Scheme and Tail Recursion Practice Problems

Important! These are all exam-level problems. Do not attempt these problems without a solid foundation in the subject and use them for exam practice.

1. Implement remove, which takes in a scheme list and outputs a new one without any instances of the passed in element. 

(define (remove lst elm))
    (cond 
      ((null? item) nil)
      ((= (car lst) item) (remove (cdr lst) item))
      (else (cons (car lst) (remove (cdr lst) item))))) 
(define (remove lst elm))
    "YOUR CODE HERE"
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2. Implement the above function, remove, tail recurisvely. Assume now, however, that the item is only present in the list at most once. 

(define (remove-tail lst item)
    (define (remove-help lst so-far)
        (cond ((null? lst) so-far)
              ((eq? (car lst) item) (append so-far (cdr lst)))
              (else (remove-help (cdr lst)
                                 (append so-far (list (car lst)))))))
    (remove-help lst) 
(define (remove-tail lst item)
  "YOUR CODE HERE"
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