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;;             U. C. Berkeley            ;;
;;      EECS Computer Science Division   ;;
;;         CS3 Lecture 06 Answers        ;;
;;               (Recursion)             ;;
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;; Mapping (every) Example : square-all

(define (square x) (* x x))
(define (square-all s)
  (cond ((empty? s) '())
        (else (se (square (first s))
                  (square-all (bf s))))))

(square-all '())        ;; ==> ()
(square-all '(1 2 3 4)) ;; ==> (1 4 9 16)

;; Finding Example : member-even

(define (member-even s)
  (cond ((empty? s) #f)
        ((even? (first s)) s)
        (else (member-even (butfirst s)))))

(member-even '())        ;; ==> #f
(member-even '(1 2 3 4)) ;; ==> (2 3 4)
(member-even '(1 3 5 7)) ;; ==> #f

;; Counting Example : count-evens

(define (count-evens s)
  (cond ((empty? s) 0)
        ((even? (first s)) 
         (+ 1 (count-evens (bf s))))
        (else (count-evens (bf s)))))

(count-evens '(1 2 3 4)) ;; ==> 2
(count-evens '(2 4 6 8)) ;; ==> 4
(count-evens '(1 3 5 7)) ;; ==> 0

;; Filtering Example : remove-evens

(define (remove-evens s)
  (cond ((empty? s) '())
        ((even? (first s))
         (remove-evens (bf s)))
        (else (se (first s)
                  (remove-evens (bf s))))))

(remove-evens '())        ;; ==> ()
(remove-evens '(1 2 3 4)) ;; ==> (1 3)
(remove-evens '(2 4 6 8)) ;; ==> ()
(remove-evens '(1 3 5 7)) ;; ==> (1 3 5 7)

;; Testing example : all-evens?

(define (all-evens? s)
  (cond ((empty? s) #t)
        ((even? (first s))
         (all-evens? (bf s)))
        (else #f)))

(all-evens? '())        ;; ==> #t
(all-evens? '(1 2 4 8)) ;; ==> #f
(all-evens? '(2 4 6 8)) ;; ==> #t
(all-evens? '(1 3 5 7)) ;; ==> #f

;; Combining example : get-min

(define (get-min s)
  (cond ((null? (bf s)) (first s))
        (else (min (first s)
                   (get-min (bf s))))))

(get-min '(795))     ;; ==> 795
(get-min '(3 1 4 1)) ;; ==> 1
(get-min '())        ;; ==> ERROR, Invalid arg