CISC 280 review sheet for second midterm exam, Tuesday, April 16, 2002

sample questions

1. What is a recognizer? __________
2. What is a constructor? __________
3. What is a proper list? __________
4. What is a generic operator? __________
   
   The following apply to the lists L = ((1 2) (3 4)) and M = (5 6 7).
5. (append L M) returns __________.
6. (list L M) returns __________.
7. (cons L M) returns __________.
8. (cons (list L (+ 1 3)) (append (list M) M)) returns __________.
9. (cdr (car L)) returns __________.
10. (length (list L M L L M)) returns __________.
    
    
11. Write (reverse L), the procedure that returns a list which has the items of L in it, but in reverse order.
    
    
12. Write a procedure split which takes a list as argument and returns a list of length 2. The two items in this output list are lists. The first one is the list of all the elements of the input list that are in odd numbered positions. The second list is all the elements in even numbered positions.

    > (split (list 1 2 3 4 5 6 7 8 9 0))  ; input may have even length
    ---> ((1 3 5 7 9) (2 4 6 8 0))
    
    > (split (list 1 2 3))  ; input may have odd length
    ---> ((1 3) (2))
    
    > (split (list 1))  ; input may be short
    ---> ((1) ())
    
    > (split '() )  ; input may be very short
    ---> (() ())
    
    > (split (list "a" 1 "b" 77 (* 2 4) "c" '(1 2))) ; it doesn't matter what's in the list 
    ---> (("a" "b" 8 (1 2)) (1 77 "c"))
    

13. In the following code, join-em is a procedure which (like append) takes two lists and forms the list consisting of all the elements in the first list followed by all the elements in the second list. What difference does it make in the number of steps to do tree->list on a tree T with n nodes if join-em is a one step procedure or is a k step procedure, where k is the number of items in the first list?

    (define (tree->list T)
      (if (empty-tree? T)
          '()
          (join-em (tree->list (left-branch T))
    	       (cons (node-value T) 
    		     (tree->list (right-branch T)) )) ))
    

    Remark: A one step procedure would be possible if lists were doubly linked circular structures rather than Scheme's singly linked lists. This is one benefit of doubly linked lists. There are also drawbacks, of course, such as using more memory.
14. Mercy hospital and the VA hospital have decided to use a common system to support their patient records. Each hospital keeps a record on new patients consisting of the patient's name, date of admission, and diagnosis. However, Mercy uses a list of the form (name date diag), whereas VA uses (diag name date). In each hospital, many programs deal with these records, so it is not possible to simply change one to conform to the other. To handle the combined record keeping system, it is necessary to provide the constructors make-Mercy-record and make-VA-record and provide the generic selectors name, date, and diag.

    Sketch how you might use data-directed programming to do this, using manifest type and using put and get on a table of procedures.

    Stuff on painters

15. Write a painter named en to draw the letter "N" with its vertical bars ON the side edges of the frame.
16. What does this-painter draw?

    (define this-painter (beside (beside en (flip-vert en)) en) )
    

17. Define a procedure (mirror p:Painter) that produces a painter that draws p twice, inverted, flip-vert, in the top half and unchanged in the bottom half of the frame.
18. Define a procedure (circus-mirror u:UPO p:Painter) that produces a painter that draws p twice, once with u applied to p in the top half, and once, unchanged, in the bottom half of the frame. (UPO means unary painter operator.)
19. Define a higher order procedure (new-mirror u:UPO) that produces a UPO so that ((new-mirror u) p) is a painter that draws the same thing as (circus-mirror u p).

Here is a quick summary of some procedures studied and other terminology,

Pairs: car cdr cons pair? null?

Uses of pairs abstraction barriers - levels from basic scheme up to application functions

Sequences (lists): nth length list append reverse list?

Symbols and quote '

Symbolic differentition: Expressions are naturally processed using tree recursion. Simplification is an issue that Make-sum, etc can handle.

rational numbers: interval arithmetic:

List processing: (map f L) (filter p? L)

More list processing: (flatten L) (extent L)

Painters: segments->painter,
Painter ops: transform-painter,
unary ops: flip-vert, rotate90, erase, etc.
binary ops: beside, below,
higher order ops: square-of-four,
recursive ops: right-split, corner-split, up-split, square-limit,

Frames: constructors and selectors

Multiple representations, Manifest type, Data directed programming

Some good exercises from chapter 2 are: 2.18, 2.21, 2.22, 2.23, 2.24