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

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) (1 2 3 4 5) > (intsto 1) (1) Same as previous lecture. (define (gauss-sum n) (insertl (intsto n) + 0)) > (gauss-sum 10) 55 (insertl (list 1 2 3 … n) + 0)  (+ 1 (+ 2 (+ 3 (+ … (+ n 0))))) 2 February 2004 CS 200 Spring 2004

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) (10 9 8 7 6 5 4 3 2 1) (define (intsfrom n) (if (= n 0) null (cons n (intsfrom (- n 1))))) 2 February 2004 CS 200 Spring 2004

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

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

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

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

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

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

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

map examples > (map (lambda (x) x) (intsto 5)) (1 2 3 4 5) > (map (lambda (x) (* x x)) (intsto 5)) (1 4 9 16 25) > (map (lambda (row) (display-one-row output-file row tile-width tile-height)) tiles) Displays a photomosaic! 2 February 2004 CS 200 Spring 2004

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