Class 10: Abstracting Procedures
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(1) The document discusses abstracting common patterns in procedures that operate on lists. (2) It presents examples of list-sum, list-product, and list-length procedures, then shows how they can be abstracted into a single list-accumulate procedure. (3) The remainder of the document discusses defining the edit-distance procedure to calculate the minimum number of operations (insertions, deletions, substitutions) needed to change one string into another.
![Plan for Today
PS2 Due Now
Abstracting List Procedures
PS2: edit-distance
PS3 posted now, due next Friday (Sept 23).
You may work with a partner you choose.
If you don’t have a partner arranged, you need to
email me by 3:55pm tomorrow:
- Subject: PS3 Partner
Either: “I want a partner for ps3.”
or “I prefer to work alone on ps3 because [ <your reason> ]”](https://image.slidesharecdn.com/lecture10-120109023433-phpapp02/85/Class-10-Abstracting-Procedures-2-320.jpg)
![s1
a c a t c a t g c
0 1 2 3 4 5 6 7 8 9
c 1
a 2
t 3 Value in square [i, j] =
s2 g 4 min (1 + value in square [i-1, j],
1 + value in square [i, j-1],
a 5 (0 or 1) + value in square [i-1, j-1])
t 6
g 7](https://image.slidesharecdn.com/lecture10-120109023433-phpapp02/85/Class-10-Abstracting-Procedures-24-320.jpg)
Class 10: Abstracting Procedures
- 1. Class 10: Abstracting Procedures cs1120 Fall 2011 David Evans 14 September 2011
- 2. Plan for Today PS2 Due Now Abstracting List Procedures PS2: edit-distance PS3 posted now, due next Friday (Sept 23). You may work with a partner you choose. If you don’t have a partner arranged, you need to email me by 3:55pm tomorrow: - Subject: PS3 Partner Either: “I want a partner for ps3.” or “I prefer to work alone on ps3 because [ <your reason> ]”
- 3. Warm-up: list-sum Define a procedure, list-sum, that takes a list of numbers as input and outputs the sum of the numbers in the input list. (list-sum (list 1 2 3)) 6 (list-sum null) 0 3
- 4. list-sum (define (list-sum p) (if (null? p) 0 (+ (car p) (list-sum (cdr p))))) Okay, what about list-product? 4
- 5. list-product (define (list-product p) (if (null? p) 1 (* (car p) (list-product (cdr p))))) Okay, what about list-length? 5
- 6. list-length (define (list-length p) (if (null? p) 0 (+ 1 (list-length (cdr p))))) 6
- 7. Comparing List Procedures (define (is-list? p) (define (list-sum p) (if (null? p) (if (null? p) true 0 (if (pair? p) (+ (car p) (is-list? (cdr p)) (list-sum (cdr p))))) false))) (define (list-product p) (define (list-length p) (if (null? p) (if (null? p) 1 0 (* (car p) (+ 1 (list-length (cdr p))))) (list-product (cdr p))))) 7
- 8. Base Cases (define (is-list? p) (define (list-sum p) (if (null? p) (if (null? p) true 0 (if (pair? p) (is-list? (cdr p)) false))) (+ (car p) (list-sum (cdr p))))) (define (list-product p) (define (list-length p) (if (null? p) (if (null? p) 1 0 (* (car p) (list-product (cdr p))))) (+ 1 (list-length (cdr p))))) 8
- 9. Recursive Calls (define (is-list? p) (define (list-sum p) (if (null? p) (if (null? p) true 0 (if (pair? p) (is-list? (cdr p)) false))) (+ (car p) (list-sum (cdr p))))) (define (list-product p) (define (list-length p) (if (null? p) (if (null? p) 1 0 (* (car p) (list-product (cdr p))))) (+ 1 (list-length (cdr p))))) What does each do with the car of the list? 9
- 10. Abstracted List Procedure (define (list-sum p) (define (list-product p) (if (null? p) (if (null? p) 0 1 (+ (car p) (list-sum (cdr p))))) (* (car p) (list-product (cdr p)))))
- 11. Master of (Almost) All List Procedures (define (list-accumulate f base p) (if (null? p) base (f (car p) (list-accumulate f base (cdr p)))) (define (list-sum p) (if (null? p) 0 (+ (car p) (list-sum (cdr p))))) (define (list-product p) (if (null? p) 1 (* (car p) (list-product (cdr p)))))
- 12. Master of (Almost) All List Procedures (define (list-accumulate f base p) (if (null? p) base (f (car p) (list-accumulate f base (cdr p)))) (define (list-length p) (if (null? p) 0 (+ 1 (list-length (cdr p))))) (define (is-list? p) (if (null? p) true (if (pair? p) (is-list? (cdr p)) false)))
- 13. PS2: Edit Distance Million Bases http://mbgd.genome.ad.jp/CoreAligner/
- 14. Defining edit-distance (define (edit-distance s1 s2) (if (and (null? s1) (null? s2)) 0 (if (null? s1) Base cases (length s2) (if (null? s2) (length s1) …
- 15. (define (edit-distance s1 s2) (if (or (null? s1) (null? s2)) (+ (length s1) (length s2)) (min (if (eq? (car s1) (car s2)) ; match or mutate (edit-distance (cdr s1) (cdr s2)) (+ 1 (edit-distance (cdr s1) (cdr s2)))) (+ 1 (edit-distance s1 (cdr s2))) ; insert in s1 (+ 1 (edit-distance (cdr s1) s2))))) ; delete from s1
- 16. (define (edit-distance s1 s2) (if (or (null? s1) (null? s2)) (+ (length s1) (length s2)) (min (+ (if (eq? (car s1) (car s2) 0 1) ; match or mutate (edit-distance (cdr s1) (cdr s2)) (+ 1 (edit-distance s1 (cdr s2))) ; insert in s1 (+ 1 (edit-distance (cdr s1) s2))))) ; delete from s1 This is the smallest correct edit-distance procedure I can find…but, if you can find a smaller one that is worth a gold star bonus! (Replacing + 1 with inc or s1/s2 with s/t doesn’t count.)
