Very sad code. Abstraction, List, & Cons. CS61A Lecture 7. Happier Code. Goals. Constructors. Constructors 6/29/2011. Selectors.

Transcription

1 6/9/ Abstrction, List, & Cons CS6A Lecture Colleen Lewis Very sd code (define (totl hnd) (if (empty? hnd) (+ (butlst (lst hnd)) (totl (butlst hnd))))) STk> (totl (h c d)) 7 STk> (totl (h ks d)) ;;;EEEK! Hppier Code (define (totl hnd) (if (empty? hnd) (+ (rnk (one-d hnd)) (totl (remining-ds hnd) )))) (define (rnk d) (butlst d)) (define (suit d) (lst d)) Selectors (define suit lst) (define (one-d hnd) (lst hnd)) (define (remining-ds hnd) (bl hnd)) Gols To tlk bout things using mening not how it is represented in the computer To be ble to chnge how it is represented in the computer without people who use our progrm ing Invented by: Turing Awrd Winner: Brbr Liskov Constructors GOAL: To tlk bout things using mening not how it is represented in the computer You still hve STk> (totl (h c d)) ; to tech STk> (totl people to use (mke-hnd your progrm (mke-d hert) (mke-d club) (mke-d dimond))) Constructors STk> (totl (mke-hnd (mke-d hert) (mke-d club) (mke-d dimond))) (define (mke-d rnk suit) (word rnk (first suit))) (define mke-hnd se) Constructors

2 6/9/ Dt Abstrction (define (totl hnd) (if (empty? hnd) (+ (rnk (one-d hnd)) (totl (remining-ds hnd) )))) (define (rnk d) (define (mke-d rnk suit) (butlst d)) (word rnk (first suit))) (define (suit d) (define mke-hnd se) (lst d)) (define (one-d hnd) (lst hnd)) (define (remining-ds hnd) (bl hnd)) Try It! Rewrite wht you need to: Crds re represented s numbers - - is A-K of Herts -6 is A-K of Spdes 7-9 is A-K of Dimonds - is A-K of Clubs Runtimes Continued Exponentil Runtime n brnches = cll brnches = brnches = 7 brnches = b brnches = b+ - clls 6 Fiboncci fib n = fib n- + fib n- ~6 ~ n brnches = n+ - clls

3 6/9/ Number Guessing Gme Logrithmic Runtime Log (N) I m thinking of number between nd How mny possible guesses could it tke you? (WORST CASE) Between nd? How mny possible guesses could it tke you? (WORST CASE) b brnches = b+ - clls n possible numbers & h clls n= h+ - Divide nd Conquer If we cn divide the problem up in hlf ech time like the number guessing gme How mny recursive clls will it tke? n is the originl problem size if h clls then: n= h+ - // Tke the log of both sides // Remember: Log (N) When we re ble to keep dividing the problem in hlf (or thirds etc.) Looking through phone book

4 6/9/ Asymptotic Cost We wnt to express the speed of n lgorithm independently of specific implementtion on specific mchine. Asymptotic Cost Which one is fstest? We exmine the cost of the lgorithms for lrge input sets i.e. the symptotic cost. In lter clsses (CS7/CS7) you ll do this in more detil Woh! One of these is WAY better fter this point. Let s cll tht point N Subset of Importnt Big-Oh Sets Function Common Nme O() Constnt O(log n) Logrithmic O( log n) Log-squred O( n ) Root-n O(n) Liner O(n log n) n log n O(n ) Qudrtic O(n ) Cubic O(n ) Qurtic O( n ) Exponentil O(e n ) Bigger exponentil Which is fstest fter some vlue N? Forml definition T( n) O( f ( n)) WAIT who es? These re ll proportionl! Sometimes we do e, but for simplicity we ignore constnts if nd only if T( n) c* f ( n) for ll n > N

5 6/9/ Simplifying stuff is importnt Cons nd Lists DEMO cons / STk> (cons ) (. ) STk> (define (cons )) STk> (define b (cons hi bye)) b STk> b (hi. bye) STk> ( ) STk> ( ) STk> ( b) hi STk> ( b) bye Pirs Dt Abstrction Points Uses of Pir from textbook X Y Intervls Frctions Complex # low high Selectors Constructors num den rel compl cons Lines X Y X Y

6 6/9/ list Lists Demo STk> (list ) ( ) STk> (list ) () STk> (list) () STk> (list +) (#[closure rglist=rgs 7ffde]) Lists re mde with pirs! STk> (define (list )) STk> (define b (list )) b The Empty List STk> (cons ()) () How cn you mke the list ( )? )(define (cons ())) b)(define (cons (cons ))) c)(define (cons (cons ()))) d)(define (cons (cons ()) ))) e)??? How mny clls to cons re mde? STk> (define (list )) A) B) C) D) E) 6 6

7 6/9/ How mny clls to cons re mde? STk> (define (list (list ) )) Accessing Elements Using nd A) B) C) D) E) 6 The Empty List w/ & How do you get the? STk> (define x (cons ()) x STk> x () x STk> ( x) STk> ( x) () STk> (define (list )) A) ( ( )) B) ( ( )) C) ( ( ( ))) D) ( ( ( ))) E) ( ( ( ))) How do you get the? Cons mkes pir STk> (define (list (list ) )) (cons b) A) ( ( ( ( )))) B) ( ( ( ( )))) C) ( ( ( ( )))) D) ( ( ( ( )))) E)??? A B 7

8 6/9/ Dots Demo STk> (cons ) (. ) Dots STk> (cons ()) () STk> (cons ()) (.( )) Dots CONSTRUCTOR SOLUTION STk> (cons ()) (. ()) () STk> (cons (cons ())) (. (.( ))) ( ) (define (mke-d rnk suit) (cond ((equl? suit 'hert) rnk) ((equl? suit 'spde) (+ rnk )) ((equl? suit 'dimond) (+ rnk 6)) ((equl? suit 'club) (+ rnk 9)) (else (error "sy wht?")) )) SELECTOR SOLUTION (define (d-rnk d) (reminder d )) (define (suit d) (cond ((> d) 'hert) ((> 7 d) 'spde) ((> d) 'dimond) (else 'club))) How mny clls to cons re mde? STk> (define (list (list ) )) A) B) C) D) E) 6 Solution: (cons (cons (cons (cons (cons ())) (cons ())))))