Overview

• Admin.
• Some notes on yesterday's lab.
• Questions and answers.
• Some key ideas from the reading.
• Lab.

Admin

• Continue partners from Monday
• New homework assignment! Choose your own partners.
• Today's writeup: Exercise 5.
• Upcoming EC opportunities
  • Los Llaneros, Tonight 7:30 pm, Herrick
  • Learning from Alumni, 2:15 Thursday, 3821, Eryn O'Neil '09
  • CS Extras, 4:30 Thursday, Max Mindock
  • CS Table, Noon Friday, TBD
  • Football, 1 pm, Saturday
  • Men's soccer, 1:30 pm, Saturday
  • Jazz Band Thursday @ 7:30, in Bucksbaum Early Music
  • ...
• Other upcoming stuff
  • Optional review stuf, 1:15 pm Thursday
  • Mentor session 7:30 pm Thursday
  • ...

Some notes on yesterday's lab

(define rgb-brightest
  (lambda (colors)
    (cond
      ((null? (cdr colors))
       (car colors))
      ((>= (rgb-brightness (car colors)) 
           (rgb-brightness (rgb-brightest (cdr colors))))
       (car colors))
      (else
       (rgb-brightest (cdr colors))))))

• If the colors are arranged brightest to darkest, the number of recursive calls is the same as the number of colors in the list (+/- 1)
• Takes longer if we order them darkest to lighest.
• Why does the order of the colors matter?
  • If the first color is darker, we do two recursive calls, rather than one
• Why isn't it just twice as bad?
  • Because each recursive call does double the work
• How many procedure calls do we do
  • On a list of length 1? 1
    • Main call
  • On a list of length 2? 3
    • Main call
    • Recursive call on list of length 1
    • Recursive call on list of length 1
  • On a list of length 3? 7
    • Main call
    • Recursive call on list of length 2: 3
    • Recursive call on list of length 2: 3
  • On a list of length 4? 15
    • Main call
    • Recursive call on list of length 3: 7
    • Recursive call on list of length 3: 7
  • On a list of length 5? 31
  • On a list of length 6? 63
• So 2^(length of list)-1
• This procedure needs at least one value in the list

• The bad behavior depends on the ordering of values, but we'd like the same behavior independent of the ordering

• When counting procedure calls with a helper, you need to count not just the main procedure, but also the helper

Questions and answers

Some key ideas from the reading

• After you've written a few procedures that use a certain approach, see if you can generalize the approach to create a template for what you're doing
• Many recursive procedures on lists

(define PROC (lambda (lst) (if (null? lst) VALUE (OP (OP1 (car lst)) (PROC (cdr lst))))))

• Some procedures expect at least one element in the list

(define PROC (lambda (lst) (if (null? (cdr lst)) (OP1 (car lst)) (COMBINE (OP2 (car lst)) (PROC (cdr lst))))))

Lab