(right-bottom (node-left tree)))
(define (in-order-successor tree)
(left-bottom (node-right tree)))
(define (left-bottom tree)
(if (empty? (node-left tree))
tree
(left-bottom (node-left tree))))
(define (right-bottom tree)
(if (empty? (node-right tree))
tree
(right-bottom (node-right tree))))
So you'd do something like this:
[(and full-l full-r)
(local [(define successor (in-order-successor bst))
(define old-right (node-right bst))
(define new-right (delete old-right (node-key successor)))]
(make-node (node-key successor) (node-value successor)
(node-left bst) new-right))]
Since this version of replace would no longer be recursive, it doesn't need to receive bst as an argument.
Also, you're getting the argument order of delete mixed up. You defined it as (delete node k) but in two places you call it as (delete k node).