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;; Scheme ;;

; Q2
(define (cube x)
  (* x x x)
)

; Q3
(define (over-or-under x y)
	(cond 
		((< x y) (- 1))
		((> x y) (+ 1))
		(else (+ 0 0)))
)

; Q4
(define (max a b) (if (> a b) a b))
(define (min a b) (if (> a b) b a))
(define (gcd a b)
	(if (or (= a 0) (= b 0)) (max a b)
   		(if (= 0 (modulo (max a b) (min a b)))
   	    	(min a b)
   	    	(gcd (min a b) (modulo (max a b) (min a b)))
   	    )
   	)
)

; Q5
(define lst
  '((1) 2 (3 . 4) 5)
)

; Q6
(define (remove item lst)
  (cond
  	((null? lst) ())
  	((= (car lst) item) (if (null? (cdr lst)) ()
  		                                     (remove item (cdr lst))
  		                                     ))
    (else (cons (car lst) (remove item (cdr lst)))))
)

;;; Tests

(remove 3 nil)
; expect ()
(remove 3 '(1 3 5))
; expect (1 5)
(remove 5 '(5 3 5 5 1 4 5 4))
; expect (3 1 4 4)

; Q7
(define (filter f lst)
  (cond 
  	((null? lst) ())
  	((f (car lst)) (cons (car lst) (filter f (cdr lst))))
  	(else (filter f (cdr lst)))
  	)
)

; Q8
(define (make-adder num)
  	(lambda (x) (+ x num))
)

; Q9
(define (composed f g)
  (lambda (x) (f (g x)))
)

;; Extra Scheme Questions ;;

; Q10
(define (num-leaves tree)
  (if (null? tree) 
      0 
      (if (and (null? (left tree)) (null? (right tree)))
          1 
          (+ (num-leaves (left tree)) (num-leaves (right tree))))
  )
)

; Q11
(define (accumulate combiner start n term)
  (if (= n 0)
      start
      (combiner (term n) (accumulate combiner start (- n 1) term))
      )
)

; Binary Tree ADT
(define (make-btree entry left right)
  (cons entry (cons left right)))

(define (entry tree)
  (car tree))

(define (left tree)
  (car (cdr tree)))

(define (right tree)
  (cdr (cdr tree)))

(define test-tree
  (make-btree 2
              (make-btree 1
                          nil
                          nil)
              (make-btree 4
                          (make-btree 3
                                      nil
                                      nil)
                          nil)))

; test-tree:
;     2
;    / \
;   1   4
;      /
;     3

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