Transcript Lecture 13: Of On and Off Grounds Sorting Coffee Bean Sorting in Guatemala CS200: Computer Science University of Virginia Computer Science David Evans http://www.cs.virginia.edu/evans.

Lecture 13:
Of On and Off
Grounds
Sorting
Coffee Bean Sorting in Guatemala
CS200: Computer Science
University of Virginia
Computer Science
David Evans
http://www.cs.virginia.edu/evans
Menu
• Find Most
• Measuring Work
• Sorting
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find-mostcaffeinated
(define (insertl lst f stopval)
(if (null? lst)
stopval
(f (car lst) (insertl (cdr lst) f stopval))))
(define (find-most-caffeinated menu)
(insertl
(lambda (c1 c2)
(if (> (coffee-caffeine-rating c1)
(coffee-caffeine-rating c2))
c1 c2))
(cdr menu) ;; already used the car as stopval
(car menu)))
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find-most-caffeinated
(define (find-most-caff menu)
(if (null? (cdr menu))
(car menu)
(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))))
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Comparing Processes
> (trace >)
(>)
> (find-most-caff todays-menu)
|(> 15 57)
|#f
|(> 12 57)
|#f
|(> 92 57)
|#t
|(> 85 92)
|#f
("BEN'S Expresso Noir
Supreme" 17.23 . 92)
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> (find-most-caffeinated todays-menu)
|(> 15 57)
|#f
|(> 12 57)
|#f
|(> 92 57)
|#t
|(> 85 92)
|#f
("BEN'S Expresso Noir Supreme"
17.23 . 92)
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(define (find-most-caffeinated menu)
(insertl
(lambda (c1 c2)
(if (> (coffee-caffeine-rating c1)
(coffee-caffeine-rating c2))
c1 c2))
(cdr menu) ;; already used the car as stopval
(car menu)))
find-most
(define (find-most cf lst)
(insertl
(lambda (c1 c2) (if (cf c1 c2) c1 c2))
(cdr lst)
(car lst)))
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(define (find-most cf lst)
(insertl
(lambda (c1 c2) (if (cf c1 c2) c1 c2))
(cdr lst)
(car lst)))
(define (find-most-caffeinated menu)
(find-most
(lambda (c1 c2)
(> (coffee-caffeine-rating c1)
(coffee-caffeine-rating c2)))
menu))
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How much work is
find-most?
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Why not just time it?
4500000
4000000
Moore’s Law: computing power
doubles every 18 months!
3500000
3000000
2500000
2000000
1500000
1000000
500000
2002
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1996
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0
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How much work is find-most?
(define (find-most cf lst)
(insertl
(lambda (c1 c2)
(if (cf c1 c2) c1 c2))
lst
(car lst)))
• Work to evaluate (find-most f lst)?
– Evaluate (insertl (lambda (c1 c2) …) lst)
These don’t depend on the length
– Evaluate lst
of the list, so we don’t care about
– Evaluate (car lst)
them.
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Work to evaluate insertl
(define (insertl f lst stopval)
(if (null? lst)
stopval
(f (car lst) (insertl f (cdr lst) stopval))))
• How many times do we evaluate f for a list
of length n?
n
insertl is (n)
“Theta n”
If we double the length of the list, we amount of work
required approximately doubles.
(We will see a more formal definition of  next week.)
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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
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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)
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All Sorts
(define (sort cf lst)
(if (null? lst) lst
(let ((most (find-most cf lst)))
(cons
most
(sort cf
(delete lst most))))))
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Caffeine Sorts
(define (sort-menu-by-caffeine menu)
(sort (lambda (c1 c2)
(> (coffee-caffeine-rating c1)
(coffee-caffeine-rating c2)))
menu))
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Sorting
(define (sort cf lst)
(if (null? lst) lst
(let ((most (find-most cf lst)))
(cons
most
(sort cf
(delete lst most))))))
(define (find-most cf lst)
(insertl
(lambda (c1 c2)
(if (cf c1 c2) c1 c2))
lst
(car lst)))
• How much work is sort?
• We measure work using orders of
growth: How does work grow with
problem size?
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Sorting
(define (sort cf lst)
(if (null? lst) lst
(let ((most (find-most cf lst)))
(cons most
(sort cf (delete lst most))))))
• What grows?
– n = the number of elements in lst
• How much work are the pieces?
find-most is (n)
delete is (n)
• How many times does sort evaluate
find-most and delete?
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Sorting
(define (sort cf lst)
(if (null? lst) lst
(let ((most (find-most cf lst)))
(cons most
(sort cf (delete lst most))))))
• n = the number of elements in lst
• find-most is (n) delete is (n)
• How many times does sort evaluate
find-most and delete? n
sort is (n2)
If we double the length of the list, the amount of
work approximately quadruples.
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Timing Sort
> (time (sort < (revintsto 100)))
cpu time: 20 real time: 20 gc time: 0
> (time (sort < (revintsto 200)))
cpu time: 80 real time: 80 gc time: 0
> (time (sort < (revintsto 400)))
cpu time: 311 real time: 311 gc time: 0
> (time (sort < (revintsto 800)))
cpu time: 1362 real time: 1362 gc time: 0
> (time (sort < (revintsto 1600)))
cpu time: 6650 real time: 6650 gc time: 0
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(n2)
35000
measured
times
30000
25000
= n2/500
20000
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0
0
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Is our sort good enough?
Takes over 1 second to sort 1000-length
list. How long would it take to sort 1
million items?
1s = time to sort 1000
4s ~ time to sort 2000
(n2)
1M is 1000 * 1000
Sorting time is n2
so, sorting 1000 times as many items will take 10002 times as long
= 1 million seconds ~ 11 days
Note: there are 800 Million VISA cards in circulation.
It would take 20,000 years to process a VISA transaction at this rate.
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Charge
• Exam review in class Wednesday
– Look over the practice exams from previous
years before Wednesday
• Exam 1 out Friday, due next Monday
• Next Monday: faster ways of sorting
• Read Tyson’s essay (before next Weds)
– How does it relate to  (n2)
– How does it relate to grade inflation
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