+#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) = 2n +;; (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 ?
+