pravi file .scm

zapiski/sicp_sec_1_2.scm

@@ -0,0 +1,230 @@
+#lang scheme
+
+
+;; 1.9
+
+;; 1. primer: rekurziven
+;; (+ 4 5) = inc((inc(inc(inc(5)))) = inc((inc(inc(6))) = inc((inc(7)) = inc(8) = 9
+;; 2. primer: iterativen
+;; (+ 4 5):
+;; (+ 3 6)
+;; (+ 2 7)
+;; (+ 1 8)
+;; (+ 0 9)
+;; 9
+
+
+;; 1.10
+;; Ackermannova funkcija
+;; https://en.wikipedia.org/wiki/Ackermann_function - tukaj malo drugacna definicija, mislim, da se indeksiranje premakne za 3
+
+( define (A x y)
+( cond ((= y 0 ) 0 )
+(( = x 0 ) ( * 2 y))
+((= y 1 ) 2 )
+( else (A ( - x 1 )
+( A x ( - y 1 ) ) ) ) ) )
+
+(A 1 10 )
+(A 2 4)
+(A 3 3)
+
+;; (f n) = 2*n
+;; (g n) = 2^n
+;; (h n) = 
+
+;;;; iz knjige
+;;;;
+(define (fib n)
+( cond (( = n 0 ) 0)
+(( = n 1) 1 )
+( else ( + ( fib ( - n 1 ) )
+( fib ( - n 2 ) ) ) ) ) )
+
+(fib 10)
+;;;;
+;;;;
+
+;; 1.11
+
+;; rekurzivno
+(define (f-rec n)
+( cond (( < n 3 ) n)
+( else ( + (f-rec ( - n 1 )) (* 2 (f-rec (- n 2))) (* 3 (f-rec (- n 3)))))))
+
+(f-rec 6)
+
+
+;;;; iz knjige
+;;;;
+( define (fib2 n)
+( fib-iter 1 0 n) )
+
+( define ( fib-iter a b count )
+( if (= count 0 )
+b
+( fib-iter (+ a b) a ( - count 1 ) ) ) )
+
+(fib2 10)
+;;;;
+;;;;
+
+;; iterativno
+( define (f2 n)
+( f-iter n (if (< n 2) n 2)) )
+
+( define ( f-iter max-count sum)
+( if (< max-count 3 )
+max-count
+(+ (f-iter (- max-count 1) sum) (* 2 (f-iter (- max-count 2) sum )) (* 3 (f-iter (- max-count 3) sum )))))
+
+(f2 6)
+
+
+;; 1.12
+(define (pascal r c)
+  (if (or (= r 0) (= c 1) (= c r))
+      1
+      (+ (pascal (- r 1) c) (pascal (- r 1) (- c 1)))))
+
+(pascal 5 3)
+
+;; 1.13 na papirju
+
+;; 1.14 na papirju
+
+
+;;;; iz knjige
+;;;;
+( define ( count-change amount )
+( cc amount 5 ) )
+
+( define ( cc amount kinds-of-coins )
+( cond (( = amount 0) 1 )
+(( or (< amount 0 ) ( = kinds-of-coins 0 ) ) 0 )
+( else (+ ( cc amount
+( - kinds-of-coins 1 ) )
+( cc ( - amount
+( first-denomination kinds-of-coins ) )
+kinds-of-coins ) ) ) ) )
+(define ( first-denomination kinds-of-coins)
+( cond (( = kinds-of-coins 1 ) 1)
+(( = kinds-of-coins 2 ) 5)
+(( = kinds-of-coins 3) 10 )
+(( = kinds-of-coins 4) 25 )
+(( = kinds-of-coins 5 ) 50) ) )
+
+( count-change 11)
+;;;;
+;;;;
+
+
+;;;; iz knjige
+;;;;
+(define (square x) (* x x))
+
+( define ( even? n)
+(= (remainder n 2 ) 0 ) )
+
+( define ( fast-expt b n)
+( cond ( (= n 0 ) 1 )
+( ( even? n ) ( square ( fast-expt b ( / n 2 ) ) ) )
+( else ( * b ( fast-expt b ( - n 1 ) ) ) ) ) )
+
+(fast-expt 2 5)
+;;;;
+;;;;
+
+;; 1.15
+;; a) 5
+;; b) O(log n) (?)
+
+;; 1.16
+( define ( fast-exp-iter n b a )
+( if (= n 0 )
+a
+(if (even? n) (fast-exp-iter ( / n 2 ) (square b) a  ) ( * b ( fast-exp-iter ( - n 1 ) (* a b) a ) ) ) ) )
+
+(fast-exp-iter 10 2 1 )
+
+;; 1.17
+
+;;;; iz knjige
+;;;;
+(define (mult a b)
+(if (= b 0)
+0
+(+ a (mult a (- b 1 ) ) ) ) )
+
+(mult 3 4)
+;;;; 
+;;;;
+
+;; naloga
+(define (double x) (+ x x))
+(define (halve x) (/ x 2)) ;; a bi to moralo biti kako drugace; zakaj uporabljam deljenje pri implementaciji mnozenja s sestevanjem
+
+( define ( fast-mult a b)
+( cond ( (= b 0 ) 0 )
+( ( even? b ) ( double ( fast-mult a (halve b) ) ) )
+( else ( + a ( fast-mult a ( - b 1 ) ) ) ) ) )
+
+(fast-mult 8 7)
+
+;; 1.18
+
+( define ( fast-mult-iter b a c)
+( if (= b 0 )
+0
+(if (even? b) (fast-mult-iter (halve b) (double a) c ) ( + a ( fast-mult-iter ( - b 1 ) a c ) ) ) ) )
+
+(fast-mult-iter 18 10 0 )
+
+;; 1.21
+
+;;;; iz knjige
+;;;;
+( define ( smallest-divisor n)
+( find-divisor n 2 ) )
+( define (find-divisor n test-divisor)
+( cond (( > ( square test-divisor) n) n)
+(( divides? test-divisor n) test-divisor)
+(else ( find-divisor n (+ test-divisor 1 ) ) ) ) )
+( define (divides? a b )
+(= (remainder b a) 0 ) )
+
+(smallest-divisor 19999)
+
+( define (prime? n)
+(= n ( smallest-divisor n) ) )
+;;;; 
+;;;;
+
+
+
+;; 1.22
+
+(define (runtime) (current-milliseconds)) ;; brez tega error: runtime: unbound identifier in: runtime
+
+;;;; iz knjige
+;;;;
+(define (timed-prime-test n)
+(newline)
+(display n)
+(start-prime-test n (runtime)))
+(define (start-prime-test n start-time)
+(if (prime? n)
+(report-prime (- (runtime) start-time)) -1))
+(define (report-prime elapsed-time)
+(display  "***" )
+(display elapsed-time))
+;;;; 
+;;;;
+
+(timed-prime-test 87178291199) ;; 35742549198872617291353508656626642567
+
+;; https://en.wikipedia.org/wiki/List_of_prime_numbers
+
+
+;; 1.26
+;; ker se s klicanjem (/ exp 2) v navadnem mnozenju parameter exp ne razpolovi v naslednjem koraku ?