CSC151 2010S, Class 51: Project Assessment: Algorithms

Overview:
* Questions on the exam
* Debriefing from yesterday.
* Students discuss programming techniques.

Admin:
* Since you'll be working on the exam, 
  there is no reading for Friday.
* Yes, you are expected to show up for class
  next week. (and this week)
* EC for Convo tomorrow.
* EC for CS Table Friday.
* EC for Belly Dancing Sunday at 1:30.
* EC for Student Art Salon
* Saturday's events

Questions on the exam?

Question on Problem 4

(average-v2 (1 2 3))
=> (kernel 1 1 (2 3))
=> (kernel _ _ _)

(average-v3 (1 2 3)
=> (... (numbers-info (1 2 3)) ...)
=> (... (let ((results (numbers-info (2 3))) ..)) ...)

Can you go over returning a procedure?

Example:

;;; Procedure:
;;;   make-log-function
;;; Parameters:
;;;   k, an integer
;;; Purpose:
;;;   Build a function that computes log_k(n)
;;; Produces:
;;;   log_k, a function from reals to reals
;;; Preconditions:
;;;   [No additional]
;;; Postconditions:
;;;   (expt k (log_k n)) = n for all positive real n
(define make-log-function
  (lambda (k)
    (lambda (n)
      (/ (log n) (log k)))))


> (define log2 (make-log-function 2))
> (log2 2)
1.0
> (log2 4)
2.0
> (log2 8)
3.0

Generalization:

(define function-that-returns-a-function
  (lambda (parameters)
    (lambda (other-parameters)
      ...)))

Other possibilities

(define make-log-function
  (lambda (k)
    (let ((log_k (lambda (n)
                   (/ (log n) (log k)))))
      log_k)))

If you're returning a recursive function, you'll
probably use the pattern

(define make-function
  (lambda (params)
    (letrec ((recursive-function (lambda (...) ...)))
      recursive-function)))

But ... neither problem 9 nor problem 10 requires a recursive function.
* 10 has a not-very concise explicitly recursive solution and a much more consise solution (w/o explicit recursion)

How do I know when I've reached a leaf in problem 5?

Presumably, your tree recursion procedure has the framework

(cond
  ((pair? tree)
   (RECURSE-ON-BOTH-HALVES-AND-COMBINE))
  ((number? tree)
   (BASE-CASE tree))
  (else
   (error "Not a tree: " tree)))a

Do we have to write error messages in all of our code?
* No
* Programming by contract: You can assume that people meet your preconditions.