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#lang racket
;;; Exercise 1
(define (^2 n)
(* n n))
(define (contains-caar elem lst)
(define (calc lst ind)
(cond [(null? lst) #f)]
[(= (caar lst) elem) ind]
[else (calc (cdr lst) (add1 ind))])
(calc lst 0))
(define (digit-occur n)
(define (calc n ret)
(cond [(= n 0) ret]
[()]
)))
(define (get-distribution n)
(sort (digit-occur n) (lambda (x y) (< (car x) (car y)))))
;;; Exercise 2
(define (find-missing lst)
(cond [(null? lst) #f]
[(> (- (cadr lst) (car lst)) 1) (add1 (car lst))]
[else (find-missing (cdr lst))]))
(define (get-missing-length xss)
(define lenlis (map (lambda (lst) (length lst)) xss))
(find-missing (sort lenlis <)))
(get-missing-length '((1 2) (4 5 1 1) (1) (5 6 7 8 9))) ; → 3
(get-missing-length '(("a", "a", "a") ("a", "a") ("a", "a", "a","a") ("a") ("a", "a", "a", "a", "a", "a"))) ; → 5
;;; Exercise 3
(define (biggest-5^k-lt n)
(define (calc current)
(if (> current n)
(quotient current 5)
(calc (* current 5))))
(calc 5))
(define (trailing-of-n n)
(define (calc 5^k sum)
(if (= 5^k 1)
sum
(calc (quotient 5^k 5) (+ sum (floor (/ n 5^k))))))
(calc (biggest-5^k-lt n) 0))
(define (trailing-zeros n)
(lambda (p)
(p (trailing-of-n n))))
((trailing-zeros 6) even?) ; → #f (броят на влачещите нули е 1. 1 не е четно)
((trailing-zeros 1000) even?) ; → #f (броят на влачещите нули е 249. 249 не е четно)
((trailing-zeros 100000) even?) ; → #f (броят на влачещите нули е 24999. 24999 не е четно)
((trailing-zeros 1000000000) even?) ; → #t (броят на влачещите нули е 249999998. 249999998 е четно)
;;; Exercise 4
(define (mult-digits n)
(define (calc n current)
(if (= n 0)
current
(calc (quotient n 10) (* current (remainder n 10)))))
(calc n 1))
(define (list-md n)
(define (calc n res)
(if (< n 10)
res
(calc (mult-digits n) (append res (list (mult-digits n))))))
(calc n '()))
(define (persistence n)
(define ys (if (< n 10) (list n) (list-md n)))
(cons ys (length ys)))
(persistence 39) ; → '((27 14 4) . 3) ; 3*9=27, 2*7=14, 1*4=4
(persistence 126) ; → '((12 2) . 2) ; 1*2*6=12, 1*2=2
(persistence 4) ; → '((4) . 1)
(persistence 999) ; → '((729 126 12 2) . 4)
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