sicp/zapiski/sicp_1_2_tina.scm

217 lines
4.0 KiB
Scheme

#lang scheme
( define a 3)
( define b ( + a 1 ) )
(+ 2 ( if (> b a) b a) )
(* ( cond (( > a b) a)
((< a b ) b)
( else - 1 ) )
(+ a 1 ) )
(/ (+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5))))) (* 3 (- 6 2) (- 2 7)))
( define ( a-plus-abs-b a b)
(( if ( > b 0 ) + - ) a b) )
(a-plus-abs-b 5 -4)
;; 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
( 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)
(define (fib n)
( cond (( = n 0 ) 0)
(( = n 1) 1 )
( else ( + ( fib ( - n 1 ) )
( fib ( - n 2 ) ) ) ) ) )
(fib 10)
;; 1.11
(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)
( 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)
( 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 )))))
;;( f-iter (+ (- count 1) (* 2 (- count 2)) (* 3 (- count 3))) (- count 1))))
(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 done
;; 1.14
( 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)
(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)
;; 1.16
( 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
( 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
(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 ?