CSC151 2007S, Class 28: Analyzing Procedures

Admin:
* Reminder: Assignment 11 is now due Friday
  * SAM NEEDS TO FIGURE OUT WHAT'S GOING WRONG WITH test-permutation!
  * EC to Abby, Dylan, Matt, Carter for dealing with the problems
* Sniff.  Missing a student.
* Reading for Thursday: Numeric Recursion.
* EC: Thursday at 4:30, Ian Young talks about regular expressions in VIM
* Other issues:
  * STUDENTS WOULD LIKE A REVIEW OF HUSK-AND-KERNEL
  * Sam needs to tell the story of how you compute 1 + 2 + 3 + ... + N

Overview:
* Comparing algorithms.
* Two related metrics: Time and Number of steps.
* Counting procedure calls by printing.
* Tools for analysis.

A few observations:
* Given a particular problem, there are often many algorithms we can
  write to solve it.
* How do we choose which one to use?  What criteria might we use?
  * Resource consumption: How much computing power and time does it use?
    * Related to time is "number of steps".
    * Something with more steps is likely to take more time.
    * E.g., if something takes 1000 steps, it's likely to be much slower
      than something that takes 100 steps.
      * But not always: 1000 additions are quicker than 100 square roots
  * Readability/Understandability
  * Number of lines
  * Generality: Does it solve just this problem, or many related problems
* At different times, you will prioritize different criteria
* We tend to prioritize "running time" (measured in wall-clock or steps)
  * But only once the correctness problem is solved

Analysis is useful for other reasons, too: Why does this algorithm seem
so slow?

Let's define count-odds
* Defined
* Added precondition testing

(define count-odds
  (lambda (lst)
    (display (list 'count-odds lst)) (newline)
    (if (not (list? lst))
        (throw "count-odds: I refuse to work for people who do not understand what lists are.")
        (if (not (all-integers? lst))
            (throw "count-odds: I only like lists of integers")
            (if (null? lst)
                0  
                (+ (if (odd? (car lst)) 1 0)
                   (count-odds (cdr lst))))))))

* Observation: Much slower than it should be (okay, we pretended to observe
this).