uebung3

Aus ProgrammingWiki

Aufgabe 6 (Robert Rosenberger, Stefan Scheumann)

ÜA: Definieren Sie die Menge der geraden Zahlen (Zahlwörter) und die der ungeraden Zahlen (Zahlwörter) und veranlassen Sie das ProgrammingWiki die 30 ersten Elemente der Vereinigungsmenge (in aufsteigender Sortierung) auszugeben.

Gegeben: $ A = {0,1,2,3,4,5,6,7,8,9} $

$ A^{*} = { \epsilon,0,1,2,...,10,11,12,...,100,101,...} $

Menge der geraden Zahlwörter $ M_{1}$ mit:

$ M_{1} \subseteq A^{*}$

$ f: \N \rightarrow M_{1} \text{ mit } f(x) = 2x $

Menge der ungeraden Zahlwörter $ M_{1}$ mit:

$ M_{2} \subseteq A^{*}$

$ g: \N \rightarrow M_{2} \text{ mit } g(x) = 1+2x $

Vereinigung:

$ M_{1} \cup M_{2} \subseteq A^{*}$

$h: \N \rightarrow M_{1} \cup M_{2}$

$$ h(i) = \begin{cases} f(\frac{i}{2}), & \text{wenn } 2|i;\\ g(\frac{i - 1}{2}), & \text{sonst}. \end{cases}$$

(define stream-car car) (define stream-cdr (lambda (stm) (force (cdr stm)))) ;; Konstruktoren (define-syntax stream-cons (syntax-rules () ((_ head tail) (cons head (delay tail))))) (define stream-item (lambda (str k) (if (= k 0) (stream-car str) (stream-item (stream-cdr str) (- k 1))))) (define print-stream (lambda (stm n) (cond ((<= n 0) (display "...\n")) (else (display (number->string(stream-car stm))) (display ", ") (print-stream (stream-cdr stm) (- n 1))))))

(define nat-stream-maker (lambda () (letrec ((n 0) (nat-stream-maker-helper (lambda (start) (stream-cons start (nat-stream-maker-helper (+ start 1)))))) (nat-stream-maker-helper 0)))) (define stream-map (lambda (stm proc) (stream-cons (proc (stream-car stm)) (stream-map (stream-cdr stm) proc)))) (define even-odd-merging-stream-maker (lambda (oddstm evenstm) (letrec ((n 0) (even-odd-merging-stream-maker-helper (lambda (n oddstm evenstm) (if (even? n) (stream-cons (stream-car evenstm) (even-odd-merging-stream-maker-helper (+ n 1) oddstm (stream-cdr evenstm))) (stream-cons (stream-car oddstm) (even-odd-merging-stream-maker-helper (+ n 1) (stream-cdr oddstm) evenstm)))))) (even-odd-merging-stream-maker-helper n oddstm evenstm)))) (define natstream (nat-stream-maker )) (define oddstream (stream-map natstream(lambda (x) (+ 1 (* 2 x))))) (define evenstream (stream-map natstream (lambda (x)(* 2 x)))) (define mergestream (even-odd-merging-stream-maker oddstream evenstream))

(display "ungerade Zahlen\n") (print-stream oddstream 30) (display "ungerade Zahlen\n") (print-stream evenstream 30) (display "Vereinigung gerade und ungerade Zahlen\n") (print-stream mergestream 30)

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