David Evans http://www.cs.virginia.edu/~evans Lecture 11: All Sorts CS200: Computer Science University of Virginia Computer Science David Evans http://www.cs.virginia.edu/~evans

find-most-caffeinated Sorting Menu find-most-caffeinated Sorting 11 February 2002 CS 200 Spring 2002

find-most-caffeinated (define (find-most-caffienated menu) (insertlg (lambda (c1 c2) (if (> (coffee-caffeine-rating c1) (coffee-caffeine-rating c2)) c1 c2)) menu (make-coffee "null-coffee" 0.00 -1))) ;; we should only get the null-coffee ;; if there are no coffees on the menu 11 February 2002 CS 200 Spring 2002

find-most-caffeinated (define (find-most-caff menu) (if (null? menu) (make-coffee "null-coffee" 0.00 -1) (let ((rest-most-caff (find-most-caff (cdr menu)))) (if (> (coffee-caffeine-rating (car menu)) (coffee-caffeine-rating rest-most-caff)) (car menu) rest-most-caff)))) 11 February 2002 CS 200 Spring 2002

Comparing Processes > (trace >) (>) > (find-most-caff todays-menu) |(> 57 -1) |#t |(> 15 57) |#f |(> 12 57) |(> 92 57) |(> 85 92) ("BEN'S Expresso Noir Supreme" 17.23 . 92) > (find-most-caffienated todays-menu) |(> 57 -1) |#t |(> 15 57) |#f |(> 12 57) |(> 92 57) |(> 85 92) ("BEN'S Expresso Noir Supreme" 17.23 . 92) 11 February 2002 CS 200 Spring 2002

Sorting 11 February 2002 CS 200 Spring 2002

Simple Sorting We know how to find-most-caffeinated How do we sort list by caffeine rating? Use (find-most-caffeinated menu) to find the most caffeinated Remove it from the menu Repeat until the menu is empty 11 February 2002 CS 200 Spring 2002

Delete ;;; Evaluates to the list parameter with ;;; exactly one instance of el removed. (define (delete lst el) (if (null? lst) (error "Element not found!") (if (eq? (car lst) el) (cdr lst) (cons (car lst) (delete (cdr lst) el))))) 11 February 2002 CS 200 Spring 2002

sort-menu (define (sort-menu menu) (if (null? menu) menu (let ((most-caff (find-most-caffeinated menu))) (cons most-caff (sort-menu (delete menu most-caff)))))) How can we generalize this? (e.g., sort by price also) 11 February 2002 CS 200 Spring 2002

All Sorts (define (sort cf lst) (if (null? lst) lst (let ((most (find-most cf lst))) (cons most (sort cf (delete lst most)))))) 11 February 2002 CS 200 Spring 2002

Caffeine Sorts (define (sort-menu-by-caffeine menu) (sort (lambda (c1 c2) (> (coffee-caffeine-rating c1) (coffee-caffeine-rating c2))) menu)) 11 February 2002 CS 200 Spring 2002

find-most (define (find-most cf lst) (insertlg (lambda (c1 c2) (if (cf c1 c2) c1 c2)) lst (car lst))) 11 February 2002 CS 200 Spring 2002

Sorting How much work is it to sort? We measure work using orders of growth How does work grow with problem size? 11 February 2002 CS 200 Spring 2002

Why not just time/count absolute amount of work? 11 February 2002 CS 200 Spring 2002

Computing Power 1969-2002 (in Apollo Control Computer Units) Moore’s Law: computing power doubles every 18 months!

How much work is find-most? (define (find-most cf lst) (insertlg (lambda (c1 c2) (if (cf c1 c2) c1 c2)) lst (car lst))) Work to evaluate (find-most f lst)? Evaluate (insertlg (lambda (c1 c2) …) lst) Evaluate lst Evaluate (car lst) These don’t depend on the length of the list, so we don’t care about them. 11 February 2002 CS 200 Spring 2002

Work to evaluate insertlg (define (insertlg f lst start) (if (null? lst) start (f (car lst) (insertlg f (cdr lst) start)))) How many times do we evaluate f for a list of length n? n insertlg is (n) If we double the length of the list, we amount of work insertlg does approximately doubles. 11 February 2002 CS 200 Spring 2002

Charge PS3 Due Wednesday Continue how much work is sorting Wednesday Lab Hours: Tonight, 7:30-9 PM in Small Hall Continue how much work is sorting Wednesday Think about other ways of sorting 11 February 2002 CS 200 Spring 2002