[FP/P03] Added work from today's practicum

1 files changed, 68 insertions, 0 deletions

diff --git a/Year 2/Functional Programming/03-Practice-20.10.2022.rkt b/Year 2/Functional Programming/03-Practice-20.10.2022.rkt
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+#lang racket
+
+;;; Задача 1
+
+(define (smallest-prime n)
+  (cond [(= (remainder n 2) 0) 2]
+        [(= (remainder n 3) 0) 3]
+        [else (define (find-prime-iter n i maxd)
+                (cond [(> (sub1 i) maxd) n]
+                      [(= (remainder n (sub1 i)) 0) (sub1 i)]
+                      [(= (remainder n (add1 i)) 0) (add1 i)]
+                      [else (find-prime-iter n (+ i 6) maxd)]))
+                (find-prime-iter n 6 (sqrt n))]))
+
+(define (sum-prime-divisors n)
+  (define smallest-prime-of-n (smallest-prime n))
+  (if (= n 1)
+  0
+  (+ smallest-prime-of-n (sum-prime-divisors (quotient n smallest-prime-of-n)))))
+
+;;; Задача 2
+
+(define (pow x n)
+  (if (= n 0)
+  1
+  (* x (pow x (sub1 n)))))
+
+;;; Задача 3
+
+(define (count-occurences d n)
+  (cond [(= n 0) 0]
+    [(= (remainder n 10) d)
+       (add1 (count-occurences d (quotient n 10)))]
+    [else (count-occurences d (quotient n 10))]))
+
+;;; Задача 4
+
+(define (ascending? n)
+  (cond [(= n 0) #t]
+        [(< (remainder n 10) (remainder (quotient n 10) 10)) #f]
+        [else (ascending? (quotient n 10))]))
+
+;;; Задача 5
+
+(define (smallest-divisor n bigger-than)
+  (define (calc-iter i)
+  (if (= (remainder n i) 0)
+    i
+    (calc-iter (add1 i))))
+  (calc-iter (add1 bigger-than)))
+
+(define (perfect-number? n)
+  (define (calc-iter current-divisor current-sum)
+    (cond [(= current-divisor n) #f]
+          [(= current-sum n) #t]
+          [else (define divisor (smallest-divisor n current-divisor))
+                (calc-iter divisor (+ current-sum divisor))]))
+  (calc-iter 1 1))
+
+;;; Задача 6
+
+(define (calc-sum x n)
+  (define (calc-iter i prev-powd sum)
+  (define curr-powd (* prev-powd x))
+  (if (= i n)
+    sum
+    (calc-iter (add1 i) curr-powd (+ sum curr-powd))))
+  (calc-iter 0 1 1))