Parsing a text to the tree in Racket/Scheme

Question

I am trying to transform my C++ code to the Racket since I am learning Racket. My simplified C++ code is:

struct Node
{
    char value = '\0';
    std::vector<Node> kids;
    explicit Node(char ch) : value(ch) {}
};

void ParseTree(const std::string& tokens, size_t& i, Node& root)
{
    while (i < tokens.size())
    {
        const Token& token = tokens[i++];
        if (token == '<')   // children begin
        {
            ParseTree(tokens, i, root.kids.back());
        }
        else if (token == '>')  // children end, go up
        {
            return;
        }
        else
        {
            root.kids.emplace_back(token);
        }
    }
}

Node ParseTree(const std::string& s)
{
    size_t i = 0;
    Node root('$');
    ParseTree(Parse(s), i, root);
    return root;
}

So very simple code. My translation to Racket is:

(define (parse-tree tokens)
    (if(empty? tokens)
       '()
       (cond
         [(eq? '< (car tokens))
           (list (parse-tree (cdr tokens)))]
         [(eq? '> (car tokens))
          (parse-tree (cdr tokens))]    ; no return, how to step up?
         [else
          (cons (car tokens)(parse-tree (cdr tokens)))])))

The problem here is I am not returning up in (eq? '> (car tokens) so new nodes are added to the bottom. A small test:

(parse-tree '(1 < 2 < 3 4 > > Z < X >))

Should be:

'(1 (2 (3 4)) Z (X))

It is:

'(1 (2 (3 4 Z (X))))

How to fix it?

Answer 1

The problem with your original approach is that you're trying to directly port an imperative solution, one that even uses pass-by-reference to keep track of the state of the traversal. That won't work, the first step would be to rethink the solution in a functional-programming style.

These kinds of problems where we have to keep track of where we're inside a nested structure, are better solved using a stack data structure. I'll use a list to implement a stack of lists, with the following helper for appending a new element on the topmost list:

(define (append-top ele stack)
  (cons (append (car stack) (list ele))
        (cdr stack)))

Now for the actual solution. Assuming that the input list is well-formed with the same number of < and > and in the correct order (no error checking is performed):

(define (parse-tree tokens)
  (let parse ([tokens tokens] [stack '(())])
    (cond [(null? tokens)
           ; solution is at the top of the stack, return it
           (car stack)]
          [(eq? (car tokens) '<)
           ; start new sublist at the top of the stack
           (parse (cdr tokens) (cons '() stack))]
          [(eq? (car tokens) '>)
           ; pop top element of the stack, append it to previous
           ; frame, continue with solution where we left it
           (parse (cdr tokens) (append-top (car stack) (cdr stack)))]
          [else
           ; add current element to top of stack
           (parse (cdr tokens) (append-top (car tokens) stack))])))

It works as expected!

(parse-tree '(1 < 2 < 3 4 > > Z < X >))
=> '(1 (2 (3 4)) Z (X))