;; Converting Python functions to Scheme

(define (one)
  1)

(define (two x y z)
  (+ x (* y z)))

(define (three n)
  (if (= n 0)
      0
      (+ (remainder n 10) (* 2 (three (quotient n 10))))))


;; Practice with lambdas

; (((f) 3)) evaluates to 1
(define (f) (lambda (x) (lambda () 1)))

; ((g g) g) evaluates to 42
(define g (lambda (x) (lambda (y) 42)))


;; Pairs practice

(define x (cons (cons 1 2) (cons (cons (cons 4 5) (cons 6 7)) 3)))

(car (car x)) ;; select 1
(cdr (cdr x)) ;; select 3
(cdr (cdr (car (cdr x)))) ;; select 7


;; Lists practice

(define (append lst1 lst2)
  (if (null? lst1)
      lst2
      (cons (car lst1) (append (cdr lst1) lst2))))


;; quicksort

(define (filter-comp comp pivot s)
  (filter (lambda (x) (comp x pivot)) s))

(define (quick-sort s)
  (if (<= (length s) 1)
      s
      (let ((pivot (car s)))
        (append (quick-sort (filter-comp < pivot s))
                (filter-comp = pivot s)
                (quick-sort (filter-comp > pivot s))))))


;; turtle graphics

(define (triangle)
  (forward 100)
  (right 120)
  (forward 100)
  (right 120)
  (forward 100)
  (right 120))


(define (repeat k fn)
  (if (> k 0)
      (begin (fn) (repeat (- k 1) fn))
      'done))

(define (tri fn)
  (repeat 3 (lambda () (fn) (lt 120))))

(define (sier d k)
  (tri (lambda () (if (= k 1) (fd d) (leg d k)))))

(define (leg d k)
  (sier (/ d 2) (- k 1)) (penup) (fd d) (pendown))