1. David Evans http://www.cs.virginia.edu/evans
Lecture 8:
Recursion Practice
CS200: Computer Science
University of Virginia
Computer Science
David Evans

2. Simpler Gauss Sum? > (intsto 5) (1 2 3 4 5) > (intsto 1) (1)
(define (insertl lst f stopval)
(if (null? lst)
stopval
(f (car lst)
(insertl (cdr lst) f stopval))))
> (intsto 5)
( )
> (intsto 1)
(1)
Same as previous lecture.
(define (gauss-sum n)
(insertl (intsto n) + 0))
> (gauss-sum 10) 55
(insertl (list … n) + 0)
 (+ 1
(+ 2
(+ 3
(+ …
(+ n 0)))))
2 February 2004
CS 200 Spring 2004

3. Reverse intsto (define (intsfrom n) (if (= n 0) null
;;; Evaluates to the list (n n-1 … 3 2 1)
;;; if n >= 1, null if n = 0.
> (intsfrom 10)
( )
(define (intsfrom n)
(if (= n 0)
null
(cons n (intsfrom (- n 1)))))
2 February 2004
CS 200 Spring 2004

4. Intsto? (define (intsto n) (if (= n 0) null
(list (intsto (- n 1)) n)))
> (intsto 5)
(((((() 1) 2) 3) 4) 5)
2 February 2004
CS 200 Spring 2004

5. append > (append (list 3) (list 4)) (3 4)
> (append (list 3) null)
(3)
> (append null (list 3))
> (append (list 1 2 3) (list 4 5 6))
( )
Checkup: Try and define append yourself.
2 February 2004
CS 200 Spring 2004

6. Intsto (define (intsto n) (if (= n 0) null
(append (intsto (- n 1)) (list n))))
> (intsto 5)
( )
2 February 2004
CS 200 Spring 2004

7. Using Intsto (define (gauss-sum n) (insertl (intsto n) + 0))
(define (factorial n)
(insertl (intsto n) * 1))
2 February 2004
CS 200 Spring 2004

8. map
(map f lst)
Evaluates to the list of values produced by applying f to each element of lst.
2 February 2004
CS 200 Spring 2004

9. map (define (map f lst) (if (null? lst) null (cons (f (car lst))
(map f (cdr lst))))
2 February 2004
CS 200 Spring 2004

10. map (define (map f lst) (insertl lst (lambda (a b) (cons (f a) b))
null))
2 February 2004
CS 200 Spring 2004

11. map examples > (map (lambda (x) x) (intsto 5)) (1 2 3 4 5)
> (map (lambda (x) (* x x)) (intsto 5))
( )
> (map
(lambda (row)
(display-one-row output-file
row tile-width tile-height))
tiles)
Displays a photomosaic!
2 February 2004
CS 200 Spring 2004

12. Challenge Problem Define a procedure
(define (for index test combine next accum) …)
that can be used like this:
(define (gauss-sum n)
(for 1 (lambda (index) (> index n))
+ (lambda (x) (+ 1 x))
0))
2 February 2004
CS 200 Spring 2004