[FP] Solved first exam from 2021

1 files changed, 86 insertions, 0 deletions

diff --git a/Year 2/Functional Programming/Exam1-2021.rkt b/Year 2/Functional Programming/Exam1-2021.rkt
new file mode 100644
index 0000000..e5b96e5
--- /dev/null
+++ b/Year 2/Functional Programming/Exam1-2021.rkt
@@ -0,0 +1,86 @@
+#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)