问题
This question is a follow-up on How do I get a subtree by index?. That question deals with depth-first indexing (for which I have provided a depth-first continuation-passing style solution). This question here is about breadth-first indexing, and specifically about solving the problem using continuation-passing style (CPS).
Suppose I have a tree that represents '(+ (* 5 6) (sqrt 3))
:
The index of nodes starts from 0 at the root, and is breadth-first. In the picture above, I have labelled all the nodes with their index to show this.
I would like to define a function subtree-bfs
that takes a tree and an index number, and returns the subtree rooted at the given index. For example:
(define tree '(+ (* 5 6) (sqrt 3)))
(subtree-bfs tree 0) ; Returns: '(+ (* 5 6) (sqrt 3)))
(subtree-bfs tree 1) ; Returns: '(* 5 6)
(subtree-bfs tree 2) ; Returns: '(sqrt 3)
(subtree-bfs tree 3) ; Returns: 5
(subtree-bfs tree 4) ; Returns: 6
(subtree-bfs tree 5) ; Returns: 3
I would like to solve the problem using continuation-passing style. How do I define subtree-bfs
?
So far, I have this:
(define (node-children node)
;; (node-children 123) -> '()
;; (node-children (+ 1 (+ 2 3))) -> '(1 (+ 2 3))
(cond [(pair? node) (cdr node)]
[(null? node) (error "Invalid node" node)]
[else '()]))
(define (traverse-row& nodes index counter k)
;; 'counter' is the index number of the first node in 'nodes'.
(cond [(null? nodes) (k counter)]
[(= counter index) (car nodes)]
[else
(traverse-row& (cdr nodes)
index
(+ counter 1)
k)]))
(define (children-k children index k)
(if (null? children)
k
(lambda (counter)
(subtree-bfs& (car children)
index
counter
(children-k (cdr children) index k)))))
(define (subtree-bfs& nodes index counter k)
(traverse-row& nodes
index
counter
(children-k (map (lambda (node)
(node-children node))
nodes)
index
k)))
(define (subtree-bfs tree index)
(subtree-bfs& (list tree)
index
0
(lambda (max-index+1)
;; (- max-index+1 1) represents the maximum valid index number.
(error "Index out of bounds" index))))
This implementation appears to work correctly. However, it seems rather long. Since I am inexperienced with CPS, I thought that there must be a better CPS solution to this problem. Is there a better CPS solution?
Note 1: Forgive me for not adequately commenting the code. I must admit that I do not completely understand the solution myself (!) I am rather amazed that I was able to find a solution in the first place.
Note 2: This question may be more suitable for the code review site. However, given the lack of attention to Scheme and Racket over there, a question like this would likely never be answered.
来源:https://stackoverflow.com/questions/65485997/get-a-subtree-by-breadth-first-index-using-continuation-passing-style