- 17. Executing edit-distance a c a t c a t g c (edit-distance ) c a t g a t a c c a t c a t g c a t g a t a c c a t c a t g c c a t g a t a c a c a t c a t g c a t g a t a c c a t c a t g c a t g a t a c
- 18. > (require racket/trace) > (edit-distance (list 1 2) (list 2 3)) > (trace edit-distance) >(edit-distance '(1 2) '(2 3)) > (edit-distance '(2) '(3)) > (edit-distance (list 1 2) (list 2)) > >(edit-distance '() '()) < <0 > >(edit-distance '(2) '()) >(edit-distance '(1 2) '(2)) < <1 > >(edit-distance '() '(3)) < <1 > (edit-distance '(2) '()) <1 > (edit-distance '(1 2) '(3)) <1 > >(edit-distance '(2) '()) < <1 > >(edit-distance '(1 2) '()) > (edit-distance '(1 2) '()) < <2 > >(edit-distance '(2) '(3)) <2 > > (edit-distance '() '()) <<0 > > (edit-distance '(2) '()) > (edit-distance '(2) '(2)) <<1 > > (edit-distance '() '(3)) > >(edit-distance '() '()) <<1 < <1 <2 < <0 > (edit-distance '(2) '(2 3)) > >(edit-distance '() '(3)) < <1 > >(edit-distance '(2) '()) > >(edit-distance '(2) '(3)) > > (edit-distance '() '()) < <1 <<0 > > (edit-distance '(2) '()) <<1 > >(edit-distance '() '(2)) > > (edit-distance '() '(3)) <<1 < <1 < <1 > >(edit-distance '() '(2 3)) < <2 <0 <1 <2 <1 2 1 7 calls to edit-distance 19 calls to edit-distance
- 19. (define (edit-distance s1 s2) (if (or (null? s1) (null? s2)) (+ (length s1) (length s2)) (min (+ (if (eq? (car s1) (car s2) 0 1) ; match or mutate (edit-distance (cdr s1) (cdr s2)) (+ 1 (edit-distance s1 (cdr s2))) ; insert in s1 (+ 1 (edit-distance (cdr s1) s2))))) ; delete from s1
- 20. (define (edit-distance s1 s2) (if (or (null? s1) (null? s2)) (+ (length s1) (length s2)) (min (+ (if (eq? (car s1) (car s2) 0 1) ; match or mutate (edit-distance (cdr s1) (cdr s2)) (+ 1 (edit-distance s1 (cdr s2))) ; insert in s1 (+ 1 (edit-distance (cdr s1) s2))))) ; delete from s1 (define (edit-distance-counter s1 s2) (if (or (null? s1) (null? s2)) 1 (+ 1 (edit-distance-counter (cdr s1) (cdr s2)) (edit-distance-counter s1 (cdr s2)) (edit-distance-counter (cdr s1) s2))))
- 21. Evaluation: Input Lists Size (each list) Calls to edit-distance 0 1 1 4 2 19 3 94 4 481 5 2,524 6 13,483 7 72,958 8 398,593 9 2,193,844 10 12,146,179
- 22. Computing Power 1969-2011 300,000,000 (in Apollo Control Computer Units) 2,500,000,000 edit-distance Applications 250,000,000 200,000,000 2,000,000,000 150,000,000 100,000,000 Number of 1,500,000,000 50,000,000 0 1,000,000,000 500,000,000 12,146,179 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Input Size
- 23. s1 a c a t c a t g c 0 1 2 3 4 5 6 7 8 9 c 1 a 2 t 3 s2 g 4 a 5 t 6 g 7
- 24. s1 a c a t c a t g c 0 1 2 3 4 5 6 7 8 9 c 1 a 2 t 3 Value in square [i, j] = s2 g 4 min (1 + value in square [i-1, j], 1 + value in square [i, j-1], a 5 (0 or 1) + value in square [i-1, j-1]) t 6 g 7
- 25. s1 a c a t c a t g c 0 1 2 3 4 5 6 7 8 9 c 1 1 1 2 3 4 5 6 7 8 a 2 2 2 1 2 3 4 5 6 7 t 3 3 3 2 1 3 4 5 6 7 s2 g 4 4 4 4 2 2 3 4 5 6 a 5 5 5 5 4 3 2 3 4 5 t 6 6 6 6 5 4 3 2 3 4 g 7 7 7 7 6 5 4 3 2 3
- 26. Is this only used for genome analysis?
- 27. Charge Problem Set 3: Posted now, due next Friday Remember to either (1) have a partner you agree to work with in place, or (2) email me a partner/solo request by tomorrow