3/06 monster lecture sketch: 0. overview of monster lecture sketch

! contains many examples and explanations not given in lecture 
  -- too many to mark
! contains material to be presented on thursday: please skim beforehand
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0. overview of monster lecture sketch
   0.0 contents
   0.1 announcements, reminders, topics, topics for next lecture
   0.2 loop invariant (review + new analogy)

1. introduction to the maximum subsequence sum problem
   1.0 problem statement -- english specification
   1.1 example
   1.2 elaboration of english specification (terminology review & introduction)
   1.3 problem statement -- technical specification
   1.4. goal: a short and efficient solution

2. (3/08 preview) analyzing program performance
   2.1 terminology and concepts for analyzing program performance
   2.2 concrete example comparing $100 n^2$ and $n^3/10$:
   2.3 big-Oh notation ("big-Oh" stands for "the capital letter `O'"):
   2.4 simple examples of analyzing programs
   2.5 easier way to get time complexity (when you get used to it):
   2.6 analyzing programs that process a sequence, e.g. an input sequence

3. naive and better solutions to max subsequence sum
   3.0 general problems with simple solutions to max subsequence sum
   3.1 naive solution
   3.2 (3/08 preview) performance of naive solution
   3.3 better solution
   3.4 (3/08 preview) performance of better solution

4. sophisticated solution to maximum subsequence sum
   4.0 memorize and use template for processing input with a stopping value!
   4.1 first technique to try: answer so far
   4.2 introspection (how *we* do it)
   4.3 zeroth --> second technique to try: maintain info. about previous value
   4.4 code for sophisticated solution

5. $makepoly$ and $evalpoly$ examples from E8.1/P4.2; error-checking
   5.1 loop invariant example: $makepoly$
   5.2 loop invariant example: $evalpoly$
   5.3 error-checking with multiple versions
   5.4 error-checking with inverses
   5.5 connections with P4.2: use error-checking ideas above in $testpoly$
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0.1 announcements, reminders, topics, topics for next lecture

Announcement:
+ see notes on "error-checking" for techniques to use for $testpoly$
  + resubmitting $testpoly$ will not take away early bonus

Reminders
+ run posted code!  look again at early Lecture Sketches!
+ Course & T1 evaluation: today is the last day
+ T2 is coming up: 
  + let us know *now* of any conflicts
  + topics, review questions will be posted later this week
  + review session is this sunday
+ P4: online submission only; submit running code!
+ E9 has been posted

Topics
+ loop invariant (review + new analogy)  
+ more loop invariant examples:
  + 3 solutions to max subsequence sum: naive, better, sophisticated
  + makepoly
  + evalpoly
+ error-checking: resubmitting $testpoly$ will not take away early bonus

Topics for 3/08 lecture:
+ coping with problems:
  + look at the line that matlab claims contains the error
  + comment out (or cut out and save) portions of code to locate error
  + display values
  + hand *and* computer trace
  + $keyboard$ command
  + debugger
+ analyzing program performance
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0.2 loop invariant (review + new analogy)
+ alternate name: loop *storyline* or *plotline*
+ intent: explanation of *what* loop does
  + not necessarily an explanation of *how* the loop does it
+ technically: a condition that is true whenever the loop guard is tested
  + usually does not explicitly explain how to make progress
+ can be as simple as
  + "maintain variable definitions above"
  + a clear picture

analogy: 
+ loop invariant is true = we are at one of many "safety zones"
+ whenever loop guard is tested, we must be at one of the safety zones
+ during execution of the loop body, 
  + we (usually) leave the safety zone to make "unsafe/dangerous" progress
  + we can leave and return to safety zones multiple times
  + by the end of the loop body, we have gone back to a safety zone

rough baseball analogy:
+ safety zone = any of the 4 bases
+ make progress = run to a later base, including stealing a